PE Chemical Reference Handbook - kpea.or.kr

Reference HandbookVersion 1.0

PE Chemica l

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Copyright ©2017 by NCEES®. All rights reserved.

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PO Box 1686Clemson, SC 29633800-250-3196www.ncees.org

First printing January 2017

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CONTENTS

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

1 MASS/ENERGY BALANCES AND THERMODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 SymbolsandDefinitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Material Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Material Balances With No Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Material Balances With Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 State Functions and Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3.2 Properties of State Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4.1 Closed Thermodynamic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4.2 Open Thermodynamic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.3 Steady-Flow Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 Behavior of Single-Component Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5.1 Ideal Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5.2 Nonideal Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5.3 Phase Equilibrium for a Pure Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.6 Behavior of Multicomponent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.6.1 Ideal Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.6.2 Nonideal Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.6.3 Phase Equilibrium for Multicomponent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.7 Power Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2 HEAT TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.1 SymbolsandDefinitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Heat-Transfer Mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2.1 Heat Transfer Without Phase Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2.2 Heat Transfer With Phase Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.3 Heat-Transfer Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.3.1 Heat-Exchange Equipment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.3.2 Heat-Exchange Equipment Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

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2.4 Tables and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.4.1 Tables of Heat-Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.4.2 Charts with Heat-Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

2.4.3 Heat-Exchanger Design Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.4.4 F-Factor Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3 KINETICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85


3.1.1 Reaction Parameters – Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.1.2 Temperature Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.1.3 Reaction Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.2 Rate Equations in Differential Form for Irreversible Reactions. . . . . . . . . . . . . . . . . . . . . . 87

3.2.1 Zero-Order ( )A R" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.2.2 First-Order A R"^ h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.2.3 Second-Order 2A R"^ h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.2.4 Second-Order A bB R"+^ h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.3 Chemical Equilibrium Constants from Rate Constants for Reversible Reactions . . . . . . . . 87

3.3.1 Gaseous Phase Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.3.2 Liquid Phase Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.3.3 Effect of Temperature on Chemical Equilibrium Constants . . . . . . . . . . . . . . . . . . . 88

3.3.4 Relationship Between Gibbs Free Energy and the Equilibrium Constant . . . . . . . . . 88

3.4 Reactor Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.4.1 Batch Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.4.2 Half-Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.4.3 Flow Reactors, Steady State (Space Time, Space Velocity) . . . . . . . . . . . . . . . . . . . . 89

3.5 Integrated Reactor Equations for Irreversible Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.5.1 Zero-Order Reactions A R, r kA" − =_ i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.5.2 First-Order Reactions A R, r kCA A" − =_ i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.5.3 Second-Order Reactions 2A R, Cr kA2A" − =` j . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.5.4 Second-Order Reactions A bB R, C Cr kA A B"+ − =_ i . . . . . . . . . . . . . . . . . . . . . . . 92

3.6 Complex Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.6.1 First-Order Reversible Reactions ( )A Rk

k

2

1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.6.2 Reactions of Shifting Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

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3.6.3 Plug-Flow Reactors With Recycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.7 Yield and Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.7.1 Two Irreversible Reactions in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.7.2 Two First-Order Irreversible Reactions in Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4 FLUIDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95


4.2 Mechanical-Energy Balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.2.2 Conservation of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.3 Flow Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.3.1 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.3.2 Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.3.3 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.3.4 Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.3.5 Turbulent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.3.6 Particle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.3.7 Two-Phase Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.3.8 Jet Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4.3.9 Open-Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4.3.10 Compressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.4 Flow Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

4.4.1 Pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

4.4.2 Fans, Compressors, and Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

4.4.3 Control Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.4.4 Mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

4.4.5 Air Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.4.6 Solids Handling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

4.4.7 Cyclone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

4.4.8 Special Flow Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

4.5 Flow and Pressure Measurement Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

4.5.1 Manometers and Barometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

4.5.2 Flow Measurement Devices (Summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154


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4.5.3 Orifice,Nozzle,andVenturiMeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

4.6 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

5 MASS TRANSFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

5.1 SymbolsandDefinitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

5.2 Phase Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

5.2.1 Phase Equilibrium Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

5.2.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

5.3 Continuous Vapor-Liquid Contactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

5.3.1 Material and Energy Balances for Trayed and Packed Units . . . . . . . . . . . . . . . . . . 192

5.3.2 Design Parameters for Trayed Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

5.3.3 Nontrayed Continuous Contact Columns (Packed Towers) . . . . . . . . . . . . . . . . . . . 225

5.4 Miscellaneous Mass Transfer Processes (Continuous, Batch, and Semicontinuous). . . . . 245

5.4.1 Membrane Separation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

5.4.2 Liquid-Liquid Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

5.4.3 Adsorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

5.4.4 Leaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

5.4.5 Batch Distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

5.4.6 Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

5.4.7 Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

5.4.8 Drying of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

5.4.9 AdiabaticHumidificationandCooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

6 PLANT DESIGN AND OPERATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

6.1 TermsandDefinitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

6.2 Economic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

6.2.1 Cost Estimation and Project Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

6.3 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

6.3.1 Process Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

6.3.2 Process Equipment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

6.3.3 Siting Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

6.3.4 Instrumentation and Process Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

6.3.5 Materials of Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

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6.4 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

6.4.1 Process and Equipment Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

6.4.2 Process Improvement and Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

6.5 Safety, Health, and Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

6.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

6.5.2 Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

6.5.3 Industrial Hygiene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

6.5.4 HazardIdentificationandManagement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

6.5.5 Environmental Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

6.6 Flammability Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

7 GENERAL INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

7.1 Terms,Symbols,andDefinitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

7.1.1 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

7.1.2 Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

7.2 Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

7.2.1 MetricPrefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

7.2.2 Base and Derived SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

7.2.3 Unit Conversion Tables (U.S. and Metric) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

7.3 General Engineering Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

7.3.1 Measures of Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

7.3.2 DensityDefinitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

7.4 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

7.4.1 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

7.4.2 Geometry and Trigonometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

7.4.3 Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

7.4.4 Statistics and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506

7.5 Chemistry and Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518

7.5.1 Periodic Table of the Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518

7.5.2 Relative Atomic Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

7.5.3 Oxidation Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

7.5.4 Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

7.5.5 Industrial Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523


viii NCEES

8 PHYSICAL PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

8.1 SymbolsandDefinitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

8.2 Physical Properties of Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528

8.2.1 U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528

8.2.2 SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

8.3 Physical Properties of Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530


8.3.2 SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

8.3.3 Chemical Resistance of Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

8.4 Physical Properties of Liquids and Gases—Temperature-Independent Properties . . . . . . 532


8.4.2 SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

8.5 Physical Properties of Liquids and Gases—Temperature-Dependent Properties . . . . . . . 536


8.5.2 SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

8.6 Physical Properties of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

8.6.1 Dry Atmospheric Air Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

8.6.2 Dry Atmospheric Air Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

8.6.3 Temperature-Dependent Properties of Air (U.S. Customary Units) . . . . . . . . . . . . . 545

8.6.4 Temperature-Dependent Properties of Air (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . 546

8.6.5 Psychrometric Chart (U.S. Customary Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

8.6.6 Psychrometric Chart (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548

8.7 Physical Properties of Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549


8.7.2 SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

8.7.3 Properties of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

8.8 Steam Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

8.8.1 Properties of Saturated Steam (U.S. Customary Units) . . . . . . . . . . . . . . . . . . . . . . 554

8.8.2 Saturated Steam (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

8.8.3 Superheated Steam (U.S. Customary Units). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562

8.8.4 Superheated Steam (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

8.9 Diagrams for Water and Steam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

ix

PREFACE

Using the Handbook for the April 2017 Paper ExamThe Principles and Practice of Engineering (PE) Chemical exam is an open-book pencil-and-paper exam through April 2017. The PE Chemical Reference Handbook is a resource you may use on exam day. Additional references that adhere to policies in the NCEES Examinee Guide are still allowed in the exam room for the April 2017 exam.

The PE Chemical Reference Handbook contains charts, formulas, tables, and other information that may help you answer questions on the PE Chemical exam. However, it does not contain all information required to answer every question; theories, conversions, formulas, and definitions that examinees are expected to know have not been included.

This Handbook is intended solely for use on the NCEES PE Chemical exam. You may bring your personal copy of the Handbook into the exam room as long as it is bound and remains bound according to the policies in the NCEES Examinee Guide.

Using the Handbook for the January 2018 Computer-Based ExamBeginning in January 2018, the PE Chemical exam will be computer-based, and the PE Chemical Reference Handbook will be the only resource material you may use during the exam. You will not be allowed to bring a copy of the Handbook into the exam room. Instead, the computer-based exam will include a PDF version of the Handbook for your use.

Updates on Exam Content and ProceduresNCEES.org is our home on the web. Visit us there for updates on everything exam-related, including specifications, exam-day policies, scoring, and practice tests.

ErrataTo report errata in this book, send your correction using our chat feature on NCEES.org.

http://ncees.org/exams/examinee-guide/

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www.ncees.org

www.ncees.org


x NCEES

1

1 MASS/ENERGY BALANCES AND THERMODYNAMICS

1.1 Symbols and Definitions

SymbolsSymbol Description Units (U.S.) Units (SI)

cP, cv Specific heat capacity†Fclbm

Btu- kg K

Js Km2

2

: :=

f Fugacity of a pure component inlbf2 Pa

mN

m skg

2 2:= =

ft Fugacity of a component in a mixture inlbf2 Pa

mN

m skg

2 2:= =

G Gibbs free energy Btu Js

kg m2

2:=

g Specific Gibbs free energy† lbmBtu

kgJ

sm2

2=

H Enthalpy Btu J

H Henry's Law constant inlbf2 Pa

mN

m skg

2 2:= =

h Specific enthalpy lbmBtu

kgJ

sm2

2=

MW Molecular weight (molar mass) lbmolelbm

molkg

m Mass lbm kg

n Number of moles lb mole mol

P Pressure inlbf2 or psi Pa

mN

m skg

2 2:= =

Pc Critical pressure inlbf2 = psia Pa

mN

m skg

2 2:= =

Pr Reduced pressure dimensionless


2 NCEES

Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)

Psat Saturation pressure, or vapor pressure inlbf2 Pa

mN

m skg

2 2:= =

p Partial pressure inlbf2 Pa

mN

m skg

2 2:= =

/ Poynting correction factor dimensionlessQ Heat Btu J

S Entropy RBtuo K

J

SG Specific gravity dimensionless

s Specific entropy†-lbm R

Btuo kg K

J:

T Temperature °R or °F K or °C

Tc Critical temperature °R or °F K or °C

Tr Reduced temperature dimensionless

t Time hr s

U Internal energy Btu J

u Specific internal energy†lbmBtu

kgJ

V Volume ft3 m3

v Velocity secft

sm

v Specific volume†lbmft3 kg

m3

W Work Btu or lbf-ft J

w Weight fraction dimensionlessx Mole fraction dimensionlessy Mole fraction dimensionlessz Compressibility factor dimensionless

aij Relative volatility for components i and j dimensionless

g Activity coefficient dimensionlessh Efficiency dimensionless

m Dynamic viscosity cP or ft seclbm- Pa s m s

kg: :=

r Density ftlbm3 m

kg3

† Property values on molar basis are denoted by ^. For example, molar volume is vt .

Chapter 1: Mass/Energy Balances and Thermodynamics

NCEES 3

1.2 Material BalancesGeneral balance equation: Accumulation = Input – Output + Generation – Consumption

1.2.1 Material Balances With No ReactionBalanced equation at steady state with no reaction: Input = Output

1.2.2 Material Balances With Reaction

1.2.2.1 GeneralBalanced equation at steady state with reaction: Input + Generation = Output + Consumption

Common Flow Configurations

PROCESS WITH BYPASS

PROCESS WITH PURGE PROCESS WITH RECYCLEAND PURGE

PROCESS WITH RECYCLE

1.2.2.2 Combustion Reactions Theoretical (stoichiometric) air is the air required for complete combustion.

Molar air-fuel ratio Moles of fuel

Moles of airFA =c m

Percent theoretical air FAFA

100

Theoretical

Actual #=c

c

m

m

Percent excess air 100FA

FA

FA

Theoretical

Actual Theoretical #=−c

c

cm

m

m

Gross or higher heating value (HHV) is the heat of combustion assuming all water generated is condensed as a liquid.

Net or lower heating value (LHV) is the heat of combustion assuming that no water is condensed.


4 NCEES

Major Components of Air

Element Volume, %Nitrogen 78.09Oxygen 20.94Argon 0.93

Selected Properties of AirProperty Amount

Molecular weight of air 28.965 lbmolelbm

Absolute viscosity (m)

at 80°F 0.045 hr ftlbm-

at 100°F 0.047 hr ftlbm-

Density

at 80°F 0.0734 ftlbm3

at 100°F 0.0708 ftlbm3

The dry adiabatic lapse rate ΓAD is 0.98°C per 100 m (5.4°F per 1000 ft). This is the rate at which dry air cools adiabatically with altitude. The actual (environmental) lapse rate Γ is compared to ΓAD to determine stability.

Stability of Adiabatic Lapse RateLapse Rate Stability Condition

Γ > ΓAD Unstable

Γ = ΓAD Neutral

Γ < ΓAD Stable

1.2.2.3 Heat of ReactionCalculate standard state heat of reaction h 0D R

t from standard heat of formation h 0D ft at 298 K (25°C) and 1 atm, using

h h h0 0 0D D D= −R f ftstanproducts reac

t t t/ /

Calculate hRDt at temperature T using

h h h hR R f f0D D D D= + +

tstanproducts reac

t t t t/ /

where hfDt includes the sensible and latent heat changes between T and 298K


NCEES 5

1.2.2.4 Standard Heat of Formation and CombustionThe standard heat of formation and combustion at 25°C are shown in the tables below. The products of combustion are H2O (l) and CO2 (g). Solids are listed as s in the tables below.

Alkanes

Name Formula Phaseh f0D t hc0D− t

HHV

molkJ

lbmolBtu

molkJ

lbmolBtu

Methane CH4 g –74.6 –32,070 890.7 382,900Ethane C2H6 g –84.00 –36,110 1560 670,700n-Propane C3H8 g –104.6 –44,970 2219 954,100Isobutane C4H10 g –134.3 –57,740 2868 1,233,000n-Butane C4H10 g –125.5 –53,960 2877 1,237,000n-Pentane C5H12 g –146.9 –63,160 3535 1,520,000n-Pentane C5H12 l –173.5 –74,600 3509 1,507,000Cyclohexane C6H12 g –124.0 –53,310 — —Cyclohexane C6H12 l –157.0 –67,500 3930 1,690,000n-Hexane C6H14 g –167.2 –71,890 4199 1,805,000n-Hexane C6H14 l –198.8 –85,470 4163 1,790,000Methylcyclohexane C7H14 g –154.78 –66,540 4601 1,978,000Methylcyclohexane C7H14 l –190.2 –81,760 4565 1,963,000n-Heptane C7H16 g –187.9 –80,790 — —n-Heptane C7H16 l –225.0 –96,740 4817 2,071,000n-Octane C8H18 g –208.4 –89,600 — —n-Octane C8H18 l –250.0 –107,500 5430 2,335,000n-Nonane C9H20 g –228.3 –98,160 — —n-Nonane C9H20 l –274.7 –118,100 6125 2,633,000n-Decane C10H22 g –249.7 –107,400 — —n-Decane C10H22 l –301.0 –129,400 6779 2,915,000


6 NCEES

Alkenes and Alkynes


HHV

molkJ

lbmolBtu

molkJ

lbmolBtu

Acetylene C2H2 g 226.8 97,510 — —Ethylene C2H4 g 52.3 22,500 1411 606,600Propylene C3H6 g 20.4 8770 2058 884,8001,3-Butadiene C4H6 g 109 46,900 2540 1,092,0001,3-Butadiene C4H6 l 91 39,100 2522 1,084,0001-Butene C4H8 g –0.630 –270 2717 1,168,0001-Pentene C5H10 g –22 –9500 — —1-Pentene C5H10 l –49 –21,000 3350 1,440,0001-Hexene C6H12 g –42 –1800 — —1-Hexene C6H12 l –73 –31,000 — —

Aromatics


HHV

molkJ

lbmolBtu

molkJ

lbmolBtu

Benzene C6H6 g 82.9 35,600 — —Benzene C6H6 l 49 21,000 3270 1,406,000Toluene C7H8 g 50 21,000 — —Toluene C7H8 l 12 5200 3920 1,685,000Styrene C8H8 g 147 63,200 — —Styrene C8H8 l 103 44,300 4390 1,887,000Ethylbenzene C8H10 g 49 21,000 — —Ethylbenzene C8H10 l 6.8 2900 4567 1,964,000p-Xylene C8H12 g 17.9 7700 — —p-Xylene C8H12 l –24.4 –10,500 4552 1,957,000o-Xylene C8H12 g 19 8200 — —o-Xylene C8H12 l –24.4 –10,500 4552 1,957,000


NCEES 7

Other Organic Compounds


HHV

molkJ

lbmolBtu

molkJ

lbmolBtu

Methanol CH4O g –205 –88,100 764 328,500Methanol CH4O l –239 –103,000 726 312,100Acetaldehyde C2H4O g –171 –73,500 — —Acetaldehyde C2H4O l –196 –84,300 — —Ethylene oxide C2H4O g –53 –22,700 1306 561,500Ethylene oxide C2H4O l –96 –41,200 1263 543,000Acetic Acid C2H4O2 l –484 –208,000 875 376,000Ethanol C2H6O g –234 –100,600 1366 587,300Ethanol C2H6O l –276 –119,000 1367 587,700Ethylene glycol C2H6O2 l –460 –197,800 1190 511,600

Inorganic Compounds


HHV

molkJ

lbmolBtu

molkJ

lbmolBtu

Ammonia NH3 g –45.9 –19,700 383.0 164,700Calcium carbide CaC2 s –62.8 –27,000 — —Calcium carbonate CaCO2 s –1207 –518,900 — —Calcium chloride CaCl2 s –795.0 –342,000 — —Calcium chloride CaCl2 6H2O s –2607 1,121,000 — —Calcium hydroxide Ca(OH)2 s –986.6 –424,200 — —Calcium oxide CaO s –635.6 –273,200 — —Carbon C, graphite s 0 0 393.5 169,200Carbon monoxide CO g –110.5 –47,510 283.0 121,700Carbon dioxide CO2 g –393.5 –169,200 — —Hydrochloric acid HCl g –92.31 –39,690 — —Hydrogen H2 g 0 0 286.0 123,000Hydrogen sulfide H2S g –20.6 –8860 546.3 234,900Iron oxide FeO s –269.0 –115,700 — —Iron oxide Fe2O3 s –822.2 –353,500 — —Iron oxide Fe3O4 s –1117 –480,300 — —Nitric acid HNO3 g –134.3 –57,740 — —Nitric oxide NO g 90.29 38,820 — —Nitrogen dioxide NO2 g 33.10 14,200 — —Nitrogen trioxide NO3 g 71.13 30,580 — —Sodium carbonate NaCO3 s –1131 –486,300 — —


8 NCEES

Inorganic Compounds (cont'd)


HHV

molkJ

lb molBtu

molkJ

lb molBtu

Sodium carbonate NaCO3 10H2O s –4082 1,755,000 — —Sodium chloride NaCl s –411.0 –176,700 — —Sodium hydroxide NaOH s –426.7 –183,500 — —Sulfur oxide SO g 5.01 2150 — —Sulfur dioxide SO2 g –296.8 –127,600 — —Sulfur trioxide SO3 g –395.8 –170,200 — —Sulfur trioxide SO3 l –442.5 –190,300 — —Water H2O g –241.83 –103,970 — —Water H2O l –285.83 –122,890 — —

1.3 State Functions and Thermodynamics

1.3.1 NomenclatureIntensive properties are independent of mass.

Extensive properties are proportional to mass.

1.3.2 Properties of State FunctionsFor a single-phase pure component, specifying any two intensive properties specifies the remaining intensive properties.

State Functions

Component Property U.S. Units SI UnitsAbsolute pressure P psia PaAbsolute temperature T °R K

Specific volume v mV=

lbmft3

kgm3

Specific internal energy u mU=

lbmBtu

kgJ

Specific enthalpy h = u + P v = mH

lbmBtu

kgJ

Specific entropy s mS= lbm-°R

Btukg KJ:

Specific Gibbs free energy g = h – T s lbmBtu

kgJ

Heat Capacity at Constant Pressure

lbm °RBtu or kg K

kJc Th

-pP :2

2= c m


NCEES 9

Heat Capacity at Constant Volume

lbm °RBtu or kg K

kJc Tu

-vv :2

2= c mThe steam tables in Chapter 8 provide T, P, v, u, h, and s data for saturated water and superheated steam.

Thermal and physical property tables for selected gases, liquids, and solids are included in Chapter 8.

1.4 First Law of ThermodynamicsThe First Law of Thermodynamics states that energy is neither created nor destroyed but can change from one form into another. The net energy crossing the system boundary is equal to the change in energy inside the system.

Heat Q q mQ=c m is energy transferred due to temperature difference and is considered positive if it is inward (added

to the system). Work W w mW=b l is considered positive if it is outward (subtracted from the system).

Changes in state functions are computed by changes in Q and W, which are path-dependent. The common paths are

Isobaric DP = 0Isochoric DV = 0Isothermal DT = 0Isenthalpic DH = 0Adiabatic DQ = 0Adiabatic and reversible (isentropic)

DS = 0

Efficiencies are used to correct irreversible processes.

1.4.1 Closed Thermodynamic SystemsIn a closed thermodynamic system, no mass crosses the system boundary:

Q – W = DU + DKE + DPE

where

DU = change in internal energy

DKE = change in kinetic energy

DPE = change in potential energy

Energy can cross the system boundary only in the form of heat or work. Work can be shaft work (ws) or other work forms, such as electrical.

Reversible work is

P dvw = #The table below displays the work, heat, and internal energy changes in closed systems for each of the four appli-cable paths for 1 mole of ideal gas. These changes assume constant heat capacities and neglect kinetic and potential energy changes.


10 NCEES

Closed System Energy Changes for 1 Mole of Ideal Gas

Path Work (W) Heat (Q) Change in Internal Energy (DU)

Isochoric (DV = 0) 0 c TVDt c TVDt

Isobaric (DP = 0) P(V2 – V1) c TPDt ( )c T P V VP 2 1D − −t

Isothermal (DT = 0)ln

ln

RT PP

RT VV2

1

1

2

e

e o

o ln

ln

RT PP

RT VV2

1

1

2

e

e o

o0

Isentropic (Ds = 0) kk RT

PP

1 1kk

1

1

21

− −−

e o> H 0 kRT

PP

1 1kk

1

1

21

− − −−

e o> H

where k ccV

P= tt

For ideal gas in an isentropic process:

TT

VV

PPk k

k

1

2

2

11

1

21

= =− −

e e eo o o

1.4.2 Open Thermodynamic SystemsIn an open thermodynamic system, mass does cross the system boundary. Flow work (Pv) is defined as the work for mass entering and leaving the system.

Reversible flow work = vw d P K E P Erev - D D= + +#The First Law applies whether or not processes are reversible.

Open System First Law (energy balance):

m h

Vg Z m h

Vg Z Q W dt

d m u2 2i ii

i e ee

e in nets s2 2

- -+ + + + + =o o o o_ i= =G G/ /

where

subscripts i and e refer to inlet and exit states of the system

Wneto = rate of net or shaft work

mo = mass flow rate

h = enthalpy

g = acceleration of gravity

Z = elevation

V = velocity

ms = mass of fluid within the system

us = specific internal energy of system

Qin = rate of heat transfer (neglecting kinetic and potential energy of the system)


NCEES 11

The table below displays the work, heat, and internal enthalpy changes in open systems for each of the five appli-cable paths for 1 mole of ideal gas. These changes assume constant heat capacities and neglect kinetic and potential energy changes.

Open System Energy Changes for 1 Mole of Ideal Gas

Path Work (W) Heat (Q) Change in Enthalpy (DH)

Isochoric (DV = 0) –V(P2 – P1) c TVDt c T V P PV 2 1D + −t _ iIsobaric (DP = 0) 0 c TPDt c TPDt

Isothermal (DT = 0)ln

ln

RT PP

RT VV2

1

1

2

e

e o

o ln

ln

RT PP

RT VV2

1

1

2

e

e o

o0

Isentropic (DS = 0) kk RT

PP

1 1kk

1

1

21

− −−

e o> H 0 kk RT

PP

1 1kk

1

1

21

− −−

e o> H

Isenthalpic (DH = 0) 0 0 0

The actual work required is

ww

actual isrevh=

where his = isentropic efficiency

In the polytropic process, the only condition for process path is reversibility.

Pvn = constant

where n = empirical constant

w nn P v P v

n MWnR T T

1 1rev2 2 1 1 2 1

-

-

-

-= =_^ ^

_hi

hi

w nnMWRT

PP

1 1revnn

1

1

2

1

- -= −−

e^o

h> H

The actual work required is

ww

actual polyrevh=

where hpoly = polytropic efficiency

Polytropic efficiencies are always higher than isentropic efficiencies for the same compression stage.


12 NCEES

For multistage compression, the pressure ratio PR is

PR P

P m

1

21

= e owhere m = number of stages

The temperature drop on isenthalpic expansion (Joule-Thomson) is

T PJTnD D=

assuming the Joule-Thomson coefficient PT

JTH2

2n = c m is constant.

1.4.3 Steady-Flow SystemsThe system does not change state with time. This assumption is valid for the steady operation of turbines, pumps, compressors, throttling valves, nozzles, and heat exchangers, including boilers and condensers. The letter V denotes velocity in the following three equations:

m h

Vg Z m h

Vg Z Q W m m2 2 0i i

ii e e

ee s i e

2 2- -/ / / /+ + + + + = =o o o o od dn n

For a single fluid-flow stream at steady state, the equation reduces to:

h V g Z w q2 0

2-D

DD+ + + =o o

If the fluid is incompressible with negligible friction losses, the equation reduces to:

P V g Z w q2 0s

2-t

D DD+ + + =o o

1.5 Behavior of Single-Component Systems

1.5.1 Ideal Systems

1.5.1.1 Ideal Gas LawFor an ideal gas,

andP v RT PPvv

TT

2

1

2

1

2

1= =t tt

where 1 and 2 indicate separate system states.

Alternatively,

andPV n RT MWmRT

PPVV

nnTT

2

1

2

121

2

1= = =

For ideal gases, c c Rp v− =t t . These are independent of both pressure and volume, as are u and h.

Assuming constant heat capacities, or average heat capacities over the temperature range T1 to T2, the following apply:

u c T h c Tv PD D D D= =

ln

lnln

lns c T

TMW

R PP

s c TT

MW

R vv

vP1

2 1

2

1

2 12

D D= − = −ee

ed

oo

on


NCEES 13

1.5.2 Nonideal Systems

1.5.2.1 Compressibility and the Theorem of Corresponding StatesThe compressibility factor is a dimensionless number defined by the equation:

Z RTP v= t

Theorem of Corresponding States

To first approximation, all fluids have the same compressibility factor when compared at the same reduced tem-perature and reduced pressure.

Reduced temperature (Tr) and reduced pressure (Pr) are defined as

andT TT P P

Pr c r c

= =

Compressibility Factor Chart

0.1

0.1

0.2

0.2

0.3

0.3

0.4

0.4REDUCED PRESSURE, Pr

0.5

0.5

0.6

0.7

0.8

0.9

1.0

1.0 2.0 3.0 4.0 5.0 10 20 30

1.1

1.2

1.3

1.4

1.5

0.0

COMPRESSIBILITY FACTOR CHART

COMP

RESS

IBILI

TY FA

CTOR

, Z

GENERALIZED COMPRESSIBILITY FACTORS(Ze = 0.27)

15.00

5.003.00

2.002.00

1.801.70

1.60

1.50

1.50

1.401.35

1.30

1.30

1.25

1.20

1.20

1.10

1.10

1.081.06

1.04

1.02

1.00

1.00

0.50

0.50

0.60

0.70 0.9

00.8

0 1.00

2.00 3.0

05.0

0

10.00

15.00

0.95

0.95

0.90

0.90

0.90

0.85

0.85

SATURATED LIQUID

SATURATED GAS

0.80

0.80

0.75

1.15

Tr

GENERALIZED COMPRESSIBILITY FACTORS(Ze = 0.27)

15.00

5.003.00

2.002.00

1.801.70

1.60

1.50

1.50

1.401.35

1.30

1.30

1.25

1.20

1.20

1.10

1.10

1.081.06

1.04

1.02

1.00

1.00

0.50

0.50

0.60

0.70 0.9

00.8

0 1.00

2.00 3.0

05.0

0

10.00

15.00

0.95

0.95

0.90

0.90

0.90

0.85

0.85

SATURATED LIQUID

SATURATED GAS

0.80

0.80

0.75

1.15

Tr

From de Nevers, Noel, Physical and Chemical Engineers, 2nd ed., New York: Wiley & Sons, 2012, p. 94.


14 NCEES

1.5.2.2 Equations of State

Virial Equation of State

Z RTP v

vB

vC

vD1 2 3 g= = + + + +t

t t t

where B, C, D = virial equation coefficients, accounting for two-body, three-body, and four-body interactions, respectively

Alternatively,

Z RTP v B P C P D P1 2 3g= = + + +l l lt

where , ,B C Dl l l= virial equation coefficients

The two sets of virial coefficients are related by:

B RTB=l

( )C

RTC B

2

2= −l

( )D

RTD BC B3 2

3

3= − +l

Generic Cubic Equation of State

( ) ( )( )

P v bRT

v b v ba Te v

= − − + +t t t

where

a(T) = substance-dependent constant

b = substance-dependent constant

e = constant for generic cubic equation of state

s = constant for generic cubic equation of state

For the Van der Waals equation, a(T) = a and .0e v= =

1.5.3 Phase Equilibrium for a Pure Component

1.5.3.1 Phase RuleFor nonreacting systems, the degrees of freedom F (for example, temperature, pressure, and composition) are

F = 2 – p + N

where

p = number of phases

N = number of chemical species


NCEES 15

1.5.3.2 Phase DiagramsThe pressure-temperature relationship for a pure fluid is often shown in a P-T plot. The intersection of the solid-liquid-vapor lines is the triple point where the three phases coexist. The critical point is where vapor and liquid properties become identical.

Four kinds of diagrams are often used for calculations involving a pure fluid. These indicate the qualitative behavior of fluid properties as shown.

Calculations Involving a Pure Fluid

PRES

SURE

PRES

SURE

ENTHALPY

ENTH

ALPY

ENTROPYENTROPY

T-S DIAGRAM FOR PURE FLUID MOLLIER DIAGRAM FOR PURE FLUID

P-h DIAGRAM FOR PURE FLUIDPRESSURE-TEMPERATURE FOR PURE FLUID

TEMPERATURE

VAPOR

VAPORPRESSURECURVE

LIQUID

CRITICALPOINT

CRITICALPOINT

CRITICALPOINT

CRITICALPOINT

CONST. T

CONST. PCONS

T. P

CONST. H

CONST. H

CONST. V

CONST. S

CONST. T

CONST. T

CONST. T

FUSIONCURVE

SOLID TRIPLE POINT

SUBLIMATION CURVE

TEMP

ERAT

URE

CONS

T. QU

ALITY

CONST. QUALITY

CONST. QUALITY

SAT. VAPOR

SAT. VAPOR

SAT.

LIQUID

SAT.

LIQUID

SAT. LIQ

UID

SAT. LIQUID


16 NCEES

1.5.3.3 Compressibility and Expansivity Volume expansivity: V T

V1P2

2b = c m

Isothermal compressibility: V P

V1T2

2l =− c m

For real liquids, assume that k and b are independent of pressure and temperature:

VdV dT dPb l= −

ln VV T T P P1

22 1 2 1b l= − − −e _ _o i i

For incompressible liquids: dV = 0

dTdP

V lb=c m

1.5.3.4 Vapor PressureVapor pressure is the pressure in a closed system containing a pure fluid with both liquid and vapor in equilibrium at a given temperature. The equilibrium phases are saturated.

The Antoine Equation expresses the temperature dependence of vapor pressure:

ln P A T CBsat = − +

where

Psat = saturation pressure or vapor pressure

A, B, and C = constants for a given species

T = absolute temperature in K or °R

1.5.3.5 Latent HeatThe Clapeyron Equation relates enthalpy change to temperature, vapor pressure, and volume in the phase change of a two-phase, single-species system.

d Td P

T vhsat

DD=

where

hD = specific latent heat for the phase change

vD = specific volume change for the phase change

For the phase transition from liquid to vapor of an ideal gas, the Clapeyron equation becomes the Clausius- Clapeyron equation:

( )ln

d T

d PRh

1

satvapD

= −c m


NCEES 17

1.5.3.6 Properties for Two-Phase (Vapor-Liquid) SystemsQuality x (for liquid-vapor systems at saturation) is defined as the mass fraction of the vapor phase:

x m mmv l

v= +

where

mv = mass of vapor

ml = mass of liquid

Specific volume of a two-phase system can be represented as

v = xvv + (1 – x) vl or v = vv + xDvvap

where

vv = specific volume of saturated vapor

vl = specific volume of saturated liquid

Dvvap = specific volume change upon vaporization

= vv – vl

Similar expressions exist for u, h, and s:

u = xuv + (1 – x) ul or u = ul + xDuvap

h = xhv + (1 – x) hl or h = hl + xDhvap

s = xsv + (1 – x) sl or s = sl + xDsvap

The energy difference between two phases in equilibrium at a given temperature (or pressure) is the latent heat. The three types of latent heat are

Latent heat of fusion (melting): Dhfusion = hl – hs

Latent heat of sublimation: Dhsubl = hv – hs

Latent heat of vaporization: Dhvap = hv – hl

1.6 Behavior of Multicomponent SystemsThe properties of a mixture can be estimated using the properties of its pure components, based on either a mass-fraction average or a mole-fraction average. The one exception is entropy, which must be estimated based only on a mole-fraction average, as shown below. Use volumes when computing the density of a mixture:

When i = 1, 2, …, n constituents, the mole fraction is

x nn

n n x 1ii

i i/ /= = =

where

ni = number of moles of component i

n = total moles in the mixture

Mass fraction: w mm

ii= m = mi/ wi/ = 1


18 NCEES

Molecular weight: MW = n

m = x MWi i/ To convert mole fractions xi to mass fractions wi:

w x MWx MW

ni

i i

i i= _ i/

To convert mass fractions to mole fractions:

x

MWw

MWw

n

i

i

ii

i

=/

To convert a component from a wet basis to a dry basis:

( )w ww1–Dry

H O

Weti

i

2

=

where

wH O2 = the weight fraction of water in the mixture

1.6.1 Ideal Mixtures

1.6.1.1 Ideal Gas Mixtures

Dalton’s Law of Partial Pressures

p V n RTi i=

results in orP p p p pnii

n

i1

g= = + +=/ and y P

pnn

ii i= =

where

pi = partial pressure of component i

ni = moles of component i

yi = mole fraction of component i in gas phase

Amagat’s Law of Partial Volumes

pV n RTi i=

results in: orV V V V Vnii

n

i1

g= = + +=/ and y V

Vnn

ii i= =

where Vi = partial volume of component i

Other properties include:

( ) ( ) ( )u y u h v h s y s smixi i i i i i= = = +// /


NCEES 19

where

ui and hi are evaluated at T

si is evaluated at T and Pr

To calculate the molar volume of an ideal gas or liquid mixture:

v x vmix i in

=t t_ i/

This equation applies to internal energy, enthalpy, and volume but not to density, which is the reciprocal of specific volume.

For terms involving entropy, include the entropy of mixing:

nlns R x x1

mix i i= d n/

When mixing pure components:

nnlns x s R x x1

mix i i i i= +t t_ di n//

and Gibbs free energy is

nnlng x g RT x x1

mix i i i i= +t t_ di n//

1.6.1.2 Raoult’s LawAssuming a vapor phase that is an ideal gas and a liquid phase that is an ideal solution:

p y P x P sati i i i= =

where

xi = mole fraction of component i in liquid phase

P sati = vapor pressure of pure component i

1.6.1.3 Henry’s LawThe partial pressure of a component in the gas phase is proportional to the concentration of the component in the liquid phase:

pi = yi P = xi Hi

where Hi = Henry’s law constant for component i

1.6.2 Nonideal Mixtures

1.6.2.1 Fugacity Coefficients and Activity Coefficients

Fugacity

The criterion for the vapor-liquid equilibrium of mixtures is

f fV Li i=t t

where


20 NCEES

f Vit = fugacity of component i in the vapor phase

f Lit = fugacity of component i in the liquid phase

Vapor Fugacity of Pure Component

f PVi iz=

where iz = fugacity coefficient of pure component i in vapor phase

The fugacity coefficient of a pure component is a function of temperature and pressure and may be determined from any of:

The residual Gibbs free energy (GR) ln RTGR

z =

An equation of state ( )ln Z P

dP1P

z = −0#

A generalized correlation, e.g., ( ) ( )ln ln ln0 1z z ~ z= +

where w = the accentric factor

Liquid Fugacity of Pure Component

f PL sat sati i i /z= ( )exp RT

v P PL sati i/ = −t= G

wheresatiz = fugacity coefficient of pure component i at saturation

/ = Poynting correction factor

v Lit = molar volume of pure component i in the liquid phase

Vapor Fugacity of Mixture

f P y PVi i i i iz z= =t t t

where izt = fugacity coefficient of component i in the vapor phase

The fugacity coefficient of a component in a mixture may be determined from an equation of state and a mixing rule.

For a pure component, using the virial equation: ln RTB P

iz =

For a mixture, using the virial equation: ln y B B RTP

mi j ijjz = −a k/where

B y y Bm i j ijji

= //

Bm = second virial coefficient of the mixture

Bij = virial coefficient that characterizes a bimolecular interaction between i and j


NCEES 21

For i = j, Bij = Bji = Bii

For i j=Y , Bij must be obtained from measured values or mixing rules.

Liquid Fugacity of Mixture

f x f x PL L sat sati i i i i i i i /c c z= =t

where gi = activity coefficient of component i

Activity coefficients are normally based on experimental measurements and fitted to an activity coefficient model, for example the Van Laar model:

ln lnandA A xA x A A x

A x1 11 12

21 2

12 12

2 2112 1

21 22

c c= + = +− −

e eo o

where A12 and A21 = Van Laar constants, typically fitted from experimental data

Gamma/Phi Approach to Vapor-Liquid Equilibrium (VLE)

y P x Psat sati i i i i i i i/z c z=t

Special cases:

Ideal vapor phase, ideal liquid solution, and low pressure:

Assume , , ,and then y P x P1 1 1 sati i i i i i/z c= = = =t

Ideal vapor phase, nonideal liquid solution, and low pressure:

Assume ,and then y P x P1 1 sati i i i i i/z c= = =t

Nonideal vapor phase, nonideal liquid solution, and moderate pressure:

Assume , then y P x P1 sat sati i i i i i i/ z c z= =t

1.6.2.2 Heat of SolutionIdeal mixing applies to gases at low pressures; liquids and high-pressure gases involve nonideal mixing. In these cases, make calculations on a mole or mass basis instead of on a mole-fraction or mass-fraction basis. For the heat of a solution for a binary mixture on a molar basis:

nh n h n h n h1 1 2 2D= + +ix, actualmt t t t

where

n = total moles of solution

n1 = moles of component 1

n2 = moles of component 2

This equation also applies to solids or gases dissolving into liquids. The hD t value must be known.

Heats of solutions often appear in charts, and enthalpies of mixing are presented as a function of composition. For evolved or absorbed heat:

n h nh n h n h1mix1-D = + 2,ix final 2m mixt t t t_ i

where hmix1 and hmix2 can be either mixtures or pure components. This is calculated on a mass basis if the data are on a mass basis.


22 NCEES

1.6.3 Phase Equilibrium for Multicomponent Systems

1.6.3.1 Vapor-Liquid Equilibrium in Binary, Fully Miscible Systems

Typical Vapor-Liquid Equilibrium Diagrams for Binary, Fully Miscible Systems

L

L

V–L

V–L

V

V

x-y x x

TP y

1.6.3.2 AzeotropesAn azeotrope is a mixture that produces a liquid and vapor of equal composition when boiled. No separation of such a mixture is possible by simple distillation.

For a positive azeotrope (minimum-boiling azeotrope):

• A positive deviation from Raoult’s Law is exhibited on a P-xy diagram, with the P-x curve lying above that for ideal behavior.

• The P-x curve and the P-y curve exhibit maxima at a point for which x = y.• A T-xy diagram exhibits a minima at the point for which x = y, which represents a boiling point lower than that

of any other composition.• A positive deviation from ideal-solution behavior results when liquid-phase intermolecular forces between like

molecules are stronger than between unlike molecules.

Positive Azeotrope Diagrams

L

V–LV–L

V

x - y

LV–L

V–LV

x - y x - y

P T y

For a negative azeotrope (maximum-boiling azeotrope):

• A negative deviation from Raoult’s Law is exhibited on a P-xy diagram, with the P-x curve lying below that for ideal behavior.

• The P-x curve and the P-y curve exhibit minima at a point for which x = y.• The T-xy diagram exhibits a maxima at the point for which x = y, which represents a boiling point higher than

that of any other composition.• A negative deviation from ideal-solution behavior results when liquid-phase intermolecular forces between

unlike molecules are stronger than between like molecules.


NCEES 23

Negative Azeotrope Diagrams

L

V–LV–L

Vy

LV–L

V–L

V

TP

x - y x - y x - y

Lever Rule for a Binary Phase System

For a vapor-liquid mixture of A and B, the relative amounts of the liquid and vapor phases in a mixture with an overall composition of xF are given by the following equations:

A a bb

y xy x

A a ba

y xx x

LA A

A F

VA A

F A

= + = −−

= + = −−

P

L

V

0 1xA

CONCENTRATION OF COMPONENT A

xF yA

a b

1.6.3.3 Liquid-Liquid Equilibrium for Partially Miscible and Immiscible SystemsMany mixtures of chemical species, when mixed in certain ranges of composition, form two liquid phases of differ-ent compositions at thermodynamic equilibrium.

The criterion for the liquid-liquid equilibrium of mixtures is

f fi i=a bt t

where

fiat = fugacity of component i in the liquid phase designated a

fibt = fugacity of component i in the liquid phase designated b

If each species exists as a liquid at the system temperature, then:

x xi i i ic c=a a b b


24 NCEES

A solubility diagram is a T-x diagram at a constant pressure for a binary system. It depicts curves that indicate the compositions of coexisting liquid phases. Such diagrams may show:

• A lower critical solution temperature, above which two liquid phases are possible and below which a single liquid phase exists for all compositions.

• An upper critical solution temperature, below which two liquid phases are possible and above which a single liquid phase exists for all compositions.

• When liquid-liquid equilibrium curves intersect a vapor-liquid equilibrium bubble point curve and where only the lower critical solution temperature exists.

• When liquid-liquid equilibrium curves intersect a solid-liquid equilibrium freezing point curve and where only the upper critical solution temperature exists.

Upper and Lower Critical Solution Temperatures

x

T

x

T

LOWER CRITICALSOLUTION TEMPERATURE

UPPER CRITICALSOLUTION TEMPERATURE

Phase Diagrams

Most of the ternary or pseudoternary systems used in extraction are of two types:

Type I System: One binary pair has limited miscibility.

Type II System: Two binary pairs have limited miscibility.

Examples of type I and II systems are shown below.

Example: Type I System Components A + B + C1.00000.90000.80000.70000.60000.50000.40000.30000.20000.10000.0000

0.0000 0.0500

TIE

LINES

COMPONENT C LAYER

0.1000 0.1500

COMPONENT ALAYER

WEIGHT FRACTION COMPONENT B

WT.

FRAC

TION

COM

PONE

NT C

0.2000 0.2500 0.3000 0.3500


NCEES 25

Type I System Type II System

Lever Rule for a Ternary Two-Phase System

In the following ternary phase diagram, two phases contain partially miscible components A, B, and C. One phase is rich in component B and one is lean in component B. The fraction of the B-lean phase is a b

a+ , where a and b

represent the length of the tie line on each side of the overall composition, denoted by the heavy black dot.

Ternary Phase Diagram

b100% B 100% A

100% C

a

1.6.3.4 Vapor-Liquid-Liquid EquilibriumThe gamma-phi approach to vapor-liquid equilibrium applies to each liquid phase. Assuming that and1 1/z = = :

andy P x P y P x P* * * *sat sati i i i i i i ic c= =a a b b

For a binary system,

P y P y P x P x P* * * * * sat sat1 2 1 1 1 2 2 2c c= + = +b b a a and y

Px P**

sat

11 1 1c=b b

where

P* = three-phase equilibrium pressure

y*1 = three-phase equilibrium concentration of component 1 in the vapor phase

PLAITPOINT

a c

e z

f

d

b

MOL FRACTION MOL FRACTION

TWO LIQUID PHASESTWO LIQUID PHASES


26 NCEES

x1b = concentration of component 1 in the liquid phase

x2a = concentration of component 2 in the liquid phase

1cb = activity coefficient of component 1

2ca = activity coefficient of component 2

a = liquid phase rich in component 2

b = liquid phase rich in component 1

In an immiscible system, , , , andx x1 1 2 2c cb b a a all are equal to 1. As a result:

andP P P y P PP* *sat satsat sat

sat

1 2 11 2

1= + =+

For the range in which the vapor is in equilibrium with pure-liquid component 1:

y PP sat

11=

And similarly, for the range in which the vapor is in equilibrium with pure-liquid component 2:

y PP sat

22=

Vapor-Liquid-Liquid Equilibrium Diagrams

L1 – L2

L1 – L2

L1L1L2 L2

V–L1

V–L1

V–L2 V–L2

V

V

x x x

P T y

1.7 Power CyclesThe most efficient means of converting heat into work is the Carnot cycle. Thermal efficiency is defined as

QWin

outh =

For the Carnot cycle,

QW

QQ

TT T

1in

out

in

out

H

H C--

h = = =

where

TC = temperature of working fluid entering the engine

TH = temperature at which heat is emitted from the engine

Refrigeration cycles are the reverse of heat-engine cycles. Heat is moved from low to high temperature, requiring work, W. Cycles can be used for refrigeration or in heat pumps.

The Coefficient of Performance (COP) is defined as

COP WQ

HPH= for heat pumps


NCEES 27

COP W

Qref

L= for refrigerators and air conditioners

The upper limit of COP is based on the reversed Carnot cycle:

COP T TT

CH L

H

-= _ i for heat pumps

COP T TT

CH L

L

-= _ i for refrigerators and air conditioners

1 ton of refrigeration = 12,000 hrBtu = 3516 W

Common Thermodynamic Cycles

P T

T

h h( () )3 4

CARNOT CYCLE

RANKINE CYCLE REFRIGERATION

CONDENSER

CONDENSER

CONDENSER

COP HPCOP

EVAPORATOR

EVAPORATOR

EXPANSIONVALVE

COMPRESSOR

COMPRESSOR

REVERSED CARNOT

v s

s

T

s

T

s

33

3

3

3

3

wT

3η

η

1

1

1

1

1

1 1

12 2

2

2

TURBINE

TURBINEEXPANSIONVALVE

= = =

BOILER

BOILER

PUMP

ref

=p p2 3

=p p2 3

=h h4 3

2

4

4

4

2

2

4

4

4 4T = TL

TL

TL TL

THTH

TH

s = c s = cs = cq = 0

s = cq = 0q = 0

s = cq = 0s = c

T = TH

=

q in

q in

q out

q out

wC

PUMP

— h h1 4— h h2 3—

h h2 1— h h2 1—h h3 2—

h h2 1——

CONDENSER

—


28 NCEES

Combustion Cycles

OTTO CYCLE(GASOLINE ENGINE)

BRAYTON CYCLE(GAS TURBINE)

P 3

2 41

s = c

s = c

v

T 3

42

1s

v = c q = 0

v = c

FUEL GAS

AIR1

EXHAUSTGAS

W

H.P./L.P. TURBINE

AXIALCOMPRESSOR

COMBUSTIONCHAMBER

43

2

P12P

1T4T ––– ==

)(( )2T3T – )(11η

( k – 1 )kr

vr

–

=

= 1η 1 – k

1v2

k =ĉv

âp

q = 0

29

2 HEAT TRANSFER



A Area ft2 m2

C Heat-capacity rate hr FBtu-c K

Ws Kkg m3

2

:

:=

Cs Heat-capacity ratio CCmax

mine o dimensionless

cp Heat capacity lbm FBtu-c kg K

Js Km2

2

: :=

D Diameter ft or in. m

d Wall thickness, width ft or in. m

F Correction factor for heat-exchanger configuration dimensionless

Fij Shape factor (radiation) dimensionless

f Moody friction factor dimensionless

g Acceleration of gravity secft2 s

m2

h Convection heat-transfer coefficient hr ft FBtu- -2 c m K

Ws Kkg

2 3: :=

hfusionD Latent heat of fusion lbmBtu

kgJ

sm2

2=

hsublD Latent heat of sublimation lbmBtu

kgJ

sm2

2=


30 NCEES


hvapD Latent heat of vaporization lbmBtu

kgJ

sm2

2=

jH Colburn factor for heat transfer dimensionless

k Thermal conductivity hr ft FBtu- -c m K

Ws Kkg m3: :

:=

L Length ft or in. m

m Mass lbm kg

mo Mass flow rate hrlbm s

kg

NTU Number of thermal transfer units dimensionless

n Number of tubes (in shell-and-tube heat exchangers) dimensionless

P Pressure psi = inlbf2 Pa

mN

m skg

2 2:= =

P Thermal efficiency dimensionless

Q Heat Btu Js

kg m2

2:=

Qo Rate of heat transfer hrBtu

Ws

kg m3

2:=

qo Heat flux (rate of heat transfer per area) -hr ftBtu

2 mW

skg

2 3=

qlo Heat-transfer rate per unit length -hr ftBtu

mW

skg m

3:=

qgeno Heat-generation rate (per volume) hr ftBtu

3- mW

m skg

3 3:=

R Heat-transfer resistance Btuhr F-c

WK

kg ms K

2

3

::=

R Heat-capacity ratio CCshell

tubee o dimensionless

Rf Fouling factor -Btu

hr ft F-o2W

m Kkgs K2 3: :=

r Radius ft or in. m

T Temperature F Rorc c C or Kc

TlmD Log-mean temperature difference F Rorc c K

t Time hr s

U Overall heat-transfer coefficient hr ft FBtu- -2 c m K

Ws Kkg

2 3: :=

Chapter 2: Heat Transfer

NCEES 31


UD Change in internal energy Btu Js

kg m2

2:=

u Velocity secft

sm

V Volume ft3 m3

x Distance ft or in. m

a Adsorptivity (radiation) dimensionless

a Thermal diffusivity hrft2 s

m2

b Coefficient of thermal expansion R1

K1

g Surface tension in.lbf

mN

skg2=

d Thickness ft or in. m

e Emissivity of a body (radiation) dimensionless

e Heat exchanger effectiveness dimensionless

e Void fraction (packed bed) dimensionless

q, f Angle dimensionless

m Dynamic viscosity cP or secftlbm- Pa s m s

kg: :=

n Kinematic viscosity hrft2

sm2

r Density ftlbm3 m

kg3

r Reflectivity (radiation) dimensionless

v Stefan-Boltzmann Constant ft hr RBtu- -2 4c m K

W2 4:

t Time constant hr s

t Transmissivity (radiation) dimensionless

2.2 Heat-Transfer Mechanisms

2.2.1 Heat Transfer Without Phase Change

2.2.1.1 Heat Capacity/Specific Heat (Cp)

Q mc dtdT

p=o

c m T

Up DD=


32 NCEES

Heat transferred in or out of a flowing material:

Q mc TpD=o o

2.2.1.2 Thermal Conductivity (k), Thermal Diffusivity (a), and Kinematic Viscosity (n)Thermal conductivity is a measure of the rate at which a substance transfers thermal energy:

k Tq

dD

= o

Thermal diffusivity is a measure of the rate at which a thermal disturbance is transmitted through a substance:

ckp

a t=

Kinematic viscosity (also called momentum diffusivity) is the ratio of the dynamic viscosity m to the density of the fluid r:

v tn=

2.2.1.3 Conduction

Fourier’s Law of Conduction

Total heat flux: Q k A dxdT= −o

Heat flux per area: q AQ

k dxdT= = −o

o

Heat flux per unit length: q LQ=loo

Conduction Through a Plane Wall T1

Q

T2

k

δ

( )Q k A T T1 2d

= −o

where

T1 = temperature of one surface of wall

T2 = temperature of the other surface of wall

Conduction Through a Composite Wall

( )Q

k

A T T

i

ii

1 2d

=−

o

/


NCEES 33

Conduction Through a Cylindrical Wall

( )

lnQ

rrk L T T2

12

1 2r= −o

d n

T1Q

T2

r2

r1k

Cylinder (Length = L)

where L = cylinder length

Conduction Through a Spherical Wall

( )Q r r

k r rT T

42 1

1 21 2

r= − −o

Conduction Through a Cube With Thick Walls (Approximation)

.Q A A T T0 725 outer inner

inner outer.d

-o e o

where AA

2inner

outer $

Steady Conduction With Internal Energy Generation

For a plane wall:

−δ +δ0

T1

T(x)

gen

T2

k

q1 q2

q

dxd T

kq

T x kq x T T x T T

0

2 1 2 2

gen

gen

2

2

2

2

22 1 1 2

d

d d

+ =

= − + − + +

o

o^ e d c dh o n m n

and

q q q

q k dxdT q k dx

dT2 gen1 2

1 2

d+ =

= =d d− +

o o o

o oc cm m

For a long circular cylinder:

T0

kr0

qʹ 0

genq

( )

r drd r dr

dTkq

T r kq r

rr T

q r q

1 0

4 1

gen

gen

gen

02

02

2

0

0 02r

+ =

= − +

=l

o

o

o o

c

f

m

p

where q 0lo = heat transfer rate per unit length in hr ftBtu or m

W-


34 NCEES

Transient Conduction Using the Lumped Capacitance Model

The lumped capacitance model is valid if

As

Body

ρ, V, c , T P

T h,Fluid

∞ Bi k A

hV 1<<s

=

where

Bi = Biot number

V = volume of body

As = surface area of body

For constant fluid temperature T3 and uniform body temperature T:

Heat transfer rate at the body surface is

( )Q h A T T V c dtdT

s pt= − =3o

Temperature variation of the body with time is

( )expT T T T ti x

− = − −3 3 c m

where

t = h AV c

s

pt = time constant

Ti = initial temperature of the body in K or °R

Total heat transferred to the body at time t is

( ) ( ) expQ V c T T V c T T t1total i ip pt t x= − = − − −3 d c mn

2.2.1.4 Convection

Newton’s Law of Cooling

( )Q h A T Tw= − 3o

where

Tw = wall surface temperature

T∞ = bulk fluid temperature


NCEES 35

2.2.1.5 Free/Forced Heat-Transfer Coefficients/Correlations

Forced Convection: External Flow

Forced Convection—External FlowGeometry Correlation Conditions

Flat plate in parallel flow (gas or liquid)

Reu L

L nt= 3

. Re PrNu kh L 0 664 L

21

31

= =LRe 10L

51

. Re PrNu kh L 0 0366 .

L0 8 3

1= =L

Re 10L52

Long cylinder in cross flow (gas or liquid)

Reu D

D nt= 3

Re PrNu kh D C D

n 31

= =D

ReD C n1–4 0.989 0.3304–40 0.911 0.385

40–4000 0.683 0.4664000–40,000 0.193 0.618

40,000–250,000 0.0266 0.805

Short cylinder (gas only)

Reu D

D nt= 3 . Re Re

Nu kh D

LD0 123 .

..

D D0 651

0 850 5

= =

+

D

c m70,000 < ReD < 110,000

L/D < 4

Sphere in flow (gas or liquid)

Reu D

D nt= 3

. . Re PrNu kh D 2 0 0 60 D

21

31

= = +D

1 < ReD < 70,000 0.6 < Pr < 400

Long, flat plate (width L), perpendicular to flow in gas

Reu L

L nt= 3

. ReNu kh D 0 20 D

32

= =D1 < ReD < 400,000

Packed bed with gas flow –heat transfer to or from the packing

( )Re

D AV

u D

6

1

pp

p

Ds p

p n e

t

=

= −

where e = void fraction us = superficial velocity Dp = equivalent packing diameter Vp = particle volume Ap = particle surface area

. .Re Re Pr

Nu kh D

1 0 5 0 2D D

p

21

32

31

p

p pee

= =

−+

D

d n,Re20 10 000Dp1 1

0.34 < e < 0.78

. Re PrNu kh D 1 075 .

Dp 0 174 3

1p pe= =D

. Re0 01 10Dp1 1


36 NCEES

Forced Convection—External Flow (cont'd)Geometry Correlation Conditions

Packed bed with gas flow – heat transfer to or from the containment wall Re Pr Re Pr

Nu kh D

C C . .D D

p

131

31

20 8 0 4

p

p p

= =

+

D40 Re 2000Dp1 1

Packing Shape C1 C2Cylinder-like 2.58 0.094Sphere-like 0.203 0.220

Tube bundle in cross flowPr Pr

Pr

Re

Nu

SSC

..

s

L

Tn

Dm

0 360 25

=−−

D

e

d

o

n

Config. Reynolds Range C m nInline 10–100 0.8 0.4 0Staggered 10–100 0.9 0.4 0

Inline1000–200,000

.SS

0 7L

T $0.27 0.63 0

Staggered1000–200,000

SS

2<L

T 0.35 0.60 0.2

Staggered1000–200,000

SS

2L

T $ 0.40 0.60 0

Inline >200,000 0.021 0.84 0

Staggered >200,000 Pr > 1 0.022 0.84 0

. ReNu kh D 0 019 .

D D0 84= = Staggered >200,000

Pr = 0.7 --- --- ---

where

u∞ = free stream velocity of the fluid

us = superficial velocity (velocity through the bed if it were empty)

Nu = average Nusselt number

h = average heat-transfer coefficient

Prs = Prandtl number based on properties at tube surface

In all cases, evaluate fluid properties at average temperature between that of the body and that of the flowing fluid.

For tube bundles in cross flow, the following applies:

Inline (square pitch): Staggered (triangular pitch): SL

SL

STFLOWLONGITUDINALROW

TRAN

SVER

SE R

OW

SL

ST

DO

FLOW

DO


NCEES 37

Forced Convection: Internal Flow

Forced Convection—Internal FlowGeometry Correlation Conditions

Laminar flow in circular tubes, Re < 2300

.Nu 4 36D = Uniform heat flux, fully developed

.Nu 3 66D = Constant surface temperature, fully developed

D . /Re PrNu L D1 86

.D

s

31 0 14

$nn= 3d dn n Constant surface temperature, inter-

mediate tube length with entry effects

D ..

.

Re Pr

Re PrNu

DLDL

3 661 0 04

0 0668 .

D

D

s

0 14

nn= +

+3

J

L

KKKKKKKdN

P

OOOOOOOn

Constant surface temperature, short tube length with entry effects:

100 Re Pr LD 1500; Pr 0.7< < >Dc m

Turbulent flow in circular tubes

. Re PrNu 0 023 .D s0 8 3

1.0 14

nn= 3

D d nUniform surface temperature or uni-form heat flux: Re > 10,000; Pr > 0.7

Liquid metals. . Re PrNu 6 3 0 0167 . .

D0 85 0 93= +D

Uniform heat flux: 0.003 < Pr < 0.05

. . Re PrNu 7 0 0 025 . .D0 8 0 8= +D

Constant surface temperature: 0.003 < Pr < 0.05

Re and Nu

u Dkh D

Dmn

t= =D

where

um = mean velocity of the fluid n3 = viscosity of the fluid at bulk fluid temperature ms = viscosity of the fluid at tube inside surface temperature

For noncircular ducts, use the equivalent hydraulic diameter: tional area-secwetted perimetercrossD 4

H#=

For a circular annulus, use the equivalent hydraulic diameter: D D DH outer inner= −

Use the Moody friction factor f to predict heat-transfer coefficients for turbulent flow:

RePr PrNu f

832

=c m

For flow in coiled tubes with Re > 104, the film coefficient for straight pipe is

.h h DD

1 3 5coil straightcoil

tube= +e o

PE C

hemical R

eference Handbook

38

NC

EES

Tube-Side Heat-Transfer Curve (Adapted from Sieder and Tate)

1000800

600500400

300

200

10080

605040

30

20

108

654

3

2

110 20 30 40 50 60 80 100 200 3 4 5 6 87 1000 32 4 5 6 000,017 8 33 22 4 5 6 87 100,000

10 20 30 40 50 60 80 100 200

HEATING AND COOLING

3 4 5 6 00017 8 32 4 5 6 87 10,000 33 22 4 5 6 87 100,000

L/D = 24364872120180220360600

= VELOCITY= DENSITY= COLBURN FACTOR= SPECIFIC HEAT OF THE FLUID= INSIDE DIAMETER OF TUBES= FILM COEFFICIENT= THERMAL CONDUCTIVITY= LENGTH OF PATH= VISCOSITY AT THE BULK TEMPERATURE= VISCOSITY AT THE TUBE WALL TEMPERATURE

uρjHcpdh ikLµµw

j H=k

kc p

h id

wµµ

µ

−−

1/30.1

4

=Red.u.ρµ

Source: Donald Q. Kern, Process Heat Transfer, New York: McGraw-Hill, 1990, p. 834.


NCEES 39

Natural (Free) Convection

Natural (Free) ConvectionGeometry Sketch Correlation Conditions

Vertical plate

∞

L

g

. PrNu Gr1 36 L 51

=L _ i PrGr 10<L4

. PrNu Gr0 59 L 41

=L _ i PrGr10 10< <L4 9

. PrNu Gr0 10 L 31

=L _ i PrGr10 10< <L9 13

Long, tilted plate with heated surface facing downward

∞θ Lg

. Pr cosNu Gr0 56 L 41i=L _ i Pr cosGr10 10

0 89< <L

5 11

# #

i

i c

Long, horizontal plate with heated surface facing downward

∞L

g. PrNu Gr0 58 L 5

1=L _ i PrGr10 10< <L

6 11

Long, horizontal plate with heated surface facing upward L

g . PrNu Gr0 16 L 31

=L _ i PrGr710 210< <L6 8

. PrNu Gr0 13L L 31

= _ i PrGr5 10 < L8#

Horizontal circular plate with heated sur-face facing downward

g

D. Pr PrNu Gr0 82 .

D 51

0 034=D _ i

Single, long horizontal cylinder ∞

Dg

PrNu GrC Dn=D _ i

Pr > 0.5GrD • Pr C n10–3 – 102 1.02102 – 104 0.850104 – 107 0.480107 – 1012 0.125

. PrNu Gr0 53 D2 41

=D ` jLiquid metals, laminar

flow

Thin horizontal wire ∞

Dg PrNu GrCD D

n= _ i

GrD • Pr C n< 10–5 0.49 0

10–5 – 10–3 0.7110–3 – 1 1.091 – 104 1.09

Vertical cylinder

∞

Dg

. PrNu Gr0 59D D 41

= _ i PrGr10 10< <D4 9

. PrNu Gr0 10D D 31

= _ i PrGr10 10< <D9 13


40 NCEES

Natural (Free) Convection (cont'd)Geometry Sketch Correlation Conditions

Sphere

Diameter D

g

.Nu Gr2 0 392D D 41

= + _ i Gr1 10< <D5

Vertical coneφ

gL

. ( . )

tan

Nu Gr

Gr

0 63 1 0 73

2

2L L

L

41

41

e

ez

= +

=

_ i. .. .logGr

3 127 5 8 70 2 0 8

< << <

< <L

z

e

c c

Vertical enclosed space heated from the side

δ

g L

. . PrPrNu RaL0 22 0 2

.41 0 28

d= + d

−

d c cm m PrRa

L2 10

1010

< <

<< 10

d

d

. . PrPrNu Ra0 18 0 2

.0 29= +d dc m

.

Pr

PrPrRa

L1 2

10 10

10 0 2

< <

<

<

3 5

3

d

+d

−

Horizontal enclosed space heated from below

δg

.Nu Ra

Ra

1 1 44 1 1708

5830 131

= + −

+ −

dd

dd

d

n

n

> HAir

1700 < Rad < 108

.

.

Nu Ra

Ra Ra

1 1 44 1 1708

5830 1 2 0140

ln Ra

31

31 1

14031

= + − +

− +

dd

d d

− d

d

d

ff

n p

n

p> H

Water 1700 < Rad < 3.5 • 109

For plates and other linear geometry: ( )

PrRa Grv

g T T Lkc

L Ls p2

3b n= =

− 3

For cylinders and spheres: ( )

PrRa Grv

g T T Dk

c vD D

s p2

3b n= =

− 3

where

Ts = surface temperature

T3 = bulk fluid temperature

For an ideal gas: T T121

sb= + 3` j

where T = absolute temperature, in K or °R


NCEES 41

2.2.1.6 Radiation

Stefan-Boltzmann Law of Radiation

Q AT4fv=o

where T = absolute temperature, in K or °R

Types of Bodies

a = absorptivity (ratio of energy absorbed to incident energy)

r = reflectivity (ratio of energy reflected to incident energy)

t = transmissivity (ratio of energy transmitted to incident energy)

a + r + t = 1

Opaque body: t = 0

Gray body: t = 0 and a = e with 0 < a < 1 and 0 < e < 1

Black body: t = 0 and a = e = 1

Real bodies are frequently approximated as gray bodies.

A black body is one that absorbs all energy incident upon it. It also emits radiation at the maximum rate for a body of its size and temperature.

Shape Factor Fij (Also Called View Factor or Configuration Factor)

Reciprocity relations:

j jiA F A Fi ij =

where

Ai = surface area of surface i

Fij = fraction of the radiation leaving surface i that is intercepted by surface j; F0 1ij# #

Summation rule for N surfaces:

j 1=

F 1ij =N

/


42 NCEES

Net energy exchange by radiation between two bodies:

When the body is small in comparison to its surroundings

Q A T T12 14

24fv= −o ` j

where T = absolute temperature in K or °R

When both bodies are black bodies

Q AF T T12 12 14

24v= −o ` j

Net energy exchange by radiation between two diffuse gray surfaces that form an enclosure:

Q

A A F A

T T1 1 112

1 1

1

1 12 2

2

14

24

2ff

ff

v= −

+ +−

−o

` j

A2, T2, ε2

A2, T2, ε2

A1, T1, ε1

A1, T1, ε1

12Q 12Q

For radiative heat loss at night, neglect any return radiation from the clear night sky, i.e., set T2 to 0 K or 0oR.

One-dimensional geometry with a thin, low-emissivity shield inserted between two parallel plates:

Q

A A F A A A F A

T T1 1 1 1 1 112

1 1

1

1 13 31

31

32

32

3 32 2 2

2

14

24

3 3ff

ff

ff

ff

v= −

+ +−

+−

+ +−

−o

` j

A3, T3

A2 , T2 ,A1, T1,

ε3,2

ε2ε1

ε3,1

RADIATION SHIELD

12Q

Energy transfer by radiation from reradiating surfaces:

Q

AA F A F A F

A

T T1

1 11 1

R R

1 1

1

1 12 1 1 2 2

1 2 2

2

14

24

ff

ff

v= −

++ +

+−

−

−

o

d

` j

n

A2 , T2 , ε2

A1 , T1 , ε1 AR , TR , εR12Q

Reradiating surfaces are considered to be insulated or adiabatic.


NCEES 43

Radiation Heat Transfer—Special Considerations

Heat input from solar radiation:

Q A F qp solar12a=o o

where a = absorptivity

Ap = projected area perpendicular to the source

Simplified Equation for the Radiation Heat-Transfer Coefficient

This equation is in the same form as the equations for the conduction and convection heat-transfer coefficients and is used when there is a combination of heat-transfer coefficients. The radiation heat-transfer coefficient must be calculated at the system temperatures.

Q h A T Trad rad 1 2= −o _ iwhere h F T T T Trad 12 1

222

1 2v= + +` _j i

2.2.1.7 Combination of Heat-Transfer MechanismsOverall heat-transfer coefficient Uov:

Q U A Tov D=o

Thermal Resistance

Q R

Ttotal

totalD=o

R U A1

totalov

=

Plane Wall Cylindrical Wall Spherical Wall Convection

R k Al= ln

R k Lrr

212

r=d n R k r r

r r4 2 1

2 1r

=−

R h A1=

Mean diameter:

Cylindrical wall ln

D

DD

D Dlm

inner

outer

outer inner=−

e o

Spherical wall D D D

D Dmean

outer inner

outer inner= −

Resistance in series:

Resistance Heat Flux Temperature

R Rtotal /= ttanconsQtotal =o T Ttotal /D D=

Intermediate Temperatures: ...Q R

T TR

T TR

T T, , , , , ,

A

A A

B

B B

i

i i1 2 1 2 1 2=−

=−

= =−

o


44 NCEES

Resistance in parallel:

Resistance Heat Flux Temperature

R R1 1total

/= Q Qtotal /=o o constantTtotal =D

Heat flux relations: ...T Q R Q R Q Ri i1 1 2 2D = = = =o o o

Heat Transfer from Fins

For a straight fin with uniform cross-section (assuming negligible heat transfer from the tip):

tanhQ h P k A T T L P

Ak Ah P

c bc

c= − +3o ` dj n= G

Circular (pin) fin: P = p D and A D4c

2r=

Rectangular fin: P = 2 (w + l) and A w lc =

where

P = perimeter of the exposed fin cross-section

Ac = fin cross-sectional area

L = length of the fin

D = diameter of a circular fin

w = width of a rectangular fin

l = height of a rectangular fin

Tb = temperature at the base of the fin

T∞ = bulk fluid temperature

Pin Fin: Rectangular Fin:

t

T ,h

w

Ac= wtP = 2( w+L)

∞

Lt

L

D

2

= πP D

4πD=

Tb Tb

Ac

T , h∞

t

T ,h

w

Ac= wtP = 2 ( w+L)

∞

Lt

Tb


NCEES 45

2.2.2 Heat Transfer With Phase Change

2.2.2.1 Latent and Sensible HeatSensible heat: Q mc Tsensible pD=

Latent heat: Q m hlatent phase changeD=

Heat-transfer rate during phase change: Q m hlatent phase changeD=o o

Rate of phase change: dtdm

hQ

phase changeD=

o

2.2.2.2 Vaporization and Evaporation

Boiling

Evaporation is occurring at a solid-liquid interface when Ts > Tsat:

q h T T h Ts sat eD= − =o ` j

where

Ts = temperature of solid

Tsat,liquid = saturation temperature of liquid at system pressure

DTe = excess temperature

Pool boiling: Liquid is quiescent; motion near the solid surface is caused by free convection and mixing induced by bubble growth and detachment.

Forced convection boiling: Fluid motion is induced by external means in addition to free convection and bubble-induced mixing.

Sub-cooled boiling: Liquid temperature is below the saturation temperature; bubbles forming at the heating surface may condense in the liquid.

Saturated boiling: Liquid temperature slightly exceeds the saturation temperature; bubbles forming at the heated surface are propelled through the liquid by buoyant forces.


46 NCEES

Typical Boiling Curve for Water at One AtmosphereSurface Heat Flux as a Function of the Excess Temperature

107

∆Te =Ts–Tsat (°C)

C

P

B

AONB

1 5 10 30 120 1,000

q"MAX

q"s(W

/m2 )

q"MIN

106

105

104

103

FREECONVECTION

ISOLATEDBUBBLES

JETS ANDCOLUMNS

NUCLEATE

BOILING REGIMES

TRANSITION FILM

∆Te,A ∆Te,B ∆Te,C ∆Te,D

- CRITICAL HEAT FLUX, q"MAX

q"MIN-LEIDENFROST POINT,

D

Free convection boiling: There is insufficient vapor in contact with the liquid phase to cause boiling at the satura-tion temperature.

Nucleate boiling: Isolated bubbles form at nucleation sites and separate from the surface; vapor escapes as jets or columns.

Equation for nucleate-boiling heat flux (Rohsenow):

( )Prq h g

C hc T T/,

nucleate liq vapliq vap

sf vap liqn

p liq s sat1 2 3

nc

t tD

D= − −

o` j> >H H

where

g = surface tension of vapor-liquid interface

Ts = surface temperature of heater

Tsat = saturation temperature of fluid

Csf = experimental constant that depends on surface-fluid combination

n = experimental constant that depends on fluid

Peak heat flux: The maximum (or critical) heat flux (CHF) in nucleate pool boiling:

q C h g/

max cr vap vap liq vap2 1 4

c t t tD= −o ` j9 C

where Ccr = constant whose value depends on the heater geometry, but generally about 0.15


NCEES 47

The critical heat flux is independent of the fluid-heating surface combination, as well as the viscosity, thermal conductivity, and specific heat of the liquid. It increases with pressure up to about one-third of the critical pressure, and then starts to decrease and becomes zero at the critical pressure. The critical heat flux is proportional to the latent heat of vaporization; large maximum heat fluxes can be obtained using fluids with a large enthalpy of vapor-ization, such as water.

Values of the coefficient Ccr for maximum heat flux:

L Lg

Kg A

* liq vap

liq vap heater1

c

t t

t t

c

=−

=−`

`

j

j

Maximum Heat Flux vs. Heater Geometry

Heater Geometry CcrCharacteristic Dimension (L) Range of L*

Large horizontal flat heater 0.149 Width or diameter L* > 27Small horizontal flat heater 18.9 K1 Width or diameter 9 < L* < 20Large horizontal cylinder 0.12 Radius L* > 1.2Small horizontal cylinder 0.12 L*-0.25 Radius 0.15 < L* <1.2Large sphere 0.11 Radius L* > 4.26Small sphere 0.227 L*-0.5 Radius 0.15 < L* < 4.26

Minimum heat flux: This occurs at the Leidenfrost point and is of practical interest because it represents the lower limit for the heat flux in the film boiling regime.

Minimum heat flux for a large horizontal plate:

.

)q h

g0 09min vap vap

liq vap

liq vap2

41

tt t

v t tD=

+

−o `

`jjR

T

SSSSSSSS

V

X

WWWWWWWW

Transition boiling: Rapid bubble formation results in vapor film on surface and oscillation between film and nucleate boiling.

Film boiling: Surface is completely covered by a vapor blanket; includes significant radiation through the vapor film.

Heat flux for film boiling on a horizontal cylinder or sphere of diameter D:

( )( ) . ( )

( )q CD T T

g k h c T TT T

0 4 ,film film

vap s sat

vap vap liq vap vap vap s sats sat

p3 4

1

n

t t t D=−

− + −−o

8 B* 4

For horizontal cylinders: Cfilm = 0.62

For spheres: Cfilm = 0.67


48 NCEES

2.2.2.3 Condensation

Heat-Transfer Coefficient for the Condensation of a Pure Vapor

Evaluate all liquid properties at the average temperature between the saturated temperature and the surface tem-perature,

where

rl = density of the liquid phase of the fluid

ml = viscosity of the liquid phase of the fluid

kl = thermal conductivity of the liquid phase of the fluid

Nu = average Nusselt number

h = average heat-transfer coefficient

Tsat = saturation temperature of the fluid

Ts = temperature of the vertical surface

P = wetted perimeter (width of a vertical plate, or pd, for a vertical tube)

mo = condensate generation rate

L = length of the vertical surface

D = tube outside diameter

Condensation Film CoefficientsGeometry Correlation Conditions

Condensation on a vertical or angled surface, laminar flow

. ( )Nu kh L

k T Tg h L

0 943.

l l sat s

l vap2 3 0 25

n

t D= =−L > H Vertical surface

. ( )cos

Nu kh L

k T Tg h L

0 943.

l l sat s

l vap2 3 0 25

n

t iD= =−L > H Inclined surface, angle q

measured from the vertical

Condensation on the out-side of a horizontal tube, laminar flow

. ( )Nu kh D

k T Tg h D

0 729.

l l sat s

l vap2 3 0 25

n

t D= =−D > H Single tube or horizontal

layer of tubes

. ( )Nu kh D

N k T Tg h D

0 729.

l l sat s

l vap2 3 0 25

n

t D= =−D > H

Tube bank with N layers of horizontal tubes, arranged vertically over one another

Condensation on a tall vertical surface or on the outside of a tall vertical tube, turbulent flow

. ReNu kh D g h D

0 0076 hl

l vap52

2

2 3 31

n

t D= =D > H

Condensation Reynolds number:

Re 4 1800

Q

Pm

m h hh A T T

>h l

vap vap

sat s

n

D D

=

= =−

o

oo ` j

Condensation on a sphere . ( )Nu kh D

k T Tg h D

0 815.

l l sat s

l vap2 3 0 25

n

t D= =−D > H


NCEES 49

2.3 Heat-Transfer Applications

2.3.1 Heat-Exchange Equipment Design

2.3.1.1 Overall Heat-Transfer CoefficientEnergy balance around a heat exchanger:

( ) ( )Q m c T T m c T Tcold p,cold cold,out cold,in hot p,hot hot,in hot,out= − = −o o o

Rate of heat transfer in a heat exchanger:

Q U AF TlmD=o

Heat-transfer area in a shell-and-tube heat exchanger:

A n D Lo or=

where n = total number of tubes

Mass flow rate in a shell-and-tube heat exchanger

m nD

u4passi2

r t=o

where npass = number of tubes in each pass

Overall heat-transfer coefficient for concentric tube and shell-and-tube heat exchangers:

ln

ln

U A h A AR

k LDD

AR

h A

U h DD R D

DkD

DD R h

1 12

1

1 12

1

ov ref i i i

fi

o

fo

o o

ov i i

ofi

i

o o

i

ofo

o

i

o

r= + + + +

= + + + +e e

e

eo o

o

o

where

Ai = inside area of the tubes

Ao = outside area of the tubes

Aref = reference areas for the overall heat-transfer coefficient U (usually the outside area)

Di = inside diameter of the tubes

Do = outside diameter of the tubes

hi = convection heat-transfer coefficient for inside the tubes

ho = convection heat-transfer coefficient for outside the tubes

Rfi = fouling factor for inside the tubes

Rfo = fouling factor for outside the tubes


50 NCEES

2.3.1.2 Fouling FactorsFouling factors are defined as:

R h h1 1

ffouled clean

= −

A table of fouling factors is shown in section 2.4.

Fouling factors increase with time. The following approximations are used:

Linear: ( )R t R a t,f f initial= +

Falling-rate: [ ( )] ( )R t R b t,f f initial2 2= +

Asymptotic: ( )R t R e1,f ft= −3 x−a k

where a, b, and t = empirical constants

2.3.1.3 Log-Mean Temperature Difference

Temperature Profiles for Counter- and Co-Current Heat Exchangers Without Phase Change

For countercurrent flow in heat exchangers:

U OV

Δ A

Δ AHOT FLUID

COLD FLUID

A

T

(THOT – TCOLD)ΔQ =

TCOLD, OUT

TCOLD, IN

TCOLD

THOT, OUT

THOT

THOT, IN

ΔQ

lnT

T TT T

T T T T

, ,

, ,

, , , ,lm

hot in cold out

hot out cold in

hot out cold in hot in cold outD =

−−

− − −`

f

`j

p

j


NCEES 51

For co-current (parallel) flow in heat exchangers:

(THOT – TCOLD)U OV

Δ A

Δ A

ΔQ

T

HOT FLUID

A

ΔQ =

COLD FLUID

TCOLD, OUT

TCOLD

TCOLD, IN

THOT, OUT

THOT

THOT, IN

lnT

T TT T

T T T T

, ,

, ,

, , , ,lm

hot in cold out

hot out cold in

hot out cold in hot in cold outD =

−−

− − −`

f

`j

p

j

Temperature Profiles for Evaporation and Condensation:

During the phase change of a pure substance, the temperature remains constant.

Evaporation:

THOT, OUT

THOT, IN

TEVAP

THOT

(THOT − TEVAP)

Δ A

T

A

U OV Δ AΔQ =

COLD FLUID

HOT FLUID

TCOLD, IN = TCOLD, OUT = TEVAP

Δ A

COLD FLUIDΔQ

lnT

T TT T

T T

,

,

, ,lm

hot out evap

hot in evap

hot in hot outD =

−−

−`

f

j

p


52 NCEES

Condensation:

TCOLD, IN

TCOLD, OUT

TCOLD

TCOND

(TCOND – TCOLD)

THOT, IN = THOT, OUT = TCOND

HOT FLUID

Δ A

T

A

ΔQ

U OV Δ AΔQ =

TCOLDTTΔ ACOLD FLUID

lnT

T TT T

T T

,

,

, ,lm

cond cold out

cond cold in

cold out cold inD =

−−

−`

f

j

p

Temperature Approach

Minimum temperature difference between a hot and a cold fluid:

Tapproach = (Thot - Tcold)min

Co-current: Tapproach = Thot, out - Tcold, out

Countercurrent, with Cmin = Chot Tapproach = Thot, out - Tcold, in

Countercurrent, with Cmin = Ccold Tapproach = Thot, in - Tcold, out

Evaporation Tapproach = Thot, out - Tevap

Condensation Tapproach = Tcond - Tcold, out

where C mcp= =o heat-capacity rate

for T 0approach "

Constant heat-transfer coefficient U0v A " 3

Constant heat-transfer rate Qo m mmin"o o

Constant flow rate mo Q Qmax"o o


NCEES 53

2.3.1.4 F-Factor (Log-Mean Temperature Correction Factor or LMTC Factor)

T F Tlogmean meanD D=

Temperature efficiency:

P T TT T

, ,

, ,

shell in tube out

tube out tube in= −−

Ratio of heat-capacity rates:

R T TT T

CC

, ,

, ,

tube out tube in

shell in shell out

shell

tube= −−

=

where C mcp= =o heat-capacity rate

Charts of the F-factors for various configurations are shown at the end of section 2.4.

2.3.1.5 Equipment Selection

Types of Evaporators

EvaporatorsType and Schematic Description and Applications Advantages and Disadvantages

Forced-Circulation Evaporator

V

S

G

C

PF

Description:

Circulating pump withdraws liquor from the flash chamber and forces it past the heat-ing surfaces. Typically, heating tubes are submerged and hydrostatic heads prevents boiling ; evaporation occurs in the flash cham-ber. Higher heat-transfer rates can be achieved if boiling is allowed in the tubes but then scal-ing and salt formation may occur. The forced circulation keeps solids in suspension. Tube velocities are limited by erosion and typically are 4–10 ft/s.

Applications:

• Crystalline products• Corrosive solutions• Viscous solutions

Advantages:

• High heat-transfer coefficients• Positive circulation• Relative freedom from salting, scaling,

and foulingDisadvantages:

• High cost• Power required for circulating pump• High hold-up and residence time

Difficulties:

• Plugging of tube inlets by detached salt deposits

• Corrosion/erosion• Salting due to boiling in the tubes• Poor circulation due to high head

losses


54 NCEES


Short-Tube Vertical Evaporator

V

S

G

CP

F

Description:

Circulation past the heating surface is gener-ated by boiling in the tubes. The liquid then returns to the chamber through a central well. For crystallizing solutions, a propeller placed in the lower end of the central well will keep solids in suspension. Best heat transfer is achieved when liquid level is halfway up the tubes. Scaling occurs in the tubes where evaporation takes place but can be mechani-cally cleaned, because the tubes are relatively wide (2–3") and short (4–6').

Applications:

• Clear liquids• Crystalline products (if using propeller)• Noncorrosive liquids• Mild scaling solutions

Advantages:

• High heat-transfer coefficients• Low head room• Easy mechanical descaling• Relatively inexpensive

Disadvantages:

• Poor heat transfer at low DT• High floor space and weight• High hold-up• Poor heat transfer for viscous liquids

Difficulties:

• Large body makes use of corrosion-resistant higher alloys cost-prohibitive

• Corrosion/erosion• Salting due to boiling in the tubes• Poor circulation due to high head

lossesLong-Tube Vertical Evaporator (Falling Film)

V

S

G

C

P

F

Description:

Liquid is fed to the top of vertical tubes. Tubes are narrow (1–2") and long (20–35'). The liquid flows down the walls as a film. Pressure drop in the tubes is low and the temperature of the liquid is essentially the same as that of the vapor head. Vapor-liquid separation typically occurs at the bottom. To ensure proper wetting of the tubes, external recirculation is usually required unless feed-to-evaporation rates are high.

Applications:

• Heat-sensitive materials• Foaming liquids• Low temperature operation• Large evaporation loads

Advantages:

• Low hold-up• Cheapest per unit of capacity• Small floor space• Good heat-transfer coefficients at all

temperaturesDisadvantages:

• High head room• Not suitable for scaling or salting

liquids• External recirculation usually required

Difficulties:

• Poor feed distribution• Plugging of the feed distributor if

solids are present in the liquid


NCEES 55


Long-Tube Vertical Evaporator (Rising Film)

V

S

ENT’T

G

C

P

F

Description:

Liquid enters the long, vertical heating tubes from the bottom and rises up, propelled by the vapors generated by the evaporation. Boiling occurs in the tubes. On top of the tubes is a small vapor head with almost no liquid hold-up, where the liquid and vapor separate. The product line can be connected to the feed line to create recirculation.

Applications:

• Black liquid (pulp and paper)• High temperature differences• High evaporation loads

Advantages:

• Good heat-transfer coefficients at reasonable temperatures

• Simple construction and compactness enables use of corrosion-resistant alloys

• Low cost• Low hold-up• Small floor space

Disadvantages:

• High head room• Not suitable for scaling or salting

liquids• Poor heat-transfer coefficients at lower

temperaturesDifficulties:

• Sensitivity to changes in operating conditions

Horizontal Tube Evaporator

V SG

CF

Description:

The evaporating liquid is on the shell side and the heating medium on the tube side. This evaporator is mainly used for boiler feedwater. It has low entrainment and can be designed for high steam and vapor temperatures and pres-sures. Tubes can be designed so that they de-form when shocked (sprayed with cold water while still heated with steam), which causes the scale to crack off, making this evaporator suitable for severe scaling applications, such as hard water.

Applications:

• Boiler feedwater• Severely scaling liquids (bent-tube type)

Advantages:

• Large vapor-liquid disengaging area• Good heat-transfer coefficients• Semiautomatic descaling (bent-tube

type)• Low cost (straight-tube type)• Minimal head room required

Disadvantages:

• Not suitable for salting liquids• Not suitable for scaling liquids

(straight-tube type)• High cost (bent-tube type)• Typically small capacity


56 NCEES


Wiped Film (Agitated Film) Evaporator

S

FV

C

P

BLADES

Description:

The liquid is spread on the tube wall by a rotating assembly of blades that maintain close clearance from the wall or ride on the film. The heating surface is one large-diameter tube that may be straight or tapered, horizontal or vertical. The expensive construction limits application to the most difficult materials.

Applications:

• Extremely viscous materials• Heat-sensitive materials in which

exposure to high temperature must be minimized

Advantages:

• Very short residence time• Ability to handle extremely viscous

materials• High feed-to-product ratios without

need for recirculationDisadvantages:

• Low heat-transfer coefficients• High installation costs• High operating costs

Submerged Combustion Evaporator

V + G

P

F

Description:

Heat transfer is provided by bubbling com-bustion gases through the liquid; thus no heat-transfer surfaces are used. The evapora-tor consists of a tank holding the liquid, a burner, and a gas distributor. The vapor from the evaporation is mixed with the combustion gases, making it impossible to recover the heat from the vapor.

Applications:

• Highly corrosive solutions• Severely scaling liquids

Advantages:

• No surface on which scale can form• Use of special alloys or nonmetallic

materials is possibleDisadvantages:

• High entrainment losses• No heat recovery from the vapor,

resulting in high fuel costs• Cannot control crystal size in crystal-

lization applications

Source of first 5 schematics: Robert H. Perry and Cecil H. Chilton, Chemical Engineer's Handbook, 5th ed., New York: McGraw-Hill, 1973, Figure 11-16.

Source of Wiped Film Evaporator schematic: www.cherd.ichemejournals.com/cms/attachment/ 2020819194/2041009035/gr1.jpg.

Source of Combustion Evaporator schematic: www.china-ogpe.com/buyingguide_content/ Submerged_combustion_evaporator__1307.html

Heat-Transfer Calculations for Evaporators

While the general heat-transfer equations apply, evaporators have some special considerations:

Heat-transfer coefficient: Depends strongly on the temperature difference.

Heat-transfer area: Surface area through which the heat transfer takes place, measured on the liquid side.


NCEES 57

Apparent temperature difference: The temperature difference can be difficult to determine because it varies along the length of the evaporator tubes. The apparent temperature difference is calculated as the difference between the heating-medium and boiling-liquid temperatures. Heating-medium temperature is the saturation temperature of the steam at steam pressure. (Superheat or subcooling are not considered.) Boiling-liquid temperature is the saturation temperature of the liquid at vapor head pressure—thus assuming a negligible boiling-point rise.

Temperature corrected for boiling-point rise: Boiling-point rise is the difference between the boiling point of the solution and the boiling point of the pure solvent at the same pressure. The temperature corrected for the boiling-point rise is the apparent temperature difference minus the boiling-point rise. This is typically used as the basis for the calculation of heat-transfer coefficients and also as a basis for comparing efficiencies of different evaporator types.

Multi-Effect Evaporators

Multi-effect evaporators reduce the energy needed for evaporation by using the steam generated in one stage as the heating medium for another stage.

The temperature difference for heat transfer in each effect is:

T T T, ,cond steam evap liquidD = −

where the condensation temperature of the steam is determined by the pressure in the effect where the steam was generated:

atT T P,cond steam sat n 1= −

The evaporation temperature of the liquid is determined by the pressure in the current effect:

atT T P,evap liquid sat n=

Different feed arrangements are common:

1. In the forward feed configuration, the product and vapor flow are parallel. This configuration is used when the feed is near the boiling point or when the product is heat-sensitive or prone to scaling and requires low temperature differences. One additional advantage is that flow of the product from one effect can be achieved by pressure difference alone, so that no intermediate liquor pumps are needed.

Forward Feed Configuration

VAPOR TOCONDENSER

THICKLIQUOR

FEED

CONDENSATE

STEAM

I I I I I I I V

Source: McCabe, Smith, Harriott, Unit Operations of Chemical Engineering, New York: McGraw-Hill, 1993, Figure 16-10.


58 NCEES

2. In the backward feed configuration, the product and vapor flow are countercurrent. It is used when the feed is cold, because most of the feed preheating is done by the vapor generated in the previous effect. It is pre-ferred for highly viscous liquor, because the temperature in the effect will be higher as the liquor becomes more concentrated.

Backward Feed Configuration

VAPOR TOCONDENSER

CONDENSATE

STEAM

THICK LIQUOR FEED

I I I I I I I V

Source: McCabe, Smith, Harriott, Unit Operations of Chemical Engineering, New York: McGraw-Hill, 1993, p. 485.

2.3.1.6 InsulationHeat loss from cylindrical, insulated pipe:

( )

lnQ

rr

h rk

k L T T2ins

ins

12

1

2

r=+

−

3

3o

d n

Surface temperature of the insulation:

ln

lnT

kh r

rr

T T kh r

rr

12

212

12

12

=+

+

3

33

d

d

n

n

Critical insulation radius (where heat loss is at a minimum): ddrQ

02

=o

r h

k, crit

ins2 =

3

1 ln

2 ( )Q

h rk

k L T Tmin

1

ins 1

ins

r=+

−

3

3o

e o

ln

lnT

h rk

T T h rk

1, crit

ins

ins

2

1

11=

+

+

3

33

e

e

o

o


NCEES 59

where

T1 = surface temperature of the pipe

T2 = surface temperature of the insulation

T∞ = temperature of surroundings

r1 = outer radius of the pipe

r2 = outer radius of the insulation

kins = thermal conductivity of the insulation

h∞ = convective heat-transfer coefficient for the surroundings

2.3.2 Heat-Exchange Equipment Analysis

2.3.2.1 Pressure Drop

Single-Phase Heat Transfer

Tube-side pressure drop for a shell-and-tube exchanger (including pressure drop in the tubes, in the heads for a multipass exchanger, and at the inlet and outlet nozzles):

. .P n f D

L u1 5 2 2 5 2tubeside

w

tm 2

nn t

D = + +c dm n> H* 4where

ut = velocity in the tubes

f = Moody friction factor

m = 0.25 for laminar flow (Re < 2,100)

m = 0.14 for turbulent flow (Re > 2,100)

Condensation

Surface temperature for the condensation of a superheated vapor:

T T T hU1surface coolant vapor= + −c m

where

h = sensible heat-transfer coefficient for the vapor

U = overall heat-transfer coefficient, based on h

Condensation only occurs if T Tsurface sat# .


60 NCEES

Evaporation

In rising film evaporators, the pressure drop in the tubes is comprised of frictional pressure drop and acceleration pressure drop from the increased velocity of the flow due to volume change during evaporation. If the inlet flow is liquid, the acceleration pressure drop is calculated from:

gP y Am 1 1 1

a cross vap liq c

2

t tD = −od dn nwhere

DPa = acceleration pressure drop

y = vapor fraction (by weight)

Across = cross-sectional area of the tube

2.3.2.2 Performance Evaluations (Number of Thermal Transfer Units)

Heat-Exchanger Effectiveness (e):

maximum possible heat transfer rateactual heat transfer rate

( )( )

( )( )

QQ

C T TC T T

C T TC T T

, ,

, ,

, ,

, ,

max

min minhot in cold in

hot hot in hot out

hot in cold in

cold cold out cold in

f

f

= = −−

= −−

= −−

o

o

Chot = Cmin Ccold = Cmin

T TT T

, ,

, ,hot

hot in cold in

hot in hot outf = −

−T T

T T, ,

, ,cold

hot in cold in

cold out cold inf = −

−

Heat-capacity rate is C:

C mcp= o

Cmin = smaller of Chot and Ccold

Cmax = larger of Chot and Ccold

Ratio of heat-capacity rates is C{ :

C CCmax

min={

where

C0 1# #{

C 0={ for exchangers with phase change (condensation or evaporation)

Number of Transfer Units (NTU)

NTU C

U Amin

=


NCEES 61

Heat-Exchanger Effectiveness and NTU RelationsFlow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution

Double Pipe

Co-Current

e ( )expC

NTU C1

1 1f =

+− − +

{

{8 B

NTU ( )lnNTU C

C11 1f

=+

− − +{

{8 B

1.0 0.00

0.25

0.500.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3

NTU

4 5

C

TUBEFLUID

SHELL FLUID

Countercurrent

e( )( )

expexpC NTU C

NTU C1 11 1

f =− − −

− − −{ {

{88

BB

:C NTUNTU1 1f= = +

{

NTU lnNTU C C11

11

ff=

− −−

{ {d n :C NTU1 1 ff= = −

{

1.0

0.000.250.500.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3

NTU

4 5

C

TUBEFLUID

SHELL FLUID


62 NCEES

Heat-Exchanger Effectiveness and NTU Relations (cont'd)Flow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution

Cross-Flow

Both Fluids, Unmixed

eNTU( )exp exp

CNTU C1 1

.

.

0 22

0 78f = −

− −− {

{> H

1.0

0.000.250.500.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3 4 5NTU

C

COLD FLUID

HOTFLUID

Both Fluids, Mixed

e ( ) ( )exp expNTU NTU CC

NTU1

11

11

f = − − +− −

−{{

1.0 0.00

0.25

0.500.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3NTU

4 5

C

COLD FLUID

HOTFLUID


NCEES 63


Cmax Mixed Cmin Unmixed

e ( )exp expC C NTU1 1 1f = − − − −{{8 B% /

NTU ( )ln lnNTU C C1 1 1 f= − + −{{< F

1.0 0.000.25

0.500.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3NTU

4 5

C

MIXEDFLUID

C

C

min

max

UNMIXEDFLUID

Cmax Unmixed Cmin Mixed

e ( )exp expC NTU C1 1 1f = − − − −{{8 B( 2

NTU ( )lnNTU C C1 1 1 f= − + −{{8 B

1.0 0.000.250.50

0.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3NTU

4 5

C Cmin

Cmax

MIXED FLUID

UNMIXEDFLUID


64 NCEES


Shell-and-Tube

One shell pass; 2, 4, 6 tube passes

eexp

expC C

NTU C

NTU C2 1 11 1

1 12

2

f = + + +− − +

+ − +{ {

{

{``

jj

NTU lnNTUC C C

C C

11

2 1 1

2 1 1

f

f= −+ − − + +

− − − +{ { {

{ {R

T

SSSSSSSS

V

X

WWWWWWWW

1.0 0.00

0.250.500.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3NTU

4 5

C

TUBE FLUID

SHELL FLUID

Two shell passes; 2, 4, 6 tube passes

1.0 0.000.250.500.751.00

0.8

0.6

0.4

0.2

0.0

0 1 2 3NTU

4 5

C

SHELL FLUID

TUBE FLUID


NCEES 65


All Exchangers With Evaporation and Condensation

C 0={

e ( )exp NTU1f = − −

NTU ( )lnNTU 1 f= − −

1.0

0.8

0.6

0.4

0.2

0.0

0 1 2 3 4 5

= ø

NTU

C

2.4 Tables and Graphs

2.4.1 Tables of Heat-Transfer Data

2.4.1.1 Heat Capacity

Typical Ranges of Heat Capacity at Ambient Temperatures

Material lbm FBtu

-c kg KkJ:

Gases at 1 atm 0.15–1 0.60–4Nonorganic liquids 0.50–1.20 2–5Organic liquids 0.25–0.75 1–3Solid nonmetals 0.20–0.50 0.80–2Metals 0.03–0.20 0.12–0.80

2.4.1.2 Thermal Conductivity

Typical Ranges of Thermal Conductivity

Material hr ft FBtu

-- c m KW:

Gases at 1 atm 0.004–0.10 0.007–0.17Insulators 0.02–0.12 0.03–0.21Nonmetallic liquids 0.05–0.40 0.09–0.70Nonmetallic solids 0.02–1.50 0.03–2.60Liquid metals 5–45 8.7–78Metallic alloys 8–70 14–120Pure metals 30–240 52–420


66 NCEES

Heat-Transfer Properties of Building and Insulating Materials (U.S. Units)

MaterialsDensity

ftlbm

3

Heat Capacity

-lbm FBtuc

TemperatureFc

Thermal Conductivity

- -hr ft FBtuc

Asbestos 36 0.183

–300 0.055–100 0.082

32 0.088200 0.111800 0.130

Brick (building) 94 0.199 — 0.416Brick (fireclay) 165 0.229 — 0.578

Calcium silicate — —100 0.033400 0.046600 0.060

Cardboard (corrugated) — — 68 0.037

Cellular glass — —100 0.030600 0.073

Clay 91 100 0.751Concrete 144 0.270 68 0.739Cork 8 68 0.025Cotton 6 0.311 68 0.028Diatomaceous earth 10.6 — 100 0.026

Fiberglass — —100 0.026300 0.034

Glass (window) 156 0.160 68 0.430Gypsum 30 68 0.045

Kaolin firebrick 19 —400 0.050

1400 0.1102100 0.260

Leather 62 — 86 0.092

Magnesia (85%) 17 —100 0.034400 0.044

Mineral wool 10 —100 0.030600 0.057

Plywood 34 — 68 0.069Rubber 72 0.332 68 0.116Rubber, foam 4.4 68 0.017Sand 95 0.420 68 0.191Sawdust 12 68 0.034Urethane foam 4.4 0.251 100 0.016Wood (oak—with the grain)

48 0.56868 0.210

Wood (oak—against the grain) 68 0.120


NCEES 67

Heat-Transfer Properties of Building and Insulating Materials (U.S. Units) (cont'd)

MaterialDensity

ftlbm

3

Heat Capacity

lbm FBtu

-c

TemperatureFc


hr ft FBtu- -c

Wood (pine—with the grain)33 0.657

68 0.148Wood (pine—across the grain) 68 0.062Wool 8.5 — 100 0.027

Heat-Transfer Properties of Building and Insulating Materials (SI Units)

MaterialsDensity

mkg

3

Heat Capacity

kg KW:

TemperatureCc


m KW:

Asbestos 577 765

–200 0.094–75 0.142

0 0.152100 0.192420 0.225

Brick (building) 1500 835 — 0.720Brick (fireclay) 2640 960 — 1.000

Calcium silicate — —40 0.057

200 0.080320 0.104

Cardboard (corrugated) — — 20 0.064

Cellular glass — —40 0.052

320 0.126Clay 1460 — 40 1.300Concrete 2300 1130 20 1.279Cork 128 — 20 0.043Cotton 96 1300 20 0.048Diatomaceous earth 170 — 40 0.045

Fiberglass — —40 0.045

150 0.059Glass (window) 2500 670 20 0.744Gypsum 481 — 20 0.078

Kaolin firebrick 304 —200 0.087750 0.190

1150 0.450Leather 1000 — 30 0.159

Magnesia (85%) 272 —40 0.059

200 0.076

Mineral wool 160 —40 0.052

320 0.099Plywood 540 — 20 0.120


68 NCEES

Heat-Transfer Properties of Building and Insulating Materials (SI Units) (cont'd)

MaterialsDensity

mkg

3

Heat Capacity

kg KW:

TemperatureCc


m KW:

Rubber 1150 1392 20 0.200Rubber, foam 70 — 20 0.030Sand 1522 1759 20 0.330Saw dust 192 — 20 0.059Urethane foam 70 1050 40 0.028Wood (oak—with the grain) 770 2380 20 0.363Wood (oak—against the grain) — 20 0.207Wood (pine—with the grain) 525 2750 20 0.256Wood (pine—across the grain) — 20 0.107Wool 136 — 40 0.047

2.4.1.3 Heat-Transfer Coefficients (Film Coefficients, h)

Typical Values of Heat-Transfer Coefficients Without Phase Change

System Description hr ft FBtu- -2 c m K

W2 :

Air and gas (free convection) 0.2–4 1–20Air and gas (flowing—low pressure) 2–20 10–100Air and gas (flowing—high pressure) 20–60 100–360Liquid (free convection) 10–175 50–1000Oils and heavy organics (flowing) 35–200 200–1200Molten salts and brines 100–200 500–1000Heat-transfer fluids and refrigerants 175–450 1000–2700Water (flowing) 150–450 900–2700

Typical Values of Heat-Transfer Coefficients With Phase Change

System Descriptionhr ft FBtu- -2 c m K

W2 :

CondensationCondensing organic vapors 150–250 850–1500Condensing ammonia 500–800 2800–4500Condensing steam 700–900 4000–5000BoilingBoiling organics 125–250 700–1500Boiling ammonia 200–350 1100–2000Boiling water 280–500 1600–2800


NCEES 69

2.4.1.4 Overall Heat-Transfer Coefficients (U)

Typical Overall Heat-Transfer Coefficients for Building Applications

Building Componenthr ft FBtu- -2 c m K

W2 :

Brick wall, uninsulated 0.45 2.55Frame wall, uninsulated 0.25 1.42Frame wall, with Rockwool 0.07 0.4Single-pane glass window 1.1 6.2Double-pane glass window 0.4 2.3

Typical Overall Heat-Transfer Coefficients for Air Coolers

System hr ft FBtu- -2 c m K

W2 :

Finned air cooler/condensing steam 5–50 30–300Finned air cooler/water 4–10 25–60Air cooler (fin-fan)/water 50–80 300–450Air cooler (fin-fan)/light organics 50–125 300–700Air cooler (fin-fan)/heavy organics 12–25 70–150Air cooler (fin-fan)/condensing hydrocarbons 50–100 300–600Air cooler (fin-fan)/condensing ammonia 110 650Air cooler (fin-fan)/condensing Freon 70 400Air cooler (fin-fan)/gas <5–10 bar/60–130 psig 10–20 60–120Air cooler (fin-fan)/gas >10–30 bar/130–420 psig 20–50 100–300


70 NCEES

Typical Overall Heat-Transfer Coefficients in Exchangers Without Phase Change (Shell-and-Tube Exchangers)


W2 :

Gas/gas 2–10 10–50Water or brine/compressed gas 10–30 60–200Water/hydrogen with natural gas 80–125 450–700Water/brine 100–200 600–1200Water/water 150–300 850–1700Water/alcohol, organic solvents 50–150 280–850Water/gasoline 60–90 340–510Water/gas oil, distillate 35–60 200–340Water/heavy oil 10–50 60–300Freon or ammonia/water 40–90 220–510Light organics/light organics 40–75 220–425Medium organics/medium organics 20–60 110–340Heavy organics/heavy organics 10–40 57–220Heavy organics/light organics 10–60 57–340Crude oil/gas oil 30–55 170–310

Typical Overall Heat-Transfer Coefficients in Water-Cooled Condensers (Shell-and-Tube Exchangers)

Condensing Fluid hr ft FBtu- -2 c m K

W2 :

Alcohol vapors 45–125 250–700Ammonia vapors 150–250 850–1400Freon vapors 45–150 250–850Aqueous vapors 200–1000 1100–5600Condensing oil 40–100 220–570Organic vapors 125–175 700–1000Organic vapors with noncondensables 90–125 500–700Vacuum condensers 35–90 200–500

Typical Overall Heat-Transfer Coefficients in Heaters With Condensing Steam (Shell-and-Tube Exchangers)

Heated Fluid hr ft FBtu- -2 c m K

W2 :

Gas 5–50 30–300Heavy oil 10–50 60–300Light oil 35–100 200–600Kerosene/gasoline 50–200 300–1100Organic Solvents 90–175 500–1000Water 250–700 1500–4000


NCEES 71

Typical Overall Heat-Transfer Coefficients for Immersed Heating Coils

Immersed Coils hr ft FBtu- -2 c m K

W2 :

Pool Liquid Heating Medium

Natural convection Agitated Natural

convection Agitated

Dilute aq. solution Steam 100–200 130–275 500–1000 700–1600Light oil Steam 35–50 50–100 200–300 300–600Heavy oil Steam 15–30 50–70 90–170 300–400Molten sulfur Steam 20–35 35–45 100–200 200–250Molasses/corn syrup Steam 15–30 60–80 70–170 350–450Aqueous solution Water 70–100 110–160 400–600 400–650Light oil Water 20–25 35–50 100–150 200–300

Typical Overall Heat-Transfer Coefficients for Plate ExchangersPlate Exchangers

hr ft FBtu- -2 c m K

W2 :Hot Fluid Cold Fluid

Light organic Light organic 450–900 2500–5000Light organic Viscous organic 45–90 250–500Viscous organic Viscous organic 20–35 100–200Light organic Process water 450–600 2500–3500Viscous organic Process water 45–90 250–500Light organic Cooling water 350–800 2000–4500Viscous organic Cooling water 45–80 250–450Condensing steam Light organic 450–600 2500–3500Condensing steam Viscous organic 45–90 250–500Process water Process water 900–1300 5000–7500Process water Cooling water 90–1200 500–7000Dilute aqueous solutions Cooling water 900–1200 5000–7000

Condensing steam Process water 600–800 3500–4500

Typical Overall Heat-Transfer Coefficients in Evaporators


W2 :

Agitated filmNewtonian liquid, m = 1 cP 400 2000Newtonian liquid, m = 100 cP 300 1500Newtonian liquid, m = 10,000 cP 120 700Vertical long tubeNatural circulation 200–600 1000–3500Forced circulation 400–1000 2000–6000


72 NCEES

Representative Values for Fouling FactorsValues for /F C125 50# c c , unless specified otherwise

Material / , , )1 ( 1tC dd P EG z n#- -c m

Wm K2 :

Seawater, brine, salt water 0.0005 0.00009Seawater, brine, salt water (> 125°F/50°C) 0.0010 0.00018River water (brackish) 0.0020 0.00035River water (muddy, silty) 0.0030 0.00053Hard water 0.0033 0.00059City/well water 0.0010 0.00018Untreated boiler feedwater (> 125°F/50°C) 0.0010 0.00018Treated boiler feedwater 0.0010 0.00018Untreated cooling tower water 0.0020 0.00035Treated cooling tower water 0.0010 0.00018Distilled water 0.0005 0.00009Fuel oil 0.0050 0.00088Asphalt and residue 0.0100 0.00176Vegetable oil and heavy gas oil 0.0030 0.00054Light hydrocarbons 0.0010 0.00018Heavy hydrocarbons 0.0040 0.00072Quenching liquids 0.0040 0.00070Refrigerating liquids, brines 0.0010 0.00018Heat-transfer media 0.0010 0.00018Polymer forming liquids 0.0050 0.00090Vaporizing liquids (organic and inorganic) 0.0020 0.00035Condensing organic liquids 0.0010 0.00018Steam (clean) 0.0005 0.00009Steam (oil-bearing) 0.0010 0.00018Organic vapors and liquids (including condensing) 0.0010 0.00018Alcohol vapors 0.0005 0.00009Industrial air or other dirty (oil-bearing) gases 0.0020 0.00035Diesel exhaust (> 125°F/50°C) 0.0100 0.00176


NCEES 73

2.4.1.5 Nucleate Boiling Heat-Transfer Data

Relative Magnitude of Nucleate Boiling Heat-Transfer Coefficients at 1 atm, Referenced to Value for Water

Fluid hhwater

Water 1.0Water with 20% sugar 0.87Water with 10% Na2SO4 0.94Water with 26% glycerin 0.83Water with 55% glycerin 0.75Water with 24% NaCl 0.61Isopropanol 0.70Methanol 0.53Toluene 0.36Carbon-tetrachloride 0.35n-Butanol 0.32

Source: Holman, J.P., Heat Transfer, New York: McGraw-Hill,1981, p. 430.

Maximum Heat Flux in Nucleate Boiling (Burnout Heat Flux)

Fluid SurfaceHeat Flux

-hr ftBtu 102

3# -DT°F

Heat Flux

mkW

2

DT°C

WaterCopper 200–270 620–850Chrome-plated copper 300–400 42–50 940–1260 23–28Steel 410 54 1290 30

BenzeneCopper 43.5 — 130 —Aluminum 50.5 — 160 —

Propanol Nickel-plated copper 67–110 76–90 210–340 42–50Butanol Nickel-plated copper 79–105 60–70 250–330 33–39

EthanolAluminum 55 — 170 —Copper 80.5 — 250 —

MethanolCopper 125 — 390 —Chrome-plated copper 111 — 350 —Steel 125 — 390 —

Liquid H2 Any metal surface 9.53 4 30 2Liquid N2 Any metal surface 31.7 20 100 11Liquid O2 Any metal surface 47.5 20 150 11

Source: Holman, J.P., Heat Transfer, New York: McGraw-Hill,1981, p. 431.


74 NCEES

2.4.1.6 Solar Radiation Data

Maximum Expected Solar Radiation at Various North Latitudes

Monthhr ftBtu

2 mW

2

30° North 40° North 45° North 30° North 40° North 45° North24-hr avg. noon 24-hr

avg. noon 24-hr avg. noon 24-hr

avg. noon 24-hr avg. noon 24-hr

avg. noon

January 65 240 40 170 30 135 205 757 126 536 95 426February 75 270 55 210 45 175 237 852 174 662 142 552March 90 305 75 255 65 230 284 962 237 804 205 726April 110 340 95 300 90 280 347 1073 300 946 284 883May 120 360 120 335 115 320 379 1136 379 1057 363 1009June 130 365 130 345 130 335 410 1151 410 1088 410 1057July 130 365 130 350 130 340 410 1151 410 1104 410 1073August 125 360 125 340 120 325 394 1136 394 1073 379 1025September 115 350 105 315 100 300 363 1104 331 994 315 946October 100 315 80 270 75 245 315 994 252 852 237 773November 80 270 60 215 50 185 252 852 189 678 158 584December 65 240 45 175 35 140 205 757 142 552 110 442

Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 7th ed., New York: McGraw-Hill, 1997, pp. 12-23.

2.4.1.7 Emissivity (f)

Emissivity of Building Materials at Ambient Temperature (Unless Specified Otherwise)

Material EmissivityAsbestos 0.96Brick (building) 0.93Brick (fireclay) at 2000°F/1100°C 0.75Enamel (white) 0.90Glass (smooth) 0.94Gypsum 0.90Marble 0.93Oak 0.90Oil 0.82Plaster 0.91Refractory (good radiator) at 1500°F/800°C 0.85Refractory (poor radiator) at 1500°F/800°C 0.70Roofing paper 0.91Rubber (grey, soft) 0.86Rubber (hard) 0.95Water 0.96


NCEES 75

Emissivity of Metals at Ambient and Elevated Temperatures

Material Emissivity at Ambient Temperatures

Emissivity at ~1000°F/540°C

Aluminum, polished 0.04 0.08Aluminum, anodized 0.94 0.60Aluminum, surface roofing 0.22 —Brass, polished 0.10 —Brass, oxidized 0.61 —Chromium, polished 0.08 0.26Copper, polished 0.02 0.18Copper, oxidized 0.78 0.77Gold, polished 0.02 0.04Iron, polished 0.06 0.13Iron, cast, oxidized 0.63 0.76Iron, galvanized 0.25 0.6Iron, oxide 0.90 0.85Magnesium 0.07 0.18Stainless steel, polished 0.15 0.22Stainless steel, weathered 0.85 0.85Tungsten 0.03 0.10Zinc, polished 0.05 0.04Zinc, galvanized 0.25 —


76 NCEES

2.4.2 Charts with Heat-Transfer Data

Overall Heat-Transfer Coefficients for Various Applications (U.S. Units): hr ft FBtu- -2 c

CONDENSATIONAQUEOUS VAPOURS

BOILING AQUEOUS

DILUTE AQUEOUSBOILING ORGANICS

CONDENSATION ORGANIC VAPORS

PARAFFINSHEAVY ORGANICS

MOLTEN SALTS

RESIDUE

BRINESAIR

AND GAS

COOLING TOWER WATER SERVICE FLUID COEFFICIENT, Btuft2 °F hr

THERMAL FUID

CONDENSATE STEAM CONDENSINGHOT HEATTRANSFER OIL

RIVER, WELL,SEAWATER

ESTIMATED OVERALL COEFFICIENT, U,

PROCESS FLUID COEFFICIENT, U

,

BOILINGWATER

REFRIGERANTS

AIR AND GASLOW PRESSURE

OILS

100

AIR AND GASHIGH PRESSURE

Btuft2 °F hr

Btu

ft2 °F hr

200 300 400 500 600 700 800 900

100

200

300

400

500

600

100

150

50

200

250

300

350

400

Source: Towler, Sinnot. Chemical Engineering Design. Oxford: Butterworth-Heinermann: 2013, p. 1052, Figure 19.1. (Converted to U.S. units)

Overall Heat-Transfer Coefficients for Various Applications (SI Units): m KW2 :

CONDENSATIONAQUEOUS VAPOURS

BOILING AQUEOUS

DILUTE AQUEOUSBOILING ORGANICS

CONDENSATION ORGANIC VAPORS

PARAFFINSHEAVY ORGANICS

MOLTEN SALTS

RESIDUE

BRINESAIR

AND GAS

1000 1500 25002000 35003000 45004000

500

250

500

750

1000

1250

1500

1750

2000

2250

COOLING TOWER WATER SERVICE FLUID COEFFICIENT, W/m2°K

THERMAL FUID

CONDENSATE STEAM CONDENSINGHOT HEATTRANSFER OIL

RIVER, WELL,SEAWATER

ESTIMATED OVERALL COEFFICIENT, U, W/m2 °K

PROCESS FLUID COEFFICIENT, U

, W/m

2 °K

BOILINGWATER

REFRIGERANTS

AIR AND GASLOW PRESSURE

OILSAIR AND GAS

HIGH PRESSURE500

1000

1500

2000

2500

Source: Towler, Sinnot. Chemical Engineering Design. Oxford: Butterworth-Heinermann: 2013, p. 1052, Figure 19.1.


NCEES 77

2.4.3 Heat-Exchanger Design Information

TEMA Heat Exchanger Types

FRONT-ENDSTATIONARY HEAD TYPES SHELL TYPES REAR-END

HEAD TYPES

FIXED TUBE SHEETLIKE "A" STATIONARY HEADONE-PASS SHELL

PASS SHELLWITH LONGITUDINAL BAFFLE

DOUBLE SPLIT FLOW

DIVIDED FLOW

KETTLE-TYPE REBOILER

CROSS FLOWSPECIAL HIGH-PRESSURE CLOSURE

CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER

CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER

BONNET (INTEGRAL COVER)

CHANNELAND REMOVABLE COVER

REMOVABLETUBE

BUNDLEONLY

SPLIT FLOW

FIXED TUBE SHEETLIKE "B" STATIONARY HEAD

FIXED TUBE SHEETLIKE ''N" STATIONARY HEAD

OUTSIDE PACKED FLOATING HEAD

FLOATING HEADWITH BACKING DEVICE

PULL-THROUGH FLOATING HEAD

U-TUBE BUNDLE

EXTERNALLY SEALEDFLOATING TUBE SHEET

AE

F

G

H

J

K

X

L

M

N

P

S

T

U

W

B

C

N

D


78 NCEES

2.4.4 F-Factor Charts1.0 0.9 0.8

F = MTD CORRECTION FACTOR

0.7 0.6 0.50

0.10.2

0.30.4

0.5P

= TEM

PERA

TURE

EFF

ICIE

NCY

MTD

CORR

ECTI

ON FA

CTOR

1 SHE

LL P

ASS

2 OR

MORE

TUB

E PA

SSES

T 2

T 1

T 1P

=––

t 1

t 1

t 2

t 2t 1

F-FACTORS CHARTS

0.60.7

0.80.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.5

1.6

2.0

3.0

4.0

6.0

8.0

15.020.0

R = 10.0

2.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.5

1.6

2.0

3.0

4.0

6.0

8.0

15.020.0

R = 10.0

2.5

1.0

T 2R

=––

t 1T 1

T 2F

ΔΔ =

t LOG

t M


NCEES 79

1.0 0.9 0.8


0.7 0.6 0.50

0.10.2

0.30.4

0.5P

= TEM

PERA

TURE

EFF

ICIE

NCY

MTD

CORR

ECTI

ON FA

CTOR

2 SHE

LL P

ASS

4 OR

MORE

TUB

E PA

SSES

T 2

T 1

T 1P

=––

t 1t 1

t 2

t 2t 1

F-FACTORS CHARTS

0.60.7

0.80.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.8

1.6

2.0

3.0

4.0

6.0

8.0

15.020.0

R = 10.0

2.6

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.8

1.6

2.0

3.0

4.0

6.0

8.0

15.020.0

R = 10.0

2.61.0

T 2R

FΔ

Δ=

=––

t 1t L

OGt M

T 1T 2


80 NCEES

1.0 0.9 0.8


0.7 0.6 0.50

0.10.2

0.30.4

0.5P

= TEM

PERA

TURE

EFF

ICIE

NCY

MTD

CORR

ECTI

ON FA

CTOR

3 SHE

LL P

ASSE

S6 O

R MO

RE T

UBE

PASS

ES

T 2

T 1

T 1P

=––

t 1t 1

t 2

t 2t 1

0.60.7

0.80.9

0.2

2.0

8.0

15.020.0

R = 10.0

2.5

0.2

0.40.4

0.60.6

0.80.8

1.01.0

1.21.2

1.41.4

1.81.8

1.61.6

2.0

3.03.0

5.05.0

4.04.0

8.0

15.020.0

R = 10.0

2.5

1.0

T 2R

FΔ

Δ=

=––

t 1t L

OGt M

T 1T 2


NCEES 81

1.0 0.9 0.8


0.7 0.6 0.50

0.1

4SH

ELLS

0.20.3

0.40.5

P = T

EMPE

RATU

RE E

FFIC

IENC

Y

MTD

CORR

ECTI

ON FA

CTOR

4 SHE

LL P

ASSE

S8 O

R MO

RE T

UBE

PASS

ES

T 2T 1

T 1P

=––

t 1t 1

t 2

t 2t 1

0.60.7

0.80.9

2.0

8.0

15.020.0

R = 10.0

2.5

0.20.2

0.40.4

0.60.6

0.80.8

1.01.0

1.21.2

1.41.4

1.81.8

1.61.6

2.0

3.03.0

6.06.0

4.04.0

8.0

15.020.0

R = 10.0

2.51.0

T 2R

FΔ

Δ=

=––

t 1t L

OGt M

T 1T 2


82 NCEES

1.0 0.9 0.8


0.7 0.6 0.50

0.1

5SH

ELLS

0.20.3

0.40.5

P = T

EMPE

RATU

RE E

FFIC

IENC

Y

MTD

CORR

ECTI

ON FA

CTOR

5 SHE

LL P

ASSE

S10

OR

MORE

TUB

E PA

SSES

T 2

T 1

T 1P

=––

t 1t 1

t 2

t 2t 1

0.60.7

0.80.9

2.0

8.0

15.020.0

R = 10.0

2.5

0.20.20.40.4

0.60.6

0.80.8

1.01.0

1.21.2

1.41.4

1.81.8

1.61.6

2.0

3.03.0

6.06.0

4.04.0

8.0

15.020.0

R = 10.0

2.5

1.0

T 2R

FΔ

Δ=

=––

t 1t L

OGt M

T 1T 2


NCEES 83

1.0 0.9 0.8


0.7 0.6 0.50

0.1

6SH

ELLS

0.20.3

0.40.5

P = T

EMPE

RATU

RE E

FFIC

IENC

Y

MTD

CORR

ECTI

ON FA

CTOR

6 SHE

LL P

ASSE

S12

OR

MORE

TUB

E PA

SSES

T 2T 1

T 1P

=––

t 1t 1

t 2

t 2t 1

0.60.7

0.80.9

1.0

T 2R

FΔ

Δ=

=––

t 1t L

OGt M

T 1T 2

2.0

8.0

15.0R = 20.0

10.0

2.5

0.20.20.40.4

0.60.6

0.80.8

1.01.0

1.21.2

1.41.4

1.81.8

1.61.6

2.0

3.03.0

6.06.0

4.04.0

8.0

15.0R = 20.0

10.0

2.5


84 NCEES

1.0


0.9 0.8 0.7

00.1

0.20.3

0.40.5

P = T

EMPE

RATU

RE E

FFIC

IENC

Y

MTD

CORR

ECTI

ON FA

CTOR

1 DIV

IDED

FLO

W S

HELL

PAS

S2 O

R MO

RE T

UBE

PASS

ES

T 2

T 1T 1

T 1P

=––

t 1

t 1

t 2

t 2t 1

0.60.7

0.80.9

1.0

T 2R

FΔ

Δ=

=––

t 1t L

OGt M

T 1T 2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

2.5

3.0

5.0

6.0

8.0

15.020.0

R = 10.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.4

1.6

1.8

2.0

2.5

3.0

5.0

6.0

8.0

15.020.0

R = 10.0

85

3 KINETICS



CA or [A] Concentration of component Aft

lb mole3 liter

mol

FA Molar feed of A slb moleec s

mol

g rDV Gibbs free energy of reaction (molar) lb moleBtu

molJ

hrDt Heat of reaction lb mole

BtumolJ

K Equilibrium constant varies varies

k Reaction rate constantsecft

lb mole n

3

1-

d^n

h

slitermol n1-c

^m

h

M Molar ratio of initial reactant concentrations dimensionless

n Moles of reactant or product lb mole g mol

n Reaction order dimensionless

P Pressure (PA = partial pressure of A) inlbf2 Pascal

rA Rate of reaction – based on component Aft seclb mole-3 L s

g mol:

SAB Selectivity to A relative to B dimensionless

SV Space velocity = space time1

sec1 1

sT Temperature °F or °R °C or K

t Time sec s


86 NCEES

Symbols (con't)Symbol Description Units (U.S.) Units (SI/metric)

V Reactor volume ft3 L

XA Fractional conversion of component A dimensionless

YA Yield of A relative to reactant use dimensionless

eAFractional volume change at full conversion of A dimensionless

x Space time = space velocity1 sec s

3.1.1 Reaction Parameters – NomenclatureA chemical reaction may be expressed by the general equation:

aA bB cC dD*+ +

The rate of reaction of any component is defined as the number of moles of that component formed per unit time per unit volume:

r V dtdn1

AA− = − (negative because A is consumed)

r dtdC

AA− = − if V is constant

The rate of reaction is frequently expressed as

, , ...r k f C CA B− =A _ iThe fractional conversion XA is defined as the moles of A reacted per mole of A fed:

X CC C

AAo

Ao A=−

if V is constant

3.1.2 Temperature DependenceThe Arrhenius equation gives the dependence of k on temperature:

k Ae R TEa

=−

where

A = pre-exponential or frequency factor

Ea = activation energy molJ or mol

calc mR = universal gas constant

For values of rate constant ki at two temperatures Ti:

lnET TRT T

kk

a1 2

1 2

2

1=−_ ei o or ln k

kRE

T TT Ta

2

1

1 2

1 2=−e o

Chapter 3: Kinetics

NCEES 87

3.1.3 Reaction OrderIf r k C CA A B

x y− = , then the reaction is x order with respect to A and y order with respect to B.

The overall order is n = x + y.

3.2 Rate Equations in Differential Form for Irreversible Reactions

3.2.1 Zero-Order A R( )"

r d t

d CC d t

d XkA

AAo

A− = − = = and d td X

CkA

Ao=

3.2.2 First-Order A R"^ h r d t

d CC d t

d XkCA

AAo

AA− = − = = and d t

d XCkC

k X1A

Ao

AA= = −_ i

3.2.3 Second-Order A R2 "^ h r d t

d CC d t

d XkCA

AAo

AA2− = − = = and d t

d XCkC

kC X1Ao

AAo

AA

22= = −_ i

3.2.4 Second-Order A bB R"+_ i r d t

d CkC CA

AA B− = − = k bC X M X1Ao A A

2= − −_ _i i when bM CC

1Ao

Bo !=

and

r k bC X1A Ao A2 2− = −_ i when M = 1

Integrated forms of these equations are presented in Section 3.5 for constant and variable volume batch, plug flow, and CSTR reactors.

3.3 Chemical Equilibrium Constants from Rate Constants for Reversible Reactions

3.3.1 Gaseous Phase ReactionsFor general reactions: aA bB cC dD*+ +

At equilibrium: r rFWD REV=

where

r k P PFWD Aa

Bb

1=

r k P PREV Cc

Dd

2=

The equilibrium constant is defined as

KP PP P

kk

PAa

Bb

Cc

Dd

2

1= =

LeChatelier's Principle describes the qualitative effect of pressure on equilibrium: For a gaseous reaction, increas-ing pressure will shift the equilibrium to the side of the reaction in the reaction equation with fewer moles.

Changes in pressure have negligible effect on liquid or solid phase reactions.


88 NCEES

3.3.2 Liquid Phase ReactionsGeneral reaction: aA bB cC dD*+ +

At equilibrium: r rFWD REV=

where

r k C CFWD Aa

Bb

1=

r k C CREV Cc

Dd

2=

The equilibrium constant is defined as

KC CC C

kk

cAa

Bb

Cc

Dd

2

1= =

When a + b = c + d, KP = Kc , and both are dimensionless.

When they are not equal:

KP has units of pressure to the power (c + d – a – b).

Kc has units of concentration to the power (c + d – a – b).

Thus:

KP = Kc (R T)(c+d-a-b)

3.3.3 Effect of Temperature on Chemical Equilibrium ConstantsThe change of the equilibrium constant with temperature is a function of the heat of reaction:

lnKd T

dRTh r2

D=^ h V

The integrated equation is

ln KK

R Th d T1 rT

1

22

1

2 D=Te oV#

Over a range where h rDV is nearly constant, this simplifies to:

ln KK

RhT T1 1r

1

22 1

D= − −d nV

3.3.4 Relationship Between Gibbs Free Energy and the Equilibrium Constant

ln lnorg RT K K RTg

rrD

D= − = −V V

Chapter 3: Kinetics

NCEES 89

3.4 Reactor Equations

3.4.1 Batch Reactor

Constant Volume

For a well-mixed, constant-volume batch reactor:

Cr d td C

d td X

AA

AoA− = − = and t C r

d XAo

A

AXA= −0#

Variable Volume

For a well-mixed, variable-volume batch reactor:

rX

Cd td X

1AA A

Ao A

f− =

+_ i and t Cr Xd X1Ao

A A A

XAA

f=

− +0 _ _i i#

where eA = fractional volume change at full conversion of A

3.4.2 Half-LifeThe half-life of a reaction, t

21 , is the batch time required to reach 50% conversion.

For r dtd C

kCAA

An− =− = t

21 occurs when C C2

1A Ao=

For n = 1 (first order) lnt k

221 =

For n 1=Y ( )

tn k C12 1

( )Aon

n

21 1

1=

−−

−

−

3.4.3 Flow Reactors, Steady State (Space Time, Space Velocity)For flow reactors, space time t is defined as the reactor volume divided by the inlet volumetric feed rate. Space velocity SV is the reciprocal of space time, that is, SV = 1/t.

3.4.3.1 Plug-Flow ReactorFor a plug-flow reactor, for all values of Af :

FC V

Cr

d XAo

Ao PFRAo

A

AXAx = =

−0 _ i#

where FAo = moles of A fed per unit time

For a constant volume plug-flow reactor ( 0Af = ):

rd C

A

A

C

C

Ao

Ax =− −#


90 NCEES

3.4.3.2 Continuous Stirred Tank Reactor (CSTR)For a well-mixed CSTR for all values of eA:

FC V

rC X

Ao

Ao CSTR

A

Ao Ax = =−_ i

where - rA is evaluated at exit stream conditions

For a constant volume CSTR ( 0Af = ):

rC C

A

Ao Ax =−−_ i

3.4.3.3 Continuous Stirred Tank Reactors in SeriesWith a first-order reaction A R" , with no change in volume:

NN reactors individualx x=−

kN

CC

1N reactorsA

AoN1

N

x = −- e o> H or CC

Nk

1A

Ao NN

N

x= +d n

where

N = number of CSTRs (equal volume) in series

CAN = concentration of A leaving the Nth CSTR

3.5 Integrated Reactor Equations for Irreversible Reactions

3.5.1 Zero-Order Reactions ,A R r kA" − =_ iConstant Volume

Batch reactor:

k t C X C CA A A A= = −q q

Plug-flow reactor or CSTR:

k C X C CA A A Ax = = −q q

Variable Volume

,V V X V V X1 A A A Af fD= + =q q_ i

Batch reactor:

ln lnk tC X C

VV1

AAo

A A AAo

of f f= + =_ i

Plug-flow reactor or CSTR:

k C XA Ax = q

Chapter 3: Kinetics

NCEES 91

3.5.2 First-Order Reactions ,A R r k CA A" − =_ i

Constant Volume

Batch reactor:

ln ln lnk t CC

X X11 1

A

Ao

AA= = − = − −_ i

Plug-flow reactor:

ln ln lnk CC

X X11 1

A

Ao

AAx = = − =− −_ i

CSTR:

k CC C

XX

1A

Ao A

A

Ax =−

= −

Variable Volume

,V V X V V X1 A A A Af fD= + =q q_ iBatch reactor:

ln ln lnk t X X VV

11 1 1

AA A of

D= − = − − = − −_ di n

Plug-flow reactor:

lnk X X1 1A A A Ax f f= − + − −_ _i iCSTR:

k XX X

11

A

A A Ax

f= −

+_ i

3.5.3 Second-Order Reactions ,A R r k C2 A A2" − =` j

Constant Volume

Batch reactor:

k t C C C XX1 11A Ao Ao A

A= − =−_ i or C

Ck tC11

Ao

A

Ao= +

Plug-flow reactor:

k C C C XX1 11A Ao Ao A

Ax = − =−_ i or C

Ck C11

Ao

A

Aox= +

CSTR:

kC

C CC X

X1A

Ao A

Ao A

A2 2x =−

=−_ i


92 NCEES

Variable Volume

V = Vo (1 + eA XA), DV = Vo eA XA

Batch reactor:

lnk t C XX

X111

1Ao A

A AA A

ff=

−+

+ −_ _i i> H

Plug-flow reactor:

lnk C X X XX1 2 1 1 1 1Ao

A A A A A AA

A2 2x f f f f= + − + + + −_ _ _i i i= G

CSTR:

kC XX X

1

1

Ao A

A A A2

2

xf

=−

+__ i

i

3.5.4 Second-Order Reactions ,A bB R r k C CA A B"+ − =_ iConstant Volume

Batch reactor:

ln lnbk t C M M CC

M XM X

11Ao

A

B

A

A− = =−−^ _h i when bM C

C1

Ao

Bo !=

bk tC k t C C

C CXX

1Bo AoA

Ao A

A

A= =−

= − when M = 1

Plug-flow reactor:

ln lnbk t C M MCC

M XM X

11Ao

A

B

A

A− = =−−^ _h i when bM C

C1

Ao

Bo !=

bk C k C C

C CXX

1Bo AoA

Ao A

A

Ax x= =−

= − when M = 1

CSTR:

b bk

C C M CC C

C X M XX

1 1A Ao A

Ao A

Ao A A

Ax =− +

−=

− −^ _ _h i i8 B when bM CC

1Ao

Bo !=

b bk

CC C

C XX1A

Ao A

Ao A

A2 2x =

−=

−_ i when M = 1

Chapter 3: Kinetics

NCEES 93

3.6 Complex Reactions

3.6.1 First-Order Reversible Reactions ( )A Rk

k

2

1

r d t

d Ck C k CA

AA R1 2− = − = −

K k

kCCA

CR

2

1

eq

eq= = and M CCAo

oR=

d td X

M Xk M X X1A

AA A

1

eqeq

= ++ −^ ah k

ln lnXX

C CC C

M XM

k t1 1A

A

Ao A

A A

A1

eq eq

eq

eq

− − = − −−

=++f

a^p h

k

At equilibrium, when X XA Aeq= , then -ln(0)"∞ and t"∞.

3.6.2 Reactions of Shifting OrderFrom zero order at high CA to first order at low CA:

r k C

k C1A

A

A

2

1− = +

ln CC

k C C k tA

AoAo A2 1+ − =e `o j

ln

C CCC

k C Ck t

Ao A

A

A

Ao A

o

21

− = − + −

e o

where

kk2

1 = zero-order rate constant

k1 = first-order rate constant

This form of the rate equation is used for elementary enzyme-catalyzed reactions and for elementary surface- catalyzed reactions.

3.6.3 Plug-Flow Reactors With Recycle

First Order (eA = 0)

( )lnRk

R CC RC

1 1 A

Ao Ax+ = +

+


94 NCEES

Second Order (eA = 0)

RkC

C C RCC C C

1Ao

A Ao A

Ao Ao Ax+ =

+

−

`` j

j

where R = recycle ratio, defined as the fraction of the reactor outlet stream that is recycled

3.7 Yield and SelectivityYield Y is defined as the molar ratio of the desired product formed to the reactant that is consumed.

Selectivity S is defined as the molar ratio of the formation of desired product to undesired product.

3.7.1 Two Irreversible Reactions in Parallel A DD"k (desired) and A UU"k (undesired)

r d td C

k C k CAA

D A U Ax y− = − = +

r d td C

k CDD

D Ax= =

r d td C

k CUU

U Ay= =

YD = instantaneous fractional yield of D d Cd C

A

D= −

overall fractional yield of DY N NN

DAo A

D= = −

where andN NA D are the final values measured at the reactor outlet

overall selectivity to D over US NN

DUU

D= =

where andN ND U are the final values measured at the reactor outlet

3.7.2 Two First-Order Irreversible Reactions in Series A D UD U

" "k k (D = desired, U = undesired)

r d td C

k CAA

D A− = − =

r d td C

k C k CDD

D A U D= = −

r d td C

k CUU

U D= =

The maximum yield of D in a plug-flow reactor is ln

at timeCC

kk

k k kkk

1max

logAo

D

U

D

mean U D

D

Uk kkU DU

x= = =−

−e `

eo

oj

The maximum yield of D in a CSTR is

at timeCC

kK

k k1

1 1,maxmax

Ao

D

D

UD U2

1 2 x=

+

=

e o> H

95

4 FLUIDS



A Area ft2 m2 Ar Archimedes diameter dimensionless

C Fitting characteristic dimensionlessCD Drag coefficient dimensionlessCv Valve flow coefficient dimensionless

cp Specific heat (constant pressure) lbm FBtu-c kg K

J:

cv Specific heat (constant volume) lbm FBtu-c kg K

J:

D Diameter ft or in. mDH Hydraulic diameter ft or in. md Diameter (minor) ft or in. mF Force lbf Nf Friction factor (Moody or Darcy) dimensionless

fFanning Fanning friction factor dimensionless

gc Gravitational conversion factorseclbf

lbm ft--2 —

H Total head ft mh Height ft mhf Head loss ft m

hf, fittingHead loss in fitting ft m

hL Head loss (general) ft mK Loss coefficient dimensionless


96 NCEES

Symbols (con't)Symbol Description Units (U.S.) Units (SI)

KE Kinetic energy Btu J

k Ratios of specific heats (cp/cv) dimensionless

L Length or thickness ft or in. m

MW Molecular weight lb molelb

kmolkg

Ma Mach number dimensionlessm Mass lbm kg

mo Mass flow rate hrlbm

skg

Ns Specific speed rpm rpm

NPSHaNet positive suction head available

ft m

NPSHrNet positive suction head required

ft m

P Pressure ftlbf2 Pa

P Wetted perimeter ft mPE Potential energy Btu J

Pvap Vapor pressure psi Pa

R Radius ft or in. m

R Universal gas constant lb mole RBtu or lb mole R

psi ft- -

- 3

c c mol KJ:

RD Relative density dimensionlessRe Reynolds number dimensionlessr Radius (minor) ft or in. mS Rotational speed rpm rpm

SG Specific gravity dimensionlessT Temperature °F or °R °C or Kt Time hr s

u Velocity secft

sm

usound Local speed of sound secft

sm

V Volume ft3 m3

Vo Volumetric flowrate secft3

sm3

Wo Power hp W

X Distance ft or in. mx Length, distance, or position ft or in. my Length ft or in. mz Length or elevation difference ft or in. ma Angle radian radian

Chapter 4: Fluids

NCEES 97

Symbols (con't)Symbol Description Units (U.S.) Units (SI)

d Thickness of a film ft me Absolute roughness ft m

ePorosity or void fraction 0 11 1e^ h dimensionless

h Efficiency dimensionlessq Angle radian radian

μ Dynamic viscosity seccP ftlbmor - Pa s s m

kgor: :

n3Infinite, plastic, or high shear viscosity seccP ft

lbmor - Pa s s mkg

or: :

n Kinematic viscosityhrft2

sm2

r Density ftlbm3 m

kg3

s Surface tension ftlbf

mN

τ Stress ftlbf2 Pa

τ0 Yield stress of fluidftlbf2 Pa

Φ Sphericity of particle (0 < Φ ≤ 1, where Φ = 1 is a perfect sphere) dimensionless

4.2 Mechanical-Energy Balance

4.2.1 General

4.2.1.1 Stress, Pressure, and ViscosityDefinitions:

Stress is

lim AF

A 0x

DD=

"D^ hwhere x = surface stress at a point

Pressure is

P nx= −

where nx = stress normal at a point

Newton’s Law of Viscosity relates shear stress (τt = stress tangential to the boundary) to the velocity gradient or shear rate (du/dy), using a constant of proportionality known as the dynamic (absolute) viscosity (μ) of the fluid:

dydu

tx n=


98 NCEES

Kinematic viscosity is

v tn=

Temperature dependence on viscosity is

For liquids (Andrade Equation): DeTB

n =

where

D and B = empirical constants

T = absolute temperature

For gases (Sutherland's Equation): T SCT 2

3

n = +

where

C and S = empirical constants


4.2.1.2 Fluid Types and Characteristics FLUID TYPES AND CHARACTERISTICS

SHEA

R ST

RESS

(

)

SHEAR RATE (du/dy)

BINGHAM PLASTIC

DILATANTNEWTONIAN

PSEUDOPLASTIC

1

0

τ

τ

Chapter 4: Fluids

NCEES 99

Classifications of FluidsFluid

Classification Fluid Type Behavior Examples

Time-Independent Viscosity

Newtonian

Viscosity is constant.

dydu

tx n=

The term μ is reserved for Newtonian fluids.

Water, light oil, blood plasma

Pseudoplastic (shear thinning)

Apparent viscosity (m) decreases with increased shear stress.

m dydu

t

n

x = d nn = power law index, n < 1

m is also known as the consistency coefficient or consistency index

Molasses, latex paint, whole blood

Dilatant (shear thickening)

Apparent viscosity (m) increases with increased shear stress.

m dydu

t

n

x = d nn = power law index, n > 1

Corn starch suspensions

Time-Dependent Viscosity

Thixotropic Apparent viscosity (m) decreases with duration of stress. Yogurt, plastisols

Rheopectic Apparent viscosity (m) increases with duration of stress.

Gypsum paste, kaolin clay suspensions

Viscoplastic Bingham plastic

Behaves as a rigid body until a minimum stress (yield stress) is applied, then reacts as a Newto-nian fluid at stresses above the yield stress.

dydu

t 0x x h= +

h = fluid viscosity 0x = yield stress

Mayonnaise, river mud, slurries

Viscoelastic Kelvin material Maxwell material

The materials exhibit both viscous and elastic characteristics during deformation under stress. Silicone putty

4.2.1.3 Surface Tension and Capillary RiseSurface tension g is the force per unit contact length

LF

c =

where

F = surface force at the interface

L = length of interface


100 NCEES

The capillary rise, h, is approximated bycosh g d

g4 ctc b= e o

where

h = height of the liquid in the vertical tube

b = angle made by the liquid with the wetted tube wall

d = the diameter of the capillary tube

4.2.2 Conservation of MassConservation of mass for flow from point 1 to point 2 is

m m1 2=o o

The continuity equation is

ρ1 A1 u1 = ρ2 A2 u2

For an incompressible fluid, ρ1 = ρ2, therefore:

A1 u1 = A2 u2 and V V1 2=o o

4.2.2.1 The Bernoulli EquationThe Bernoulli equation states, in energy per unit mass

ttan. c nlbmft lbf

sft or kg

Nmsm o s

P g u g z32 2 2- c

2

2

2

2 2

t= = + + =

For one-dimensional flows (with uniform velocity profiles) through conduits with flow from point 1 to point 2, expressed in:

Energy Per Unit Mass (Energy Basis)

lossP g u

g z wP g u

g z2 2c

inc1 1

2

12 2

2

2t t+ + + = + + +

where

win = net shaft work in = power/mass flow rate

Energy Per Unit Volume (Pressure Basis)

lossP gu

gg z

w P gu

gg z

2 2c c inc c1

12

12

22

2t tt

t tt+ + + = + + + ^ h

Height of Fluid (Head Basis)

gP g

gu

z h gP g

gu

z h2 2c

sc

L1 1

2

12 2

2

2t t+ + + = + + +

where

hs = shaft work head

hL = head loss

Chapter 4: Fluids

NCEES 101

4.2.2.2 The Impulse-Momentum PrincipleThe resultant force in a given direction acting on a fluid equals the rate of change of momentum of the fluid,

where

F V u V u2 2 2 1 1 1t t= −o o// /F/ = result of all external forces acting on the control volume

V u1 1 1to/ = rate of momentum of the fluid flow entering the control volume in the same direction as the force

V u2 2 2t =o/ rate of momentum of the fluid flow leaving the control volume in the same direction as the force

4.2.2.3 Energy Line and Hydraulic Grade Line

Energy Line (or Energy Grade Line)

The Energy Line (EL) represents the total head available to a fluid and can be expressed as:

For inviscid incompressible flow:

EL gP g

gu z2

c2

t= + + = constant along a streamline

For incompressible flow with losses:

EL gP g

gu z h2

cL

2

t= + + −

Hydraulic Grade Line (or Hydraulic Gradient Line)

The Hydraulic Grade Line (HGL) represents the total head available to a fluid, minus the velocity head, and can be expressed as:

For inviscid incompressible flow:

HGL gP g

zct= +

For incompressible flow with losses:

HGL gP g

z hcLt= + −

Note: The energy or hydraulic grade lines do not represent “sources” or “sinks” of energy such as the effects of pumps or turbines.

Energy Line and Hydraulic Grade Line for Incompressible Fluid Between Two Points (With Losses)

DATUM

HYDRAULIC GRADE LINE

1

2

z1

z2

1 cP 1 g cg

12

2u 1

2

2 g

2 cP 2 g cg

22

2u 2

2

2 g

h L

FLOW

ENERGY LINE


102 NCEES

4.3 Flow Behavior

4.3.1 VelocityVelocity is defined as the rate of change of position with respect to time

u dtdx=

where x = position

Velocity of a Newtonian fluid in a thin film is

u t uyd

=^ h dydu u

d=

BOUNDARY

THIN FILM

δy

u

The velocity distribution for laminar flow in circular tubes or between planes is

u r u Rr1max

2= −^ ch m= G

where r = distance from the centerline

R = radius of the tube or half the distance between the parallel planes

u = local velocity at r

umax = velocity at the centerline of the duct

u = average velocity in the duct

Flow Conditions

Fully turbulent flow Circular tubes in laminar flow

Parallel planes in laminar flow

uumax = 1.18 2 1.5

The shear stress distribution is

Rr

wxx =

where τ and τw = shear stresses at radii r and R, respectively

4.3.2 Reynolds NumberDimensionless number describing flow behavior with the general definition:

Re viscous forcesinertial forces=

Chapter 4: Fluids

NCEES 103

4.3.2.1 Hydraulic DiameterDH = hydraulic diameter (also known as the characteristic length)

tional areasecwetted perimetercrossD P

A4 4H #= =

Hydraulic Diameters for Various Flow Configurations

Flow Configuration Diagram Hydraulic Diameter DH =

Through a circular tube

u

D

D = inside diameter

Through a square duct

u

a

a

a

Through a rectangular duct

u

a

b

a bab2+

Through a circular annulus uD1

D2

D2-D1

Through a partially filled pipe (tube)

lh

cr

lrl c r h2 - -_ i8 B

where

c h r h2 2= -_ i


104 NCEES

Hydraulic Diameters for Various Flow Configurations (cont'd)

Flow Configuration Diagram Hydraulic Diameter DH =

Around a sphere (or sphere through a fluid)

FLUID APPROACH VELOCITY (uo)

FLUID STREAMLINESPROJECTED AREA (Ap)

Sphere diameter

Around any object (or an any object through a fluid)

FLUID APPROACH VELOCITY (uO)

FLUIDSTREAMLINES

PROJECTED AREA (Ap)

P = PERIMETER OF SHAPE PRESENTED NORMAL TOTHE APPROACH VELOCITY

PA4 p

4.3.2.2 Newtonian Fluid Re

D uHnt=

where u = approach velocity

Various Forms of Reynolds Numbers and Their UnitsReynolds

Number FormHydraulic Diameter

D

Fluid Velocity

u

Fluid Density

ρ

Fluid Viscosity

μ

Volumetric Flow rate

Vo

Mass Flow rate

mo

Kinematic Viscosity

νD uHnt ft

secft

ftlbm3 secft

lbm-

D uHnt m s

mmkg3

Pa s ormN s

2::

or m s

kg:

.D u32 2Hnt ft

secft

ftlbm3

secft

lbf-2

.D u

123 9 Hnt in.

secft

ftlbm3 cP

, DV22 700Hnto in.

ftlbm3

cPsecft3

Chapter 4: Fluids

NCEES 105

Various Forms of Reynolds Numbers and Their Units (cont'd)

Reynolds Number Form

Hydraulic Diameter

D

Fluid Velocity

u

Fluid Density

ρ

Fluid Viscosity

μ

Volumetric Flow rate

Vo

Mass Flow rate

mo

Kinematic Viscosity

ν

. DV50 6Hnto in.

ftlbm3 cP gpm

. Dm6 31Hno in. cP

hrlbm

. DV35 42Hnto in.

ftlbm3 cP

hrbarrels

vD uH ft

secft

secft2

vD uH m m/s

sm2

vD u12H in.

secft

secft2

7740 vD uH in.

secft cS

, , D vV1 419 000H

o in.secft3 cS

3160 D vVH

o in. gpm cS

4.3.2.3 Power Law Fluid Re

K nn

D u

43 1 8( )

( )x

nn

n n

1

2 t=

+ −

−

f d

`_ in

j

p

where

n = power law index

K = consistency index

4.3.2.4 Bingham PlasticBingham plastic flow through a pipe:

ReD

VD g

V

124

4

cBP 3

0r nn

r x

t=+3

3o

o

f p

where

n3 = infinite viscosity, or plastic viscosity, or high shear limiting viscosity

0x = yield stress of the fluid


106 NCEES

Viscosity as a Function of Temperature for a Variety of Gases and Liquids

SAE 10 LUBRICATING OIL (21° API)

35° API DISTILLATE

CARBON TETRACHLORIDE

ETHYL ALCOHOL (100%)GASOLINEWATER

BENZENEACETONE (LIQUID)

N - PENTANE (LIQUID)

n - PENTANE

AMMONIA (LIQUID)

AIR AT ATMOSPHERE PRESSURE

OXYGEN (1 ATM)

CHLORINE CARBON DIOXIDE CARBON DIOXIDE

METHANEMETHANE

PROPANE

AMMONIA VAPOR

WATER VAPOR (1 ATM)

WATER VAPOR HYDROGEN

SAE 10 LUBRICATING OIL (21° API)

35° API DISTILLATE

CARBON TETRACHLORIDE

ETHYL ALCOHOL (100%)GASOLINEWATER

BENZENEACETONE (LIQUID)

N - PENTANE (LIQUID)

n - PENTANE

AMMONIA (LIQUID)

AIR AT ATMOSPHERE PRESSURE

OXYGEN (1 ATM)

CHLORINE CARBON DIOXIDE CARBON DIOXIDE

METHANEMETHANE

PROPANE

AMMONIA VAPOR

WATER VAPOR (1 ATM)

WATER VAPOR HYDROGEN

VISC

OSIT

Y, CE

NTIP

OISE

S (cP

)

TEMPERATURE, °F

0 100 200 300 400 500 600 700

10080

60

40

30

20

8

6

4

3

2

10

0.8

0.6

0.4

0.3

0.2

1

0.08

0.06

0.04

0.03

0.02

0.1

0.008

0.006

0.004

0.1

Source: G.G. Brown et al, Unit Operations, New York: Wiley, 1951, p. 586.

Chapter 4: Fluids

NCEES 107

4.3.2.5 Critical Reynolds NumberThe critical Reynolds number (Rec ) is the minimum Reynolds number at which flow is expected to become turbulent, as shown in the following table:

Flow Regime Rec

Flow through a pipe 2100Flow around a sphere 10

Circular flow (rotating cylinder, Taylor-Couette flow)

hr1708 1

where the inner cylinder has a diameter (r1) and height (h)

4.3.3 Friction

4.3.3.1 Absolute Roughness and Relative RoughnessRelative roughness is D

f .

Absolute Roughness or Specific Roughness (f) of Various Pipes

Materialε

ft in. m mmPVC and Plastic Pipes 0.0000033 0.00004 1.0E-06 0.001Copper, Lead, Brass, Aluminum (new) 0.000005 0.00006 1.5E-06 0.0015Stainless steel 0.00005 0.0006 1.5E-05 0.015Steel commercial pipe 0.0002 0.0024 6.0E-05 0.06Asphalted cast iron 0.0004 0.0048 1.2E-04 0.12Galvanized iron 0.0005 0.006 1.5E-04 0.15Smoothed cement 0.001 0.012 3.0E-04 0.3New cast iron 0.0016 0.019 5.0E-04 0.5Well-planed wood 0.0016 0.019 5.0E-04 0.5Ordinary concrete 0.0026 0.031 8.0E-04 0.8Worn cast iron 0.004 0.048 1.2E-03 1.2Coarse concrete 0.0065 0.078 2.0E-03 2.0Ordinary wood 0.002 0.024 6.1E-04 0.6

4.3.3.2 Friction Factors for Laminar FlowFor laminar flow (Re < 2100)

Ref 64=

4.3.3.3 Friction Factors for Turbulent FlowThe Colebrook equation

..log

RefD

f1 2

3 72 5110

f=− +

J

L

KKKKKK

N

P

OOOOOO


108 NCEES

For fully turbulent flow

. logf D1 1 74 2 2

10f= − c m

Moody Friction Factor Chart (Also Darcy or Stanton Diagram)MOODY FRICTION FACTOR CHART0.1

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.025

0.02

0.015

7 9 2103 104 105 106 107 108

3 4 5 6 7 9 2 3 4 5 6 7 9 2 3 4 5 6 7 9 2 3 4 5 6 7 9 2 3 4 5 6 7 9

0.01

0.009

0.008

MOODY DIAGRAM. (FROM L.F. MOODY, TRANS. ASME, VOL. 66, 1944.)REYNOLDS NUMBER Re

f

SMOOTH PIPES

RELA

TIVE

ROU

GHNE

SSe D

COMPLETELY TURBULENT REGIMETRANSITION

ZONE

CRITICALZONELAMINAR

FLOW

64Re

Rcr

f = 0.050.04

0.03

0.02

0.015

0.0080.006

0.004

0.002

0.0010.00080.00060.0004

0.0002

0.0001

0.000,05

0.000,01

0.01

0.000,0010.000,005

0.000,0010.000,005

4.3.4 Laminar Flow

4.3.4.1 Pressure Drop for Laminar FlowThe Hagen-Poiseuille equation for Vo in terms of the pressure drop DPf is

V LR P

LD P

8 128f f

4 4

nr

nrD D

= =o

This relation is valid only for flow in the laminar region.

Chapter 4: Fluids

NCEES 109

4.3.5 Turbulent Flow

4.3.5.1 Head Loss in Pipe or ConduitThe Darcy-Weisbach equation is

h f DLgu K g

u2 2L

2 2= =

where

f = the Moody friction factor (also called Darcy or Stanton friction factor)

D = inside diameter of the pipe or hydraulic diameter (DH) of conduit

L = length over which the pressure drop occurs

f DL = K = the loss coefficient

The total loss coefficient for a system is

K Ki= /

where Ki = the loss coefficient for individual fittings, valves, and other components

Changes in K for different pipe internal diameter are

K K DD

a bb

a4

= e oAn alternative formulation is

h Dgf Lu2

LFanning

2

=

where the Fanning friction factor is

ff4Fanning =


110 NCEES

Loss Coefficients and Equivalent Lengths for Fittings and Valves

Fitting

Equivalent Length*

Loss Coefficient

Re IDKK

K 1 1inches

1= + +3d n

DL K1 K3

Elbows

90o

Standard dr 1=c m, threaded 35 800 0.40

Standard dr 1=c m, flanged or welded 20 800 0.25

Long radius .dr 1 5=c m 16 800 0.20

Mitered 100 1000 1.15

45o


Long radius .dr 1 5=c m 13 500 0.15

Mitered, 1 weld (45°) 20 500 0.25

180o


Standard dr 1=c m, flanged or welded 30 1000 0.35

Long radius .dr 1 5=c m 25 1000 0.30

Tees

Used as elbows

Standard, threaded 60 500 0.70Long radius, threaded 35 800 0.40Standard, flanged or welded 65 800 0.80Stub-in branch 85 1000 1.00

Run through

Threaded 10 200 0.10Flanged or welded 40 150 0.50Stub-in branch 5 100 0.05

Chapter 4: Fluids

NCEES 111

Loss Coefficients and Equivalent Lengths for Fittings and Valves (cont'd)

Fitting

Equivalent Length*

Loss Coefficient

Re IDKK

K 1 1inches

1= + +3d n

DL K1 K3

Valves

Gate, ball, or plug

Full line size 1.0DD

pipe

opening =f p 10 300 0.10

Reduced trim .DD

0 9pipe

opening =f p 12 500 0.15

Reduced trim .DD

0 8pipe

opening =f p 20 1000 0.25

GlobeStandard 330 1500 4.00Angle or Y type 165 1000 2.00

Diaphragm Fully open 165 1000 2.00

Butterfly Full open 20 800 0.25

Check

Lift 830 2000 10.00Swing 125 1500 1.50Tilting disk 40 1000 0.50

* Approximated from the loss coefficient equation using friction factors for fully turbulent flow for pipe sizes 1" through 24"


112 NCEES

4.3.5.2 Loss Coefficients for Contraction and ExpansionNotes:

1. Reynolds Number (Re) and friction factor (f) are based on inlet velocity.2. D

db =

Contraction: CONTRACTION

D dFLOW

When θ < 45° and

Re < 2500, then . . Re sinK 1 6 1 2 160 1 1 24bi= + −c e cm o m

Re > 2500, then . . . sinK f1 6 0 6 1 92 124

2

b

b i= + −` fj pWhen θ > 45° and

Re < 2500, then . . Re sinK 1 6 1 2 160 1 1 2421

bi= + −c e cm o m< F

Re > 2500, then . . sinK f0 6 0 48 1

24

2 21

b

b i= + −` f cj p m< F

Expansion: EXPANSION

DDFLOW

When θ < 45° and

Re < 4000, then . sinK 5 2 1 24b

i= −` cj m

Re >4000, then . . sinK f2 6 1 3 2 1 24b

i= + −` ` cj j m

When θ > 45° and

Re < 4000, then K 2 1 4b= −` j

Re > 4000, then .K f1 3 2 1 4 2b= + −` `j j

Chapter 4: Fluids

NCEES 113

4.3.5.3 Loss Coefficients for Pipe Entrance and Exit

Loss Coefficients

Fitting Type Configuration

Loss Coefficient

Re IDKK

K 1 1inches

1= + +3d n

K1 K∞

Entrance

Inward projecting or reentrant FLOW 160 1.0

Sharp-edged

FLOW 160 0.5

Rounded

r

dFLOW

160

r/d K∞

0.02 0.280.04 0.240.06 0.150.10 0.090.15 & up 0.04

Exit All geometries 0.0 1.0

4.3.5.4 Valve Flow Coefficient (Cv)

Valve flow coefficient (Cv ) is a value of the relationship between the pressure drop across a valve and the corre-sponding flow rate:

C V PSG

v D= o

Also:

CKad

v

2=

where

a = constant, . .in psigpm

orm Pasm

29 9 0 03522 2

3

d = effective diameter of the valve, in inches or meters

K = loss coefficient

Note: Values of Cv are not interchangeable between unit systems.


114 NCEES

The estimated flow rate with a known K value is

VKad

SGP

gpm

2 D=o

where ΔP = pressure drop (psi or Pa)

4.3.6 Particle FlowThe force exerted by a fluid that opposes the weight of an immersed object (buoyant force) can be expressed in terms of differential densities:

F ggV

G c

p f pt t=

−` j

where

FG = buoyant force

rp = particle density

rf = fluid density

Vp = volume of particle

The force exerted by a fluid flowing past a solid body (drag force) can be expressed in terms of a drag coefficient (CD):

F gC u A

2Dc

D f P2t= 3

where

FD = drag force

u3 = approach velocity

AP = the projected area of object with axes perpendicular to the flow

4.3.6.1 Stokes Law or Stokes FlowFor a sphere moving through a fluid at Re << 1:

ReC 24D =

where

ReD upnt

= 3

Dp = the particle diameter

In Stokes flow, viscosity can be determined using:

u

D g18 t

p p f2

nt t

=−` j

where ut = terminal (or settling) velocity of particle

Chapter 4: Fluids

NCEES 115

Drag Coefficients

For spheres in a flowing fluid with Reynolds numbers (1 < Re < 2×105), the Dallavalle equation applies:

. .ReC 0 632 4 8

D

2

= +e o

For cylinders in a flowing fluid with Reynolds numbers (1 < Re < 2×105) and with the axis normal to the flow, this equation applies:

. .ReC 1 05 1 9

D

2

= +e o

Drag Coefficients for Spheres and Flat Disks

EFFECT OF SURFACE ROUGHNESS OR MAIN-STREAM TURBULENCE

CIRCULAR DISK

REYNOLDS NUMBER (Re)

V

10

10

1

10

101-1 4 426 68 8 1042 2 36 8 1042 6 8 1042 6 8 4 1042 6 8 5 1042 6 8 6 71042 6 810

2x10

V

d

d

SPHERE

STOKES LAW:CD = 24/Re

CD

DRAG COEFFICIENTS FOR SPHERES AND FLAT DISKS 2864

2

864

2

8

-1

-2

64

2

864

2

4.3.6.2 Terminal Velocity (ut)For a sphere of diameter Dp, equation applies for any Reynolds number (Newton's Law of falling particles):

u C

g D3

4t

f D

p sphere f

t

t t=

−` j

For a small sphere of diameter Dp, following Stokes Law:

u

D g18t

p sphere f2

nt t

=−_ i

4.3.6.3 Reynolds Numbers for Particles in a FluidReynolds number when particle velocity (ut) is unknown and Dp, rs, r, and μ are known:

. . .Re Ar14 42 1 827 3 79821 2

= + −_ i; Ewhere the Archimedes number (Ar) is:

Ar

D gp f p f2

3

n

t t t=

−` j


116 NCEES

Reynolds number when particle diameter (Dp ) is unknown and ut, ρs, ρ, and μ are known:

. . .

Re ReC1 0 00433 0 203 0 0658D 2

1

= + −d n

where Re

Cu

g3

4D

f t

p f2 3t

n t t=

−` j

Reynolds number when fluid viscosity (μ) is unknown and Dp, ut, rs, and r are known:

..

Re C 0 6324 8

D

2

= −e o Use known quantities to solve for CD.

4.3.6.4 Settling OperationsFree Settling: Particle-to-particle interactions are negligible.

Hindered Settling: Particle settling is at a reduced rate relative to the settling velocity of a single particle caused by interactions with neighboring particles.

Approximate Regions of Free and Hindered Settling for Given Solids' Concentration and Density

50

40

30

20

100.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

HINDERED

FREE

wt. %

SOL

IDS

PARTICLE

PARTICLE FLUID—

If upwards fluid velocity ( uf ) is less than the settling velocity of the particle (us ), then the particles will settle.

For settling operations, the settling velocity (us ) equals the terminal velocity (ut).

Chapter 4: Fluids

NCEES 117

4.3.6.5 Settling DiameterFor Stokes flow, the smallest diameter spherical particle (Dp ) that will settle is

Dg

u18p

p f

f

t t

n=−` j

For general flow up to Re < 2×105, the smallest diameter spherical particle that will settle is

D uRe

p f ftn=

where the Reynolds number can be estimated using

. . .Re Re

C1 0 00433 0 203 0 0658D 21

= + −d n where ReC

ug3

4D

f t

p f2 3t

n t t=

−` j

4.3.6.6 Flow Through Porous Media and Packed BedsA porous, fixed bed of solid particles can be characterized by:

L = length of particle bed

ds = average particle diameter (diameter of a sphere with the same volume of the particle)

Φ = sphericity of particle (0 –1)

e = porosity or void fraction of the particle bed (dimensionless)

Porosity (e) or void fraction:

Total volumeTotal volume Volume of solids

AA

AA1 solid voidse =

−=

−=

_ i

where

Asolid = area of the solid phase in a cross-section of area A

Avoids = void area in a cross-section of area A

Interstitial velocity (actual velocity of fluid within the pores or voids):

u AV u

i e e= =o

where u = approach velocity (or superficial velocity)

Sphericity of a particle (shape factor):

surface area of particlesurface area of sphere with same volume as particle

U =

Friction loss through porous media:

h f dL

gu

43 1

sf

2

3e

e=−d e_n i o

Reynolds number for flow through porous media:

Re d u32

11

nt

e= −e_ i o


118 NCEES

Use the Ergun equation to estimate the pressure loss through a packed bed (DP) under laminar and turbulent conditions:

.LP

du

du150 1 1 75 1

s s2 2 3

2 2

3n

e

e t

e

eD

U U=

−+

−_`

_ `_ e_j

i iij i o

Typical Shape FactorsParticle Φ

Spheres 1.00Torus 0.89Ideal cylinder (h = d) 0.87Octahedron 0.85Cube 0.81Sand (average) 0.75Cylinder (h = 5d) 0.70Cylinder (h = 10d) 0.58Tetrahedron 0.67Berl saddles 0.30–0.37Raschig rings 0.26–0.53

4.3.6.7 FluidizationFor a fluid passing vertically through a bed of particles, ΔP increases as fluid velocity u increases. The net upward force FB on the bed is

FB = AΔP

where A = cross-sectional area of the bed

At fluidization, net upward force (fluid drag force) equals the weight of the bed (FB = WB), while the fluid velocity above the bed is less than the terminal velocity of the particles (ut).

The Reynolds number for a fluidized bed can be approximated by:

Re C C Ar C1 2 1= + −

where

Ar = Archimedes number

.C 3 5180 1

1e

=−_ i

.C 1 752

3e=

where ϵ = minimum bed void fraction (porosity) at the point of fluidization

The minimum bed void fraction for bed height H at the first indication of fluidization is

H Am

1particles

particlese t

= −

Chapter 4: Fluids

NCEES 119

4.3.7 Two-Phase Flow

4.3.7.1 Flow PatternsBubble or Froth Flow: Bubbles of gas are dispersed throughout the liquid. Gas bubbles move at roughly the same velocity as the liquid.

BUBBLE FLOWPlug Flow: Alternate plugs of liquid and gas move along the upper portion of the pipe, with mostly liquid moving along the lower portion.

PLUG FLOW

Stratified Flow: Gas flow moves on top and over the liquid forming a distinct, relatively smooth, liquid-gas inter-face.

STRATIFIED FLOW

Wavy Flow: Similar to stratified flow, the fast-moving gas flow creates waves in the liquid phase.

WAVY FLOW

Slug Flow: High velocity gas picks up waves to form frothy slugs of liquid. These slugs move at higher velocity than the bulk liquid phase and can create dangerous vibrations that can damage equipment.

SLUG FLOW

Annular Flow:As gas velocity increases, liquid forms around the inside of the pipe wall, with the high-velocity gas flowing through the center.

ANNULAR FLOW


120 NCEES

Dispersed Flow (or Spray Flow or Mist Flow): Liquid is entrained as fine droplets in the gas phase.

DISPERSED FLOW4.3.7.2 Flow Regimes

Flow Patterns for Horizontal Two-Phase Flow

DISPERSED

100,000

10,000

1,000

1000 1 10 100 1,000 10,000

ANNULARBUBBLE OR

FROTH

SLUG

PLUG

STRATIFIED

By

Bx

WAVE

Source: O. Baker, Oil and Gas Journal, Nov. 10, 1958, p. 156.

Baker parameters for the previous chart:

B W

W531G

L

LLx

L

L G

32

21

31

t

t t

cn= e _ fo i p

R

T

SSSSSSSSS

V

X

WWWWWWWWW

.B AW2 16

1G

L Gy 2

1t t

= d f_n i pwhere

A = internal pipe cross-sectional area, in ft2

WG = gas flow rate, in hrlbm

WL = liquid flow rate, in hrlbm

ρL = liquid density, in ftlbm3

ρG = gas density, in ftlbm3

μL = liquid viscosity, in cP

gL = liquid surface tension, in cmdyn

Chapter 4: Fluids

NCEES 121

4.3.8 Jet PropulsionThe force produced by jetting action is

F m u u2 1= −o _ iJET PROPULSION

m, u1

m, u2

Therefore, according to the conservation of mass:

F gV u V u

c2 2 2 1 1 1t t=

−o o

Jet Forces on PlatesJet on a Vertical Plate Jet on a Horizontal Plate Jet on an Inclined Plate

JET FORCES ON PLATES

JET ON A VERTICAL PLATE JET ON A HORIZONTAL PLATE JET ON AN INCLINED PLATE

h

F gmuc

jetx =

− oF g

m u g h2c

jety

23=

− −o sinF g

muc

jet i=

− o

4.3.9 Open-Channel Flow

4.3.9.1 Specific Energy (or Specific Head) E g

u y22

a= +

where

E = specific energy (or head)

u = fluid velocity

y = depth of liquid

Critical Depth: The depth of flow for a given discharge where the specific energy is at q minimum.

y gq

c

2 31

= e o


122 NCEES

where

yc = critical depth

q = unit discharge BVoc m

Vo = total discharge, volumetric flow rate

B = channel width

Specific Energy Diagram

y

E

CHAN

NEL D

EPTH

SPECIFIC ENERGYEmin

yc

4.3.9.2 Froude Number Fr g y

ug AV T

h

2

3= =o

where

yh = hydraulic depth = TA

A = cross-sectional area of flow

T = width of fluid surface

Supercritical flow: Fr > 1

Subcritical flow: Fr < 1

Critical flow: Fr = 1

Chapter 4: Fluids

NCEES 123

4.3.9.3 Hydraulic Jump

Hydraulic Jump

FLOW DIRECTION

HYDRAULIC JUMPSUPERCRITICAL FLOW

(Fr1 > 1)

SUBCRITICAL FLOW(Fr2 < 1)

(2)

(1)y1

y2

yy

Fr21 1 1 8

12

12= − + +` j

where

y1 = flow depth at upstream supercritical flow location

y2 = flow depth at downstream subcritical flow location

Fr1 = Froude number at upstream supercritical flow location

Fr2 = Froude number at downstream subcritical flow location

4.3.9.4 Manning Equation v AR S3

221

hl=

Ho

where

vo = discharge volumetric flow rate

k = 1.0 for SI units; 1.49 for U.S. units

A = cross-sectional area of flow

RH = hydraulic radius

S = slope of hydraulic surface

h = Manning's roughness coefficient


124 NCEES

Manning's Roughness Coefficients

Material hCast iron pipe 0.013Wrought iron pipe 0.015Riveted steel pipe 0.016Corrugated storm pipe 0.024Glass 0.010Vitrified sewer pipe 0.014Concrete pipe 0.013Excavated canal—earth, uniform 0.023Natural channel—uniform cross-section 0.050

4.3.10 Compressible Flow

4.3.10.1 Isentropic Flow RelationshipsIn an ideal gas for an isentropic process, the following relationships exist between static properties at any two points in the flow:

PP

TT k

k k

1

2

1

2 1

12tt= =

−e d^o nh

where k = ratio of specific heats = ccv

p

The stagnation temperature T0 at a point in the flow is related to the static temperature:

T T cu2 p

0

2= +

Energy relation between two points is

hu

hu

2 2112

222

+ = +

The relationship between the static and stagnation properties (T0, P0, and r0) at any point in the flow can be expressed as a function of the Mach number (Ma):

MaTT k1 2

10 2= + −

MaPP

TT k1 2

1kk

kk

0 0 1 2 1= = + −− −d c^ ^n mh h

MaTT k1 2

1kk

k0 0 1 2 11

tt = = + −− −d c^ ^n mh h

Chapter 4: Fluids

NCEES 125

Compressible flows are often accelerated or decelerated through a nozzle or diffuser. For subsonic flows, the velo-city decreases as the flow cross-sectional area increases and vice versa. For supersonic flows, the velocity increases as the flow cross-sectional area increases and decreases as the flow cross-sectional area decreases, The point at which the Mach number is sonic is called the throat; its area is represented by the variable A*. The following area ratio holds for any Mach number:

MaMa

AA

k

k1

21 1

1 21 1

*

kk

2 2 11

=+

+ − −+

__

^^i

i

hhR

T

SSSSSSSSS

V

X

WWWWWWWWW

where

A = area (length2)

A* = area at the sonic point (Ma = 1.0)

4.3.10.2 Net Expansion Factors of Gases for Orifices and Nozzles

Expansion Factors for Compressible Flow-Through Orifices and Nozzles

Y —

EXP

ANSI

ON FA

CTOR

PRESSURE RATIO –

SQUAREEDGEORIFICE

SQUAREEDGEORIFICE

=====

0.20.50.60.70.75

β

=====

0.20.50.60.70.75

β

WHERE IS P1 THE ABSOLUTE UPSTREAM PRESSURE

1.0

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

ΔP—P1

0 0.2 0.4 0.6

k = 1.3 approximately [CO2, SO2, H2O (steam),H2S, NH3, N2O, Cl2, CH4, C2H2, and C2H4]

k = 1.4 approximately [Air H2, O2, N2,CO, NO, and HCl]

Y —

EXP

ANSI

ON FA

CTOR

PRESSURE RATIO –

SQUAREEDGEORIFICE

SQUAREEDGEORIFICE

=====

0.20.50.60.70.75

β

=====

0.20.50.60.70.75

β

1.0

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

ΔP—P1

0 0.2 0.4 0.6

where Pl = absolute upstream pressure


126 NCEES

4.3.10.3 Net Expansion Factors of Gases for Pipes

Expansion Factors for Compressible Flow-Through Pipes

1.0

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.550 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

K = 100

K = 40

K = 20

K = 15

K = 10

K = 8.0

K = 6.0

K = 4.0

K = 3.0K = 2.0

K = 1.5

K = 1.2

K = 100

K = 40

K = 20

K = 15

K = 10

K = 8.0

K = 6.0

K = 4.0

K = 3.0K = 2.0

K = 1.5

K = 1.2

PRESSURE RATIO –

LIMITING FACTORSFOR SONIC VELOCITY

1.2 .525 .612 1.5 .550 .631 2.0 .593 .635 3 .642 .658 4 .678 .670 6 .722 .685 8 .750 .698 10 .773 .705 15 .807 .718 20 .831 .718 40 .877 .718 100 .920 .718

k = 1.3

ΔP—P1

ΔP—P1

Y

YK

LIMITING FACTORSFOR SONIC VELOCITY

1.2 .552 .588 1.5 .576 .606 2.0 .612 .622 3 .662 .639 4 .697 .649 6 .737 .671 8 .762 .685 10 .784 .695 15 .818 .702 20 .839 .710 40 .883 .710 100 .926 .710

k = 1.4

ΔP—P1

YK

k = 1.3 approximately [CO2, SO2, H2O (steam), H2S, NH3, N2O, Cl2, CH4, C2H2, and C2H4]

1.0

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.550 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

K = 100

K = 40

K = 20

K = 15

K = 10

K = 8.0

K = 6.0K = 4.0

K = 3.0K = 2.0K = 1.5

K = 1.2

K = 100

K = 40

K = 20

K = 15

K = 10

K = 8.0

K = 6.0K = 4.0

K = 3.0K = 2.0K = 1.5

K = 1.2

PRESSURE RATIO – ΔP—P1

Y

k = 1.4 approximately [Air, H2, O2, N2, CO, NO, HCl]

WHERE P1 IS THE ABSOLUTE UPSTREAM PRESSUREwhere Pl = absolute upstream pressure

Chapter 4: Fluids

NCEES 127

4.3.10.4 Critical Pressure Ratio, rc , for Compressible Flow

Critical Pressure Ratio Through Nozzles and Venturi Tubes (Only)

β

0.64

0.60

0.62

0.58

0.56

0.54

0.85

0.80

0.75

0.70

0.650.60

0.500.400.200

k = CP / CV

r c =

P 2 /P

1

1.25 1.30 1.35 1.40 1.45

where P1 and P2 = absolute pressures upstream and downstream of the nozzle or venturi tube, respectively

4.3.10.5 Choked FlowChoked flow is a limiting condition where the mass flow will not increase with a further decrease in the down-stream pressure environment while upstream pressure is fixed. Choked flow occurs when the Mach number is 1.0 at the minimum cross-section area.

Mass velocity of gas at choked flow:

m C A k P g k 1

2d c

kk

1 111

t= +−+

c mwhere

Cd = discharge

r1 = density of gas before restriction

P1 = pressure of gas before restriction (absolute)


128 NCEES

4.4 Flow Applications

4.4.1 Pumps

Types and Subtypes of Pumps

PUMPS

POSITIVE DISPLACEMENT

KINETIC

RECIPROCATING

BLOW CASE

ROTARY

CENTRIFUGAL

SPECIAL EFFECT

VANE SCREWCIRCUMFERENTIAL PISTONGEAR

FLEXIBLE MEMBER LOBE

CANNED PUMPOVERHUNG IMPELLERIMPELLER BETWEEN BEARINGSTURBINE TYPEREGENERATIVE TURBINE

REVERSE CENTRIFUGALROTATING CASING

STEAMPOWERCONTROLLED VOLUMEPISTON

4.4.1.1 Affinity Laws for Pumps, Fans, and CompressorsFor small changes in impeller diameter (changes not to exceed 20%):

DD

VV

HH

2

1

2

1

2

1= =oo

and B PB P

DD

2

1

2313

=

For variations in speed (constant impeller diameter):

SS

VV

HH

2

1

2

1

2

1= =oo

and B PB P

SS

2 2313

=1

where

B P = brake power

D = impeller or wheel diameter

H = head (height of fluid)

Vo = volumetric capacity

S = speed (rpm)

Chapter 4: Fluids

NCEES 129

4.4.1.2 Pump Similitude

Predicting Performance of Homologous Pumps

Volume capacity estimate:

VV

SS

DD

DD

HH .

2

1

2

1

2

13

2

12

2

10 5

= =o

o e e eo o o

Pressure or head estimate:

HH

SS

DD

2

1

2

12

2

12

= e eo o

Brake power estimate:

B PB P

SS

DD

DD

HH .

2

121

2

13

2

15

21

2

12

2

11 5

tt

tt= =e e e eo o o o

Impeller or wheel speed estimate:

SS

DD

HH

VV

HH. . .

2

1

1

2

2

10 5

1

20 5

2

10 75

= = o

oe e eo o o

4.4.1.3 Pump HeadPump head (Hp) is a variation of the head-basis Bernoulli equation:

H g

P P gg

u uz z h2p

d s c d sd s f

2 2

t=−

+−

+ − −` ` `j j j

where

Ps = suction pressure at suction reference point (absolute)

Pd = discharge pressure at discharge reference point (absolute)

us = velocity at the pump suction

ud = velocity at the pump suction

zs = elevation at the suction reference point

zd = elevation at the discharge reference point

hf = friction loss in the pipe between the reference points


130 NCEES

Centrifugal PumpPUMP HEAD

CENTRIFUGAL PUMP

PsSUCTIONREFERENCE POINT

DISCHARGEREFERENCE POINTPd

UdUs

ZdZs

Pump Head in Common Units

Pump Head Calculations

Component

U.S. Units SI Units

.H SG

p pg

u uz z h

2 312p

d s d sd s f

2 2

=−

+−

+ − −_ `

_i j

i Hp p

gu u

z z h2pd s d s

d s f

2 2

t=−

+−

+ − −` ` `j j j

Hp ft mp psi Pau

secft

sm

z ft mg .

secft32 2 2

.sm9 81 2

hf ft m

r ftlbm3 m

kg3

Chapter 4: Fluids

NCEES 131

4.4.1.4 Pump CurveA pump curve, head-capacity curve, or H-Q curve is provided by pump manufacturers.

Pump Curve for a Fixed Impeller Diameter and Pump Speed

POW

ER

TOTA

L HEA

D

VOLUMETRIC CAPACITY

BEP

BRAKE POWER

HEAD

EFFIC

IENCY

NPSHr

where BEP = best operating point

4.4.1.5 Net-Positive Suction Head (NPSH)NPSH: Total suction head minus the vapor pressure of the liquid being pumped (units are in height of liquid (absolute) and the referenced datum is the suction nozzle.)

NPSHa: Net-positive suction head available to the pump

NPSHr: Net-positive suction head required by the pump (provided by the pump manufacturer)

For suction lift:

NPSHa = ha – hvap – hst – hL

For flooded suction:

NPSHa = ha – hvap + hst – hL

where

ha = absolute pressure (in height of liquid) on the surface of the liquid supply level

hvap = vapor pressure (in height of liquid) of the liquid at the temperature being pumped

hst = static height of liquid supply, either above or below the pump centerline or impeller eye

hL = suction line losses in height of liquid


132 NCEES

4.4.1.6 Pump PowerPower required to move the fluid, or water power (WP):

U.S. units ( ) ,

( ) ( )horsepower

Flowrate gpm ft ftlbm

WPH

246 7803# # t

=d n

Metric units ( )W Flowrate s mmkg

smWP m H g

33 2# # #t= c ^ e dm h o n

Power required at the pump shaft, or brake power (BP):

BP WPpumph=

Power required by the pump driver, or supplied power (SP):

SP WPpump driver transmissionh h h=

4.4.1.7 Temperature Rise in a Centrifugal Pump

cT VBP 1

p

pump

t

hD =

−o

` j

4.4.1.8 Specific Speed (Ns ) at the BEP N

HSV

.

.

s 0 75

0 5=o

where head (H) and flow rate Vo^ hare taken at the BEP

4.4.1.9 Suction-Specific Speed (Ns ) at the BEP N

NPSHSV

.

.

sa0 75

0 5=

o

_ i

4.4.1.10 System CurvesSystem curves are developed from different flow rates through a given system, using the Bernoulli equation.

Note: The velocity head terms are usually omitted because the changes in gu2

2 are negligible.

Hs = pressure head + static head (hs ) + pipe losses* (hf )

*Include friction, entrance, and exit losses:

H g

P P gh hs

B A cs ft=

−+ +

_ i

Chapter 4: Fluids

NCEES 133

Simple Pumping System

PB

PA PUMPSTAT

IC H

EAD

(HS)

System Curve Plot

TOTA

L HEA

D

CAPACITY

STATIC HEAD (hs )

PRESSURE HEAD

SYSTEM CURVE


134 NCEES

4.4.1.11 Pumps in Parallel and SeriesOperating Point: Centrifugal pumps operate at the intersection of the pump curve and the system curve.

For pumps in parallel, capacities are added horizontally. For pumps in series, heads are added vertically:

Pumps Operating in Parallel

SYSTEM CURVE

CAPACITY

TOTA

L HEA

D

OPERATINGPOINT

COMBINED (A+B)PUMP CURVE

PUMP B

PUMP A

A B

A+B

Pumps Operating in Series

TOTA

L HEA

D

OPERATINGPOINT

COMBINED (A+B)PUMP CURVE

PUMP B

PUMP A

SYSTEMCURVE

A

B A+B

CAPACITY

Chapter 4: Fluids

NCEES 135

4.4.2 Fans, Compressors, and Turbines

4.4.2.1 FansTypical backward curved fans:

CONSTANT N, D, ρ

FLOW RATE

POWER

Δ

f

pW PV

fhD=oo

where

Wo = fan power

DP = pressure rise

hf = fan efficiency

4.4.2.2 CompressorsCompressors consume power to add energy to the working fluid. This addition of energy results in an increase in fluid pressure (head).

For an adiabatic compressor with DPE = 0 and negligible DKE:

W•

INLET

EXIT

COMPRESSORin

W m h hcomp e i=− −o o ` j

For an ideal gas with constant specific heats:

W mc T Tcomp p e i=− −o o ` j

Per unit mass:

W c T Tcomp p e i=− −o ` j

Compressor Isentropic Efficiency

ww

T TT T

C as

e i

es ih = = −−

where

wa = actual compressor work per unit mass

ws = isentropic compressor work per unit mass

Tes = isentropic exit temperature

For a compressor where DKE is included:

W m h hu u m c T T u u2 2comp e i

e ip e i

e i2 2 2 2

= − − +− = − − +

−o o od d `n j n


136 NCEES

Adiabatic compression:

WkmP k

PP

1 1compi C

i

i

e k1 1

t h=

− −−

o o

_ ei o> H = MW kmRT k P

1 1C

i

ie k1 1

h t- --o

_ di n> H

where

Wcompo = fluid or gas power

Pi = inlet or suction pressure

Pe = exit or discharge pressure

ri = inlet gas density

hC = isentropic compressor efficiency

Isothermal compression:

ln lnMWW

mRTPP mP P

comp C

i

i

ei Ci

ie

h t h t= =o o o

where

, , , andW P Pcomp e i Cho = as defined for adiabatic compression, above

R = univeral gas constant

Ti = inlet temperature of gas

4.4.2.3 TurbinesTurbines produce power by extracting energy from a working fluid. The energy loss shows up as a decrease in fluid pressure (head).

For an adiabatic turbine with DPE = 0 and negligible DKE:

W•

INLET

EXIT

TURBINEout

W m h hturb i e= −o o ` j

For an ideal gas with constant specific heats:

W mc T Tturb i ep= −o o ` j

Per unit mass:

w c T Tturb i ep= −` j

Turbine isentropic efficiency:

ww

T TT T

T sa

i es

i eh = = −−

For a turbine where DKE is included:

W m h hu u m c T T u u2 2turb e i

e ip e i

e i2 2 2 2

= − +− = − +

−o o od d `n j n

Chapter 4: Fluids

NCEES 137

4.4.3 Control Valves

4.4.3.1 Control Valve Flow CharacteristicsFlow characteristic of a control valve: The relationship between valve capacity and valve stem travel (or valve lift).

Control Valve Flow Versus Stem Travel

0 20 40 60 80 100

20

40

60

80

100

PERCENT OF RATED STEM TRAVEL

PERC

ENT

OF M

AXIM

UM F

LOW

QUICK OPENING

LINEAR

MODIFIEDPARABOLIC

EQUAL PERCENTAGE

Linear: Flow capacity increases linearly with stem travel.

Equal Percentage: Flow capacity increases exponentially with stem travel. Equal increments of stem travel produce equal percentage changes in the existing CV.

Modified Parabolic: Valve characteristic is approximately midway between linear and equal-percentage characteristics. It provides fine throttling at low flow capacities and approximately linear characteristics at higher flow capacities.

Quick Opening: Provides large changes in flow for very small changes in early stem travel.


138 NCEES

4.4.3.2 Control Valve Sizing (Traditional Method)

Control Valve Sizing Equations for Liquids (Incompressible Flow)Equation Use Notes

V C SGP

VD=o

Basic sizing equation; does not consider viscosity effects or valve recovery capabilities

CV is the flow coefficient for a control valve. The value of CV is dependent on the type of valve and also varies with stem travel or per-centage of valve opening. The units and values for the flow coefficient are provided by the manufacturer.

C V PSG

V D= o

Flow coefficient For Newtonian fluids of viscosities similar to water.

C C FV Corr V V=−Corrected flow coefficient for viscosity

Use the appropriate FV to predict pressure drop, select valve size, or predict flow rate.

P K P r pmax m C v1D = −_ i

Maximum allowable differential pressure

where:

Km = valve recovery coefficient (provided by manufacturer)

P1 = valve body inlet pressure (absolute)

pv = liquid vapor pressure (absolute) at the valve body inlet temperature

rC = critical pressure ratio

The critical pressure ratio is provided by the manufacturer or, in the absence of correlation data, the equation below can be used.

. .r pp

0 96 0 28C cv= −

Critical pressure ratio (when manufacturer data is not available)

pc is the critical pressure of the fluid (absolute).

,ReCV17 250

Vn

t=o Control valve Reynolds number For engineering units only, where Vo is in gpm,

ΔP is in psi, μ is in cP, and ρ is in ftlbm3

.

Chapter 4: Fluids

NCEES 139

4.4.4 Mixing

4.4.4.1 Tank Mixing

Tank Mixing

BAFF

LE

IMPE

LLER

BAFF

LE

LIQUIDLEVEL

TANK

D

NW

BAFF

LE

BAFF

LE

H

T

B

TDNVBW

WHERE:======

TANK DIAMETERIMPELLER DIAMETERROTATIONAL SPEEDTANK VOLUMEBAFFLE WIDTHIMPELLER WIDTH

Impeller Reynolds number

Re D N2nt=

Flow Number

NNDq

Q 3=

where q = volumetric flow rate through the impeller

Power Number

NN DPg

Pc

3 5t=

where P = impeller power

Ratio of tangential liquid velocity at blade tips to blade tip velocity (K):

K NNQ

P2r=

Froude number for tank agitation:

Fr gN D2=

Power function ( f ) is defined by:

FrNPmz =

where log Re

m ba 10=

−


140 NCEES

Examples of Mixing Configurations

Configuration (Unbaffled) a bSix-blade turbine (vertical blades) 1.0 40.0Three-blade propeller (pitch 2:1) 1.7 18.0Three-blade propeller (pitch 1:1) 2.3 18.0

Power delivered to the liquid by an impeller:

P gFr N D

c

m 3 5z t=

For tanking mixing where the liquid surface has insignificant wave formation, the Froude number is not a factor:

P gN D

c

3 5z t=

For Re < 10

P gK N D

cL

2 3n=

where KL = empirical constant (laminar)

For Re > 10,000

P gK N D

cT

3 5t=

where KT = empirical constant (fully turbulent)

Values of Constants KL and KT for Baffled Tanks Having Four Baffles Attached to the Tank Wall With Width Equal to 10% of the Tank Diameter

Type of Impeller KL KT

Propeller, square pitch, 3 blades 41.0 0.32Propeller, pitch = 2, 3 blades 43.5 1.00Turbine, 6 flat blades 71.0 6.30Turbine, 6 curved blades 70.0 4.80Fan turbine, 6 blades 70.0 1.65Flat paddle, 2 blades 36.5 1.70Shrouded turbine, 6 curved blades 97.5 1.08

Power required to suspend particles to a maximum height (Z) using a turbine impeller is

P g V u DT e1 .

m m t m32 2

14 35t f= − b_ ci m

where

.TZ E 0 1b = − − , with E = clearance between impeller and tank floor

rm , Vm = density and volume, respectively, of solid-liquid suspension, not including the clear liquid in zone above height Z

ut = terminal velocity of particles

em = volume fraction of liquid in zone occupied by suspension

Chapter 4: Fluids

NCEES 141

and

x1 1 1 1m liquid solids solids liquidst t t t= + −d n

with xsolids = mass fraction of the solid particles in the solid-liquid suspension

Suspension of Particles in a Tank

Z

E

TANK

SOLID-LIQUIDSUSPENSION

CLEAR LIQUID

T

D

4.4.4.2 Blending of Miscible Liquids in a Tank

Correlation of Blending Times for Miscible Liquids in a Turbine-Agitated, Baffled Vessel

Re = _________ND2p

CORRELATION OF BLENDING TIMES FOR MISCIBLELIQUIDS IN A TURBINE-AGITATED BAFFLED VESSEL

1000

100

fT

10

11 10610510410310210

μ

Blending time factor (fT) (for miscible Newtonian fluids only):

fH T

t N D g DT

21

23

2 32

61

21

=_ i

where t = blend time (sec)


142 NCEES

4.4.5 Air Lift

Air Lift Operation

AIR INLETNO AIR

LIQUID LIQUID

LIQUIDAND AIR

AIR INLETNO AIR

LIQUID LIQUID

LIQUIDAND AIR

Common Air Lift TermsDISCHARGE LEVEL

GROUND LEVEL

STATIC WATERLEVEL

PUMPING WATERLEVEL

AIR INLET

PUMPINGSUBMERGENCE

STARTINGSUBMERGENCE

DRAW-DOWN

TOTALPUMPING

LIFT

TOTALSTARTING

LIFTSTATICLEVEL

LIFTABOVE

GROUND

DISCHARGE LEVEL

GROUND LEVEL

STATIC WATERLEVEL

PUMPING WATERLEVEL

AIR INLET

PUMPINGSUBMERGENCE

STARTINGSUBMERGENCE

DRAW-DOWN

TOTALPUMPING

LIFT

TOTALSTARTING

LIFTSTATICLEVEL

LIFTABOVE

GROUND

Air lifts are used to pump liquids and mixtures of liquids and solids. The air required to pump is

logV

C SL

3434a

10

= +

Chapter 4: Fluids

NCEES 143

where

Va = quantity of free air required per gallon of liquid pumped gallon pumpedft3e o

C = constant found for outside airline (VA) and inside airline (VC) in figure below

S = pumping submergence (%) in figure below

L = total pumping lift (ft)

Constant in Formula for Va

INSIDE AIRLINE – VCOUTSIDE AIRLINE – VA375

350

325

300

275

250

225

200

175

150

12530 35 40 45 50 55

CONSTANT IN FORMULASUBMERGENCE – PERCENT

VALU

ES O

F CO

NSTA

NT “C

”

60 65 70 75 80

Approximate Percent Submergence for Optimum Efficiency70

60

50

40

30

TOTAL PUMPING LIFT – FEET

SUBM

ERGE

NCE

– PE

RCEN

T

30 100 200 300 400 500 600 700 800 900

Use for either system with straight or tapered pipe. Graphs only available in U.S. units; SI not available.

Source: Gibbs, C.W., editor, New Compressed Air and Gas Data, 2nd ed., Davidson, N.C.: Ingersoll-Rand Company, 1971, p. 31–8.


144 NCEES

4.4.6 Solids Handling

4.4.6.1 Granular Media Storage

Vertical Normal Stress Profile in a Silo

BULK SOLIDS

HYDROSTATIC

PRESSURE

Z

Source: Chase, George G., Solids Notes 10, Akron: University of Akron, p.10-10.

Compressive normal stress (Pv) in silos can be calculated by the Janssen equation:

expP K gg D

DK z

4 1 4c

V nt n= − −d n= G

where

r = granular bulk density

μ = solids coefficient of friction

D = silo diameter

K = lateral pressure ratio, where PW = K PV (Janssen's assumption that vertical normal stress is proportional to the lateral normal stress)

z = bed depth at which pressure is being measured

Sources: Don McGlinchey, editor, Bulk Solids Handling: Equipment Selection and Operation, and J.M. Rotter, Silo and Hopper Design for Strength, Oxford: Blackwell Publishing Ltd., 2008.

Chapter 4: Fluids

NCEES 145

4.4.6.2 Pneumatic TransportPneumatic transport (or pneumatic conveying) is using gas to transport particulate solids through a pipeline (such as flour, pulverized coal, powdered clay).

Flow Regimes:

Dilute Phase—Particles are fully suspended at loadings less than 1%.

Dense Phase—Particles are not suspended (or periodically suspended) with loadings greater than 20%.

Pressure Systems

BLOWER

BLOWER

POSITIVE PRESSURE SYSTEM (PUSH)

DISCHARGE HOPPERS

DISCHARGEHOPPER

NEGATIVE PRESSURE SYSTEM (PULL)

FILTERFEED

HOPPER

FEED HOPPERS

FILTER

FILTER

FILTER

A “PUSH-PULL” SYSTEM USES BLOWERS TO SIMULTANEOUSLYPUSH (POSITIVE PRESSURE) AND PULL THE SOLIDS (NEGATIVE PRESSURE)

Characteristics of Pneumatic Conveying Flow RegimesDilute Phase Dense Phase

High velocity Low velocityParticles subject to attrition Low particle attritionLow pressure High pressureLow cost/simple operation Complex operationLow loadings High solids loading


146 NCEES

Flows in Pneumatic Transport

DILUTE PHASE

DILUTE PHASE

DILUTE PHASEFLOW

CONTINUOUS DENSEPHASE FLOW

PLUG FLOW

DISCRETE PLUG FLOW

DUNE FLOW

DISCONTINUOUS DENSEPHASE FLOW

SALTATING FLOW

DENSE PHASE

PRES

SURE

GRA

DIEN

T

HIGH VELOCITYPARTICLES SUBJECT TO ATTRITIONLOW PRESSURELOW COST / SIMPLE OPERATIONLOW LOADINGS

DENSE PHASE

CHARACTERISTICS OF PNEUMATICCONVEYING FLOW REGIMES

LOW VELOCITYLOW PARTICLE ATTRITIONHIGH PRESSURECOMPLEX OPERATIONHIGH SOLIDS LOADING

GAS VELOCITY

Definitions

Saltation—Settling of solid particles in the bottom of the pipe during dilute phase pneumatic transport

Superficial gas velocity u g_ i—The gas volumetric flow Vgo` j divided by the pipe cross-sectional area (A): u A

Vg

g=o

Superficial solids velocity u s^ h—The solids volumetric flow Vso_ i divided by the pipe cross-sectional area: u A

Vs

s=o

where Vm

s sst=o o

, with andms sto as the mass flow rate and density of the solid particles, respectively

Actual gas velocity (ug): u A

Vg

gf

=o

where e = void fraction

Actual particle velocity (us): u

AV1ss

f=

−o

_ i

Chapter 4: Fluids

NCEES 147

Relationships

In vertical pipes, the minimum gas velocity (umin) to suspend particles is when the net upward force on the bed provided by the gas equals the net weight of the solids bed (see Section 4.3.6.7):

F WB B=

Practical minimum gas velocity:

u u C

g D2 2 3

4 1min

D

gstt

= =−te o

where ReC 24D =

Mass flowrate of the solid particles:

m Au 1s s sf t= −o _ i

Mass flowrate of the gas:

m Aug gg ft=o

Solids loading (R):

R mmgs= oo

Concentration (volume fraction) of solids:u

u us

sC V VV

ss g

s

g= + =

+o o

o

Dilute phase pressure drop: The total pressure drop is the sum of the contributions from the carrier gas pressure drop, acceleration of the solid particles, the friction of the solid particles against the pipe wall and fittings, the lift-ing of the solid particles through the vertical sections, and miscellaneous factors.

P P P P P P Pgf sa sf sb sv miscD D D D D D D= + + + + +` j

Carrier gas pressure drop ( DPgf ): For the purpose of this equation, compressible flow equations are not used. Treat the gas as an incompressible fluid:

P g Df Lu2gf

c

g g2t

D =

Acceleration of solids pressure drop (DPsa):

P Agm u

sac

s sD = o

where A = pipe cross-sectional area


148 NCEES

Solids friction in straight pipe pressure drop (DPsf ):

P D gR u L2sf

c

s g g actual2m t

D =

where

ls = solids friction factor (if unknown, assume 0.2)

R = solids loading

Lactual = actual length of pipe (not equivalent length)

Solid friction in bends pressure drop (DPsb):

P L LP

sb eqactual

sDD= e o

Vertical lift pressure drop (DPsv):

P g uR g Z u

sv c s

g gtD =

where Z = total length of vertical pipe where the flow is upwards

Miscellaneous pressure drop (DPmisc):

where Pmisc /D additional pressure drop for other components, interferences, and other special conditions

Saltation velocity ( usalt ):

Rg Du

101 salta

b

= f p (Rizk correlation)

where

D = inside diameter of conveying pipe

a = 1440 Dp + 1.96 (SI units)

= 439 Dp + 1.96 (U.S. units)

b = 1100 Dp + 2.5 (SI units)

= 325 Dp + 2.5 (U.S. units)

Dp = mean particle diameter

Chapter 4: Fluids

NCEES 149

4.4.7 Cyclone

Cyclone SeparatorFINES + AIR

IMMERSION TUBE(OR GAS OUTLET TUBE)

FEED(DIRTY AIR)

CONICALSECTION

CYCLONEBODY

De

s

a

Dh

z

H

B

TAILS

b

where

a = height of tangential inlet

b = width of tangential inlet

De = diameter of immersion tube

s = immersion length of outlet tube

D = cyclone diameter

h = length of cylindrical section

z = length of conical section

H = cyclone height

B = diameter of tail outlet

Particle Removal Efficiency

DD

1

1

p

pc2h =

+ f p

where

Dpc = diameter of particle collected with 50% efficiency

Dp = diameter of particle of interest

h = fractional particle collection efficiency


150 NCEES

Effective Number of Turns N H h z1

2e = +c mwhere

Ne = number of effective turns the gas makes in the cyclone

h = length of body of cyclone

z = length of cone of cyclone

Cyclone 50% Particle Efficiency for Particle Diameter

DN u

b2

9.

pce i p g

0 5

r t t

n=−` j> H

where

Dpc = diameter of particle that is collected with 50% efficiency, in meters

μ = dynamic viscosity of gas

ui = inlet velocity into cyclone

rp = density of particle

rg = density of gas

Cyclone Collection EfficiencyCYCLONE COLLECTION EFFICIENCY

100

10

10.1 1

PARTICLE SIZE RATIO

CYCL

ONE

EFFI

CIEN

CY (%

)

Dpc

Dp

10

Chapter 4: Fluids

NCEES 151

Cyclone Ratio of Dimensions to Body Diameter (D) CapacityDimension High Efficiency Conventional High Throughput

Inlet height, a 0.44 0.50 0.80Inlet width, b 0.21 0.25 0.35Cylindrical section length, h 1.40 1.75 1.70Cone length, z 2.50 2.00 2.00Immersion length, s 0.50 0.60 0.85Gas exit diameter, D 0.40 0.50 0.75Tails outlet diameter, B 0.40 0.40 0.40Cyclone height, H 3.90 3.75 3.70

Source: Adapted from D.C. Cooper and F.C. Alley. Air Pollution Control: A Design Approach, 2nd ed., Illinois: Waveland Press, 1986.

4.4.8 Special Flow Applications

4.4.8.1 Submerged Orifice

Submerged Orifice Operating Under Steady-Flow Conditions

1 – 2

A A

V

h1h

h h

2

2

V A u C A g h h22 2 1 2= = −o _ iwhere u2 = velocity of fluid exiting the orifice


152 NCEES

4.4.8.2 Orifice Discharging Freely into Atmosphere

Orifice Discharging Into Atmosphere

2A0A

h

Atm

Torricelli's equation:

u gh2=

V CA gh20=o

where

h = distance from the liquid surface to the centerline of the orifice opening

A0 = cross-sectional area of flow

4.5 Flow and Pressure Measurement Techniques

4.5.1 Manometers and Barometers

4.5.1.1 Simple Manometer

Simple Manometer

z1

2zAz FLUID 2

( fluid 2)

PA

Patm

P2

P1

ρ

FLUID 1( fluid 1) ρ

P P P P gg z z z zA atm A c fluid fluid A2 2 2 1 1 1t t− = − = − − −_ _i i9 C

Chapter 4: Fluids

NCEES 153

4.5.1.2 Manometer With Multiple Fluids

Manometer With Multiple Fluids

zAPA

zBPB

z2P2 z2P2

z1P1z1P1z3P3 z3P3

FLUID 1 (ρfluid 2)

FLUID 3 (ρfluid 2)

FLUID 4 (ρfluid 4)FLUID 2 (ρfluid 2)

A

P P P P P P P P P P

P P gg z z z z z z z z

A B A B

A B c fluid A fluid fluid fluid B

1 1 2 2 3 3

1 1 2 2 1 3 3 2 4 3t t t t

− = − + − + − + −

− = − + − + − + −

___ _

__

_ _i

ii j

ij

j j9 C

4.5.1.3 Inclined U-Tube Manometer

Inclined U-Tube Manometer

MANOMETERFLUID

P2P1

Δ h

X

θ

sinP P g

gX g

gh

c m mc1 2 : : :t i t D− = =

where

x = difference in tube fill length

rm = density of the manometer fluid (densities of the fluids on each side of the manometer are equal)

q = angle of inclination (horizontal = 0°)


154 NCEES

4.5.1.4 BarometersAnother device that works on the same principle as the manometer is the simple barometer.

P P P gg h

P gg h

atm A v c B c

t t= = + = +

where Pv = vapor pressure of the barometer fluid

BarometerPV PB

PA

h ρ

4.5.2 Flow Measurement Devices (Summary)

Flow Measurement DevicesClass Meter Type Description Advantages Drawbacks

Mec

hani

cal Rotary

pistonRotary piston spins within a chamber of known volume. For each rotation, an amount of fluid passes through the piston chamber. The rotations are counted and the flow rate is determined from the rate of rotations.

• Accurate; suitable for fuel metering

• Suitable for low volume metering and laboratory or bench scale testing

• High permanent pressure drop at high flows

• Clear liquids only• High cost

Gear Two rotating gears with synchronized, close-fitting teeth. A fixed quantity of liquid passes through the meter for each revolution. Permanent magnets in the rotating gears transmit a signal to a transducer for flow measurement.

OPERATION OF AN OVAL GEAR METER

Operation of an oval gear meter

• Accurate; suitable for fuel metering

• Suitable for low volume metering and laboratory or bench scale testing

• High permanent pressure drop at high flows

• Clear liquids only• High cost

Chapter 4: Fluids

NCEES 155

Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks

Mec

hani

cal (

cont

'd) Nutating

DiskAlso known as a wobbly plate meter. Fluid enters a chamber of known volume. When the chamber is filled, the fluid is released, which causes the disk to perform a nutating action (wobble in a circular path without actually spinning on its axis). The motion is detected by either gearing or magnetic transducers. The flow rate is determined from the rate of motions.

SHAFTHOLE

NUTATING DISK

OUTLETINLET

• Accurate and repeatable; used for water service metering

• Good for hot liquids

• Accuracy is ad-versely affected by viscosities below the meter's desig-nated threshold

Helical Counter-rotation of the gears carries known volumes of liquid axially down the length of the gears. The rotation rate is measured using sensors, which in turn correlates to flow rate.

Source: Flowserve Corp., Irving, TX

• Used for heavy and high-viscous liquids

• Highest accuracy of any positive displacement flow-meter

• Can only measure liquids

• Low corrosion al-lowance

• Cannot handle abrasive fluids

Rotameter (variable area)

Fluid flows upward through a clear tapered tube and suspends a bob. The higher the flow rate, the higher the bob suspends in the tube. The bob is the indicator and the reading is obtained from the scale marked on the tube.

FLOW

FLOW

PIPE

TAPERED TUBE

BOB

• Simple operation with few moving parts and no exter-nal power source

• Inexpensive and widely available

• Accurate provided the fluid properties remain unchanged

• Resistant to shock and chemical ac-tion

• Cannot be read by machine

• Must be mounted vertically

• Changes in fluid properties gives erroneous results

• Not suited for large pipes (< 6 inches)

• Readout uncertainty near bottom of the scale

• Some fluids may obscure reading.


156 NCEES


Mec

hani

cal (

cont

'd) Turbine (or

Woltmann Type)

Fluid flows past a turbine wheel positioned in the center of the pipe with the shaft in line with the pipe. The rotational speed is proportional to the flow rate. Shaft rotation is detected electronically.

FLOW

METERHOUSING

TURBINEROTORSUPPORT

ELECTRONICPICKUP

• Simple and du-rable structure; can be installed vertically or hori-zontally

• Can be designed to detect flow in either direction

• Operates under a wide range of temperatures and pressures

• Low pressure drop across the flow meter

• Effective in ap-plications with steady, high-speed flows

• Can be used for gasses but not suit-able for steam

• Cannot tolerate cavitation

• Accuracy ad-versely affected by entrained gas

• Sensitive to chang-es in fluid viscosity

• Long straight runs of pipe upstream and downstream of the meter are needed

• Bearings are prone to wear (though some are provided “bearingless”)

• Not suitable for steam

Paddle Wheel Type

Fluid flows past a paddle wheel positioned off-center of the pipe with the shaft perpendicular with the pipe. The rotational speed is proportional to the flow rate. Shaft rotation is detected electronically.

FLOW ROTATION

PADDLE WHEEL

DETECTOR(MOUNTED

EXTERNALLY)

Other meters in this class: Single Jet Multi Jet Pelton Wheel

• Simple and du-rable structure; can be installed vertically or hori-zontally

• Easy installation into existing sys-tems for insertion models

• Can be designed to detect flow in either direction

• Operates under a wide range of temperatures and pressures

• Low pressure drop across the flow meter

• Effective in ap-plications with steady, high-speed flows

• Requires a full pipe of liquid

• Not suitable for steam

• Bearings are prone to wear

Chapter 4: Fluids

NCEES 157


Pres

sure Venturi The meter constricts the fluid flow and sensors

measure the differential pressure before and within the constriction. The differential pressure is then converted to a corresponding flow rate.

FLOW

PRESSURE MEASUREMENT

• Highly accurate over a wide range of flows

• No moving parts• Low pressure drop

• Flow must be derived from pres-sure drop

• Pipe must be full (mostly used for liquid service)

• Occupies space ( DL of approxi-

mately 50)• Cannot measure

fluids in reverse flow

Orifice Plate (also square-edge orifice plate)

Flow is restricted using a plate with a hole drilled through it. Sensors measure the differential pres-sure before and after the meter (two tap configura-tions are shown). The differential pressure is then converted to a corresponding flow rate.

FLOW

dP MEASUREMENT(FOR FLANGE TAP OPTION)

dP

dP

dP MEASUREMENT(FOR VENA CONTRACTATAP OPTION)

Note: Orifices may be drilled in the middle of the plate (concentric) or off-center (eccentric) to ac-commodate certain fluid types and flow regimes. Orifices may also be round or segmented.

• Accurate over a wide range of flows, but not suitable for trade use (2–4% of full scale)

• No moving parts• Low cost; price

does not drama-tically increase with pipe size

• Low maintenance (orifice plates can be replaced dur-ing maintenance operations)

• Easy to convert to different applica-tions or fluids by replacing the orifice plate

• In common use


• Accuracy reduced at low flows

• Plate materials prone to wear and corrosion, which adversely effects accuracy

• Accuracy effected by high-viscous fluids

• Moderate to high permanent pres-sure drop

• Pipe must be full (for liquids)


158 NCEES


Pres

sure

(con

t'd) Nozzle Similar to a venturi meter, but the inlet section is

in the shape of an ellipse and there is no exit sec-tion.

FLOW

dP MEASUREMENTdP

• More accurate than orifice plates

• High flow capa-city and high velocity applica-tions

• Less susceptible to wear and corro-sion than orifice plates

• Can operate in higher turbulence

• Tolerant of fluids containing sus-pended solids

• Less expensive than the venturi meter

• Physically smaller than the venturi meter

• Can indicate a reverse-flow condition


• More expensive than orifice plates

• Takes up slightly more room than orifice plates

• Higher permanent pressure drop than venturi meters

• Pipe must be full (for liquids)

Dall Tube Similar to the venturi meter but more compact at the expense of some loss in accuracy and addi-tional permanent pressure loss.

FLOW

dP

• Similar perfor-mance as the venturi meter

• Shorter length than the venturi meter

• Low unrecover-able pressure loss

• Accurate to within 1% of full scale

• More expensive than orifice plates or flow nozzle meters

• Sensitive to turbu-lence

• More complex to manufacture

• Accuracy depen-dent on actual flow data

• Cannot indicate a reverse-flow condition

Chapter 4: Fluids

NCEES 159


Pres

sure

(con

t'd) Wedge Similar in principle to the orifice meter, a wedge

placed in the flow stream creates the differential pressure element. The fluid is forced downward, similar to a segmented orifice plate, but is guided along a sloping wedge shape rather than a sharp edge. The differential pressure is then converted to a corresponding flow rate.

FLOW

WEDGE

dP

• Well suited for sludge, slurry, or high-viscous fluid service

• Differential pres-sure to flow rate dependent on em-pirical data unique to each model and application

• High permanent pressure drop

Pitot Tube The pitot tube is primarily used for gas or air service. The Pitot tube measures the total pres-sure (dynamic and static pressures combined). The static tube measures the static pressure only. The difference between the two measurements reveals that the dynamic pressure is converted into flow rate.

STATIC TUBE

PITOT TUBE

dP

FLOW

Note: The pitot tube (impact tube) and the static tube are sometimes provided within a single ele-ment.

• Essentially no pressure drop

• Easy to install and use

• Instrument can be removed when not in service

• Can be used to measure gas velocities and to establish a velo-city profile

• Low accuracy (dif-ferential pressure between static and dynamic is small and therefore prone to error)

• Accuracy depen-dent on placement within the flow cross-section

• Low rangeability• Requires clean

fluids (tube easily plugs)


160 NCEES


Pres

sure

(con

t'd) Annubar The annubar or averaging pitot-tube flow meter

measures the difference between the total pressure (upstream) and the static pressure (downstream) to derive the flow rate.

dP

FLOW DOWNSTREAMSENSINGPORTS

SIMPLIFIED CROSS-SECTIONOF SENSING (IMPACT) TUBE

UPSTREAMSENSINGPORTS

ANNUBAR(IMPACT TUBE)

FLOW

Note: Temperature elements can be made integral with the impact tube to provide temperature com-pensation and corrections.

• Accurate (1% of full scale)

• Compact design (sensing lines not required)

• Not suitable for dirty or viscous fluids

• Element must be centered within the pipe

Cone (or V-Cone)

A cone is inserted in the flow stream to create a differential pressure similar to a venturi meter or Dall tube meter, which is then correlated to flow rate.

FLOW

dP

• Excellent accu-racy (0.5% of full scale)

• Suitable for fluids with suspended solids

• Compact design (0–2 pipe dia-meters)

• Suitable for gas flow measurement

• Moderate perma-nent pressure drop

• Requires exten-sive calibration to achieve rated accuracy

• Must operate within rated β-ratio range

Chapter 4: Fluids

NCEES 161


The

rmal Thermal

Mass Meters

A known amount of heat is applied to the heating element. Some of this heat is lost to the flowing fluid. As flow increases, more heat is lost. The amount of heat lost is sensed using temperature el-ements (comparing the upstream and downstream values). The fluid flow is derived from the known heat input and the temperature measurements.

HEATING ELEMENT DOWNSTREAMTEMPERATUREELEMENT

UPSTREAMTEMPERATUREELEMENT

FLOW

T2T1 ==

• Used primarily for gas service (stack flow measurement and emissions monitoring)

• Low pressure drop• The temperature

and heating ele-ments come in a single element assembly for a compact design

• Detects low flows (laminar flows)

• Can be used as a velocity meter

• Results are in true mass flow

• Thermal properties of the gas must be known

• Moderate accuracy• Not for steam

service

Vort

ex Vortex Shedding

Vortices (or eddy currents) created by an obstruc-tion are detected by ultrasonic or optical transduc-ers. The rate of vortex formation and subsequent shedding caused by the bluff body or obstruction is proportional to the fluid velocity.

RECEIVINGTRANSDUCER

EDDYS (VORTICES)

TRANSMITTINGTRANSDUCER

BLUFF BODY(STRUT)

FLOWFLOW

• Can be used for liquids, gases, and steam

• Low wear• Low cost to install

and maintain• Low sensitivity to

variations in pro-cess conditions

• Stable long-term accuracy and repeatability

• Applicable to a wide range of pro-cess temperatures

• Available for a wide variety of pipe sizes

• Not suitable for low flow rates

• Minimum length of straight pipe is required upstream and downstream of the meter


162 NCEES


Mag

netic Mag Meter The operation of a magnetic flow meter or mag

meter is based upon Faraday's Law, which states that the voltage induced across any conductor as it moves at right angles through a magnetic field is proportional to the velocity of that conductor.

E u B D\ # #

where

E = voltage generated in a conductor

u = velocity of the conductor

B = magnetic field strength

D = length of the conductor

The flowmeter applies a magnetic field through the entire cross-section of the flow tube. The velocity is then determined by the meter by measuring the magnetic strength.

• Ideal for dirty water or other con-ductive fluids

• Suitable for fluids with two-phase flow

• No pressure drop (models are avail-able for full pipe bores)

• Accurate• Measures true

volumetric flow

• Does not work on nonconductive fluids (e.g., hydro-carbons)

• Expensive• Does not correlate

to mass flow until fluid or bulk slurry density is known

Ultr

ason

ic For a simple Doppler system, sound waves are used to determine the velocity of a fluid flowing in a pipe. At zero flow, the frequencies of an ultrason-ic wave transmitted into a pipe and its reflections from the fluid are the same. At flow, the frequency of the reflected wave is different because of the Doppler effect. As fluid velocity increases, the frequency shift increases linearly. A transmitter evaluates the frequency shift to determine the flow rate.

For a Transit time system, ultrasonic waves are sent and received between transducers in both directions in the pipe. At zero flow, it takes the same time to travel upstream and downstream be-tween the transducers. At flow, the upstream wave travels more slowly and takes more time than the downstream wave. As fluid velocity increases, the difference between the upstream and downstream times also increases. A transmitter evaluates the delay times to determine the flow rate.

Note: Either method can be deployed as a clamp-on unit (dry) or be installed integral to the fluid (wet).

• Sufficiently ac-curate for custody transfer

• Clamp-on systems suitable for field testing and verifi-cation of installed flow meters

• Expensive• Sensitive to stray

vibrations• Unwanted

attenuation can occur

• Fluid must be able to transmit ultra-sonic waves

Chapter 4: Fluids

NCEES 163


Impu

lse Coriolis A Coriolis flow meter uses the natural phenom-

enon in which an object begins to “drift” as it travels from or toward the center of a rotation occurring in the surrounding environment. Coriolis flow meters generate this effect by diverting the fluid flow through a pair of parallel U-tubes with an induced vibration (by an actuator, not shown) perpendicular to the flow. The vibration simulates a rotation of the pipe and the resulting Coriolis “drift” in the fluid causes the U-tubes to twist and deviate from their parallel alignment. The force producing this deviation is proportional to the mass flow rate through the U-tubes.

FLOWVIBRATIONVIBRATION

NO DEFLECTION DEFLECTION

• Suitable for highly viscous fluids

• Insensitive to tem-perature and fluid properties

• Measures mass flow rate directly

• Not accurate for gases at low flow rates

• High permanent pressure drop

4.5.3 Orifice, Nozzle, and Venturi Meters

4.5.3.1 Square-Edge Orifice Meter (Vena Contracta Taps)

FLOW

SQUARE-EDGE ORIFICE METER

d2

Re

104

0.60

0.62

0.64

0.66

0.58105 105 107 108

d2d2

2

d1

C orific

e

DISCHARGE COEFFICIENTCorifice FOR SQUARE-EDGEORIFICE METERS

d2

d1——β = = 0.7

0.60.5

0.40.2


164 NCEES

Flow Coefficient (C) and Orifice Loss Coefficient

CC

KC11orifice

4 2 4

2,

b b

b=−

−

Incompressible Flow

V C Ag P2

orificectD=o

Compressible Flow

V Y C Ag P2

orificectD=o

where Y = net expansion factor

4.5.3.2 Flow Nozzle Meter

FLOW

NOZZLE METER Re

1040.94

0.96

0.98

1.00

105 105 107 108

C orific

e

d2

d2 d1

d2

2

d2

d1——β = = 0.8

0.60.4

0.2

DISCHARGE COEFFICIENTCorifice FOR NOZZLE METERS

Flow Coefficient (C)

C

C1nozzle

4b=

−

Incompressible Flow

V C A

g P2nozzle

ctD=o

Compressible Flow

V Y C A

g P2nozzle

ctD=o


Chapter 4: Fluids

NCEES 165

4.5.3.3 Venturi Flow Nozzle MeterThe Venturi discharge coefficient is a function of the specific geometry of the meter.

FLOW

PRESSURE MEASUREMENT

Flow Coefficient (C)

C

C1venturi

4b=

−

Incompressible Flow

V C A

g P2venturi

ctD=o

Compressible Flow

V Y C A

g P2venturi

ctD=o


4.5.3.4 Pitot Tube Flow Meter

STATIC TUBE

PITOT TUBE(OR IMPACT TUBE)

FLOW

P1 P2

P1 measures the static pressure. Assuming elevation effects are negligible, P2 is the stagnation pressure:

P gu2 c

1

2t+

Therefore:

u

g P P2 c 2 1t=

−_ i


166 NCEES

4.5.3.5 Permanent Pressure Drop PERMANENT PRESSURE DROP

FLOW

P1

P 1

P 2

P 2

FLOW RESTRICTION

PERMANENTPRESSURE

DROP

P VC

P vc

P = P 2 – P 1 (P vc – P 1) (1 – 1.9 )

VENA CONTRACTA

The fraction of the orifice differential pressure that is permanently lost can be approximated by the relation, 1 – β1.9. Therefore, the permanent pressure drop for orifice meters for incompressible fluids is

P g

C Am

2 1 .c

1 9t bD = −

oc`m

j

P g C AV

2 1 .c

21 9tbD = −

oc `m jwhere

C = flow coefficient of the orifice

A = area of the orifice

Chapter 4: Fluids

NCEES 167

4.5.3.6 Weir Meters

Rectangular Weir—Suppressed V-Notch Weir (90o Notch)

H

L L

H

V C LH 23

=o V C H 25

=o

where C = 3.33 secft .0 5 where C = 2.5 sec

ft .0 5

C = 1.84 sm .0 5

C = 1.4 sm .0 5

Rectangular Weir—Contracted

H

L

.V C L H H0 2 2

3= −o _ i

where C = 3.33 secft .0 5

C = 1.84 sm .0 5

with

,secin ft or s

m

in ft or mVH L

3 3o


168 NCEES

4.6 Tables

Pipe Dimensions and WeightsWeights are based on carbon steel pipe

Pipe Size OD Identification Wall Thickness Weight Inside Diameter

inchesmm

inchesmm

Steel StainlessSteel

Scheduleinches mm ft

lbmmkg inches mmIron

PipeSchedule

No.

1/86

0.40510.3 STD

XS

104080

10S40S80S

0.0490.0680.095

1.241.732.41

0.190.240.31

0.280.370.47

0.3070.2690.215

7.826.845.84

1/48

0.5413.7 STD

XS

104080

10S40S80S

0.0650.0880.119

1.652.243.02

0.330.430.54

0.490.630.80

0.4100.3640.302

10.409.227.66

3/810

0.67517.1 STD

XS

104080

10S40S80S

0.0650.0910.126

1.652.313.20

0.420.570.74

0.630.841.10

0.5450.4930.423

13.8012.4810.70

1/215

0.84021.3

STDXS

XX

5104080160

5S10S40S80S

0.0650.0830.1090.1470.1880.294

1.652.112.773.734.787.47

0.540.670.851.091.311.72

0.801.001.271.621.952.55

0.7100.6740.6220.5460.4640.252

18.0017.0815.7613.8411.746.36

3/420

1.05026.7

STDXS

XX

5104080160

5S10S40S80S

0.0650.0830.1130.1540.2190.308

1.652.112.873.915.567.82

0.690.861.131.481.952.44

1.031.281.692.202.903.64

0.9200.8840.8240.7420.6120.434

23.4022.4820.9618.8815.5811.06

125

1.31533.4

STDXS

XX

5104080160

5S10S40S80S

0.0650.1090.1330.1790.2500.358

1.652.773.384.556.359.09

0.871.411.682.172.853.66

1.292.092.503.244.245.45

1.1851.0971.0490.9570.8150.599

30.1027.8626.6424.3020.7015.22

1-1/432

1.66042.2

STDXS

XX

5104080160

5S10S40S80S

0.0650.1090.1400.1910.2500.382

1.652.773.564.856.359.70

1.111.812.273.003.775.22

1.652.693.394.475.617.77

1.5301.4421.3801.2781.1600.896

38.9036.6635.0832.5029.5022.80

1-1/240

1.90048.3

STDXS

XX

5104080160

5S10S40S80S

0.0650.1090.1450.2000.2810.400

1.652.773.685.087.14

10.15

1.282.092.723.634.866.41

1.903.114.055.417.259.55

1.7701.6821.6101.5001.3381.100

45.0042.7640.9438.1434.0228.00

Chapter 4: Fluids

NCEES 169

Pipe Dimensions and Weights (cont'd)Weights are based on carbon steel pipe


inchesmm

inchesmm

Steel Stain-less Steel Schedule

inches mm ftlbm

mkg inches mmIron

PipeSchedule

No.

250

2.37560.3

STDXS

XX

5104080160

5S10S40S80S

0.0650.1090.1540.2180.3440.436

1.652.773.915.548.74

11.07

1.612.643.665.037.479.04

2.393.935.447.48

11.1113.44

2.2452.1572.0671.9391.6871.503

57.0054.7652.4849.2242.8238.16

2-1/265

2.87573

STDXS

XX

5104080160

5S10S40S80S

0.0830.1200.2030.2760.3750.552

2.113.055.167.019.53

14.02

2.483.535.807.67

10.0213.71

3.695.268.63

11.4114.9220.39

2.7092.6352.4692.3232.1251.771

68.7866.9062.6858.9853.9444.96

380

3.588.9

STDXS

XX

5104080160

5S10S40S80S

0.0830.1200.2160.3000.4380.600

2.113.055.497.62

11.1315.24

3.034.347.58

10.2614.3418.6

4.526.46

11.2915.2721.3527.68

3.3343.2603.0682.9002.6242.300

84.6882.8077.9273.6666.6458.42

3-1/290

4101.6 STD

XSXX

5104080

5S10S40S80S

0.0830.1200.2260.3180.636

2.113.055.748.08

16.15

3.484.989.12

12.5222.87

5.187.41

13.5718.6434.03

3.8343.7603.5483.3642.728

97.3895.5090.1285.4469.30

4100

4.5114.3

STDXS

XX

5104080120160

5S10S40S80S

0.0830.1200.2370.3370.4380.5310.674

2.113.056.028.56

11.1313.4917.12

3.925.62

10.815.0019.0222.5327.57

5.848.37

16.0822.3228.3233.5441.03

4.3344.2604.0263.8263.6243.4383.152

110.08108.20102.2697.1892.0487.3280.06

4-1/2115

5127

STDXSXX

4080

40S80S

0.2470.3550.710

6.279.02

18.03

12.5517.6332.56

18.6726.2448.45

4.5064.2903.580

114.46108.9690.94

5125

5.563141.3

STDXS

XX

5104080120160

5S10S40S80S

0.1090.1340.2580.3750.5000.6250.750

2.773.406.559.53

12.7015.8819.05

6.367.78

14.6320.8027.0632.9938.59

9.4611.5621.7730.9740.2849.1257.43

5.3455.2955.0474.8134.5634.3134.063

135.76134.50128.20122.24115.90109.54103.20


170 NCEES



inchesmm

inchesmm


inches mm ftlbm

mkg inches mmIron

PipeSchedule

No.

6150

6.625168.3

STDXS

XX

5104080120160

5S10S40S80S

0.1090.1340.2800.4320.5620.7190.864

2.773.407.11

10.9714.2718.2621.95

7.599.30

18.9928.6036.4345.3953.21

11.3113.8328.2642.5654.2167.5779.22

6.4076.3576.0655.7615.5015.1874.897

162.76161.50154.08146.36139.76131.78124.40

7175

7.625193.7

STDXSXX

40 40S80S

0.3010.5000.875

7.6512.7022.23

23.5738.0863.14

35.1056.6994.00

7.0236.6255.875

178.40168.30149.24

8200

8.625219.1

STD

XS

XX

5102030406080100120140

160

5S10S

40S

80S

0.1090.1480.2500.2770.3220.4060.5000.5940.7190.8120.8750.906

2.773.766.357.048.18

10.3112.7015.0918.2620.6222.2323.01

9.9213.4122.3824.7228.5835.6743.4351.0060.7767.8272.4974.76

14.7819.9733.3236.8242.5553.0964.6475.9290.44

100.93107.93111.27

8.4078.3298.1258.0717.9817.8137.6257.4377.1877.0016.8756.813

213.56211.58206.40205.02202.74198.48193.70188.92182.58177.86174.64173.08

9225

9.625244.5

STDXSXX

40S80S

0.3420.5000.875

8.6912.7022.23

33.9448.7781.85

50.5472.60

121.85

8.9418.6257.875

227.12219.10200.04

10250

10.75273 STD

XS

XX

5102030406080100120140160

5S10S

40S80S

0.1340.1650.2500.3070.3650.5000.5940.7190.8441.0001.125

3.404.196.357.809.27

12.7015.0918.2621.4425.4028.58

15.2118.6728.0634.2740.5254.7964.4977.1089.38

104.23115.75

22.6127.7841.7651.0160.2981.5395.98

114.71133.01155.10172.27

10.48210.42010.25010.13610.0209.7509.5629.3129.0628.7508.500

266.20264.62260.30257.40254.46247.60242.82236.48230.12222.20215.84

11275

11.75298.5

STDXSXX

40S80S

0.3750.5000.875

9.5312.7022.23

45.6060.13

101.72

67.9189.51

151.46

11.00010.75010.000

279.44273.10254.04

Chapter 4: Fluids

NCEES 171



inchesmm

inchesmm


inches mm ftlbm

mkg inches mmIron

PipeSchedule

No.

12300

12.75323.8

STD

XS

XX

2030

40

6080100120140160

5S10S

40S

80S

0.1560.1800.2500.3300.3750.4060.5000.5620.6880.8441.0001.1251.312

3.964.576.358.389.53

10.3112.7014.2717.4821.4425.4028.5833.32

21.0024.1933.4143.8149.6153.5765.4873.2288.71

107.42125.61139.81160.42

31.2435.9849.7165.1973.8679.7197.44

108.93132.05159.87186.92208.08238.69

12.43812.39012.25012.09012.00011.93811.75011.62611.37411.06210.75010.50010.126

315.88314.66311.10307.04304.74303.18298.40295.26288.84280.92273.00266.64257.16

14350

14355.6

STD

XS

10203040

6080100120140160

10S

40S

80S

0.1880.2500.3120.3750.4380.5000.5940.7500.9381.0941.2501.406

4.786.357.929.53

11.1312.7015.0919.0523.8327.7931.7535.71

27.7636.7545.6554.6263.5072.1685.13

106.23130.98150.93170.37189.29

41.3654.6967.9181.3394.55

107.40126.72158.11194.98224.66253.58281.72

13.62413.50013.37613.25013.12413.00012.81212.50012.12411.81211.50011.188

346.04342.90339.76336.54333.34330.20325.42317.50307.94300.02292.10284.18

16400

16406.4

STDXS

102030406080100120140160

10S

40S80S

0.1880.2500.3120.3750.5000.6560.8441.0311.2191.4381.594

4.786.357.929.53

12.7016.6621.4426.1930.9636.5340.49

31.7842.0952.3262.6482.85

107.60136.74164.98192.61223.85245.48

47.3462.6577.8393.27

123.31160.13203.54245.57286.66333.21365.38

15.62415.50015.37615.25015.00014.68814.31213.93813.56213.12412.812

396.84393.70390.56387.34381.00373.08363.52354.02344.48333.34325.42


172 NCEES



inchesmm

inchesmm


inches mm ftlbm

mkg inches mmIron

PipeSchedule

No.

18450

18457

STD

XS

1020

30

406080100120140160

10S

40S

80S

0.1880.2500.3120.3750.4380.5000.5620.7500.9381.1561.3751.5621.781

4.786.357.929.53

11.1312.7014.2719.0523.8329.3634.9339.6745.24

35.8047.4458.9970.6582.2393.54

104.76138.30171.08208.15244.37274.48308.79

53.3170.5787.71

105.17122.38139.16155.81205.75254.57309.64363.58408.28459.39

17.62417.50017.37617.25017.12417.00016.87616.50016.12415.68815.25014.87614.438

447.44444.30441.16437.94434.74431.60428.46418.90409.34398.28387.14377.66366.52

20500

20508

STDXS

102030406080100120140160

10S

40S80S

0.2180.2500.3750.5000.5940.8121.0311.2811.5001.7501.969

5.546.359.53

12.7015.0920.6226.1932.5438.1044.4550.01

46.1052.7878.67

104.23123.23166.56209.06256.34296.65341.41379.53

68.6178.56

117.15155.13183.43247.84311.19381.55441.52508.15564.85

19.56419.50019.25019.00018.81218.37617.93817.43817.00016.50016.062

496.92495.30488.94482.60477.82466.76455.62442.92431.80419.10407.98

22550

22559

STDXS

1020306080100120140160

10S

40S80S

0.2180.2500.3750.5000.8751.1251.3751.6251.8752.125

5.546.359.53

12.7022.2328.5834.9341.2847.6353.98

50.7658.1386.69

114.92197.60251.05303.16353.94403.38451.49

75.5586.55

129.14171.10294.27373.85451.45527.05600.67672.30

21.56421.50021.25021.00020.25019.75019.25018.75018.25017.750

547.92546.30539.94533.60514.54501.84489.14476.44463.74451.04

24600

24610

STDXS

1020

30406080100120140160

10S40S80S

0.2500.3750.5000.5620.6880.9691.2191.5311.8122.0622.344

6.359.53

12.714.2717.4824.6130.9638.8946.0252.3759.54

63.4794.71

125.61140.81171.45238.57296.86367.74429.79483.57542.64

94.53141.12187.07209.65255.43355.28442.11547.74640.07720.19808.27

23.50023.25023.00022.87622.62422.06221.56220.93820.37619.87619.312

597.30590.94584.60581.46575.04560.78548.08532.22517.96505.26490.92

Chapter 4: Fluids

NCEES 173



inchesmm

inchesmm


inches mm ftlbm

mkg inches mmIron

PipeSchedule

No.

26650

26660 STD

XS

10

2040S80S

0.3120.3750.500

7.929.53

12.70

85.68102.72136.30

127.36152.88202.74

25.37625.25025.000

644.16640.94634.60

28700

28711

STD10

2030

40S0.3120.3750.5000.625

7.929.53

12.7015.88

92.35110.74146.99182.90

137.32164.86218.71272.23

27.37627.25027.00026.750

695.16691.94685.60679.24

30750

30762

STDXS

10

2030

10S40S80S

0.3120.3750.5000.625

7.929.53

12.7015.88

99.02118.76157.68196.26

147.29176.85234.68292.2

29.37629.25029.00028.750

746.16742.94736.60730.24

32800

32813

STDXS

10

203040

40S80S

0.3120.3750.5000.6250.688

7.929.53

12.7015.8817.48

105.69126.78168.37209.62230.29

157.25188.83250.65312.17342.94

31.37631.25031.00030.75030.624

797.16793.94787.60781.24778.04

34850

34864

STDXS

10

203040

40S80S

0.3120.3750.5000.6250.688

7.929.53

12.7015.8817.48

112.36134.79179.06222.99245.00

167.21200.82266.63332.14364.92

33.37633.25033.00032.75032.624

848.16844.94838.60832.24829.04

36900

36914 STD

XS

10

2040S80S

0.3120.3750.500

7.929.53

12.70

119.03142.81189.75

176.97212.57282.29

35.37635.25035.00

898.16894.94888.60

421050

421067

3060

0.3750.500

9.5312.70

166.86221.82

248.53330.21

41.25041.000

1047.941041.60

481200

481219

3060

0.3750.500

9.5312.70

190.92253.89

284.25377.81

47.25047.000

1199.941193.60


174 NCEES

Tubing Sizes (U.S.)

Size(inches)

OD(inches)

Gauge (nominal inches)24ga 22ga 20ga 18ga 16ga 14ga 12ga 11ga 9ga 7ga 1/4" 3/8"

Inside Diameter (inches)0.022 0.028 0.035 0.049 0.062 0.083 0.109 0.120 0.148 0.180 0.250 0.375

1/4 0.2500 0.206 0.1943/8 0.3750 0.331 0.3191/2 0.5000 0.444 0.430 0.402 0.376 0.3345/8 0.6250 0.555 0.527 0.501 0.4593/4 0.7500 0.680 0.652 0.626 0.584 0.532 0.5107/8 0.8750 0.805 0.777 0.751 0.709 0.657 0.6351 1.0000 0.930 0.902 0.876 0.834 0.782 0.760

1.050 1.0500 0.980 0.952 0.926 0.884 0.832 0.8101-1/8 1.1250 1.055 1.027 1.001 0.959 0.907 0.8851-1/4 1.2500 1.180 1.152 1.126 1.084 1.032 1.0101-5/16 1.3125 1.243 1.215 1.189 1.147 1.095 1.0731-3/8 1.3750 1.305 1.277 1.251 1.209 1.157 1.1351-1/2 1.5000 1.430 1.402 1.376 1.334 1.282 1.2601-5/8 1.6250 1.555 1.527 1.501 1.459 1.407 1.3851.660 1.6600 1.590 1.562 1.536 1.494 1.442 1.420 1.3641-3/4 1.7500 1.680 1.652 1.626 1.584 1.532 1.510 1.4541-7/8 1.8750 1.805 1.777 1.751 1.709 1.657 1.635 1.5791.900 1.9000 1.830 1.802 1.776 1.734 1.682 1.660 1.604

2 2.0000 1.930 1.902 1.876 1.834 1.782 1.760 1.704 1.6402-1/4 2.2500 2.152 2.126 2.084 2.032 2.010 1.9542-3/8 2.3750 2.277 2.251 2.209 2.157 2.135 2.079 2.0152-1/2 2.5000 2.402 2.376 2.334 2.282 2.260 2.204 2.1402-7/8 2.8750 2.751 2.709 2.657 2.635 2.579 2.515

3 3.0000 2.902 2.876 2.834 2.782 2.760 2.704 2.6403-1/8 3.1250 3.001 2.959 2.907 2.885 2.829 2.7653-1/2 3.5000 3.376 3.334 3.282 3.260 3.204 3.1403-3/4 3.7500 3.584 3.532 3.510 3.454 3.390

4 4.0000 3.834 3.782 3.760 3.704 3.6404-1/2 4.5000 4.334 4.282 4.260 4.204 4.140 4.000

5 5.0000 4.834 4.782 4.760 4.704 4.640 4.5006-1/4 6.2500 6.010 5.890 5.750 5.500

Chapter 4: Fluids

NCEES 175

Tubing Sizes (Metric)

Size OD(mm)

Gauge (nominal mm)24ga 22ga 20ga 18ga 16ga 14ga 12ga 11ga 9ga 7ga 1/4" 3/8"

Inside Diameter (mm)0.600 0.700 0.900 1.300 1.600 2.100 2.800 3.100 3.800 4.600 6.400 9.600

1/4" 6.4 5.2 5.03/8" 9.5 8.3 8.11/2" 12.7 11.3 10.9 10.1 9.5 8.55/8" 15.9 14.1 13.3 12.7 11.73/4" 19.1 17.3 16.5 15.9 14.9 13.5 12.97/8" 22.2 20.4 19.6 19.0 18.0 16.6 16.01" 25.4 23.6 22.8 22.2 21.2 19.8 19.2

1.050" 26.7 24.9 24.1 23.5 22.5 21.1 20.51-1/8" 28.6 26.8 26.0 25.4 24.4 23.0 22.41-1/4" 31.8 30.0 29.2 28.6 27.6 26.2 25.6

1-5/16" 33.4 31.6 30.8 30.2 29.2 27.8 27.21-3/8" 35.0 33.2 32.4 31.8 30.8 29.4 28.81-1/2" 38.1 36.3 35.5 34.9 33.9 32.5 31.91-5/8" 41.3 39.5 38.7 38.1 37.1 35.7 35.11.660" 42.2 40.4 39.6 39.0 38.0 36.6 36.0 34.61-3/4" 44.5 42.7 41.9 41.3 40.3 38.9 38.3 36.91-7/8" 47.7 45.9 45.1 44.5 43.5 42.1 41.5 40.11.900" 48.3 46.5 45.7 45.1 44.1 42.7 42.1 40.7

2" 50.8 49.0 48.2 47.6 46.6 45.2 44.6 43.2 41.62-1/4" 57.2 54.6 54.0 53.0 51.6 51.0 49.62-3/8" 60.4 57.8 57.2 56.2 54.8 54.2 52.8 51.22-1/2" 63.5 60.9 60.3 59.3 57.9 57.3 55.9 54.32-7/8" 73.1 69.9 68.9 67.5 66.9 65.5 63.9

3" 76.2 73.6 73.0 72.0 70.6 70.0 68.6 67.03-1/8" 79.4 76.2 75.2 73.8 73.2 71.8 70.23-1/2" 88.9 85.7 84.7 83.3 82.7 81.3 79.73-3/4" 95.3 91.1 89.7 89.1 87.7 86.1

4" 101.6 97.4 96.0 95.4 94.0 92.44-1/2" 114.3 110.1 108.7 108.1 106.7 105.1 101.5

5" 127.0 122.8 121.4 120.8 119.4 117.8 114.26-1/4" 158.8 152.6 149.6 146.0 139.6


176 NCEES

177

5 MASS TRANSFER



A Area ft2 or in2 m2 A Absorption factor dimensionless

a Effective interfacial mass-transfer area per unit volumeftft3

2

mm3

2

B Bottom product flow rate hrlb mole

smol

c Concentration ftlb mole

3 mmol

3

cp Heat capacity lbm FBtu-c kg K

Js Km2

2

: :=

D Distillate flow rate hrlb mole

smol

DAB Mass diffusivity (diffusion coefficient)hrft2

sm2

D, d Diameter ft or in. mE Efficiency dimensionless

F Molar feed flow hrlb mole

smol

f Ratio of vapor phase flow to feed flow (fraction vaporized) dimensionlessf Darcy friction factor dimensionless

f Fugacity of a pure component inlbf

2 Pa mN

m skg

2 2:= =

ft Fugacity of a component in a mixture inlbf

2 Pa mN

m skg

2 2:= =


178 NCEES


G Gas flow rate (stripper/absorber) hrlb mole

smol

GS Gas flow rate, solute-free basis hrlb mole

smol

g Gravitational accelerationsecft

2 sm2

gt Molar Gibbs free energy lb moleBtu

molJ

H Henry’s Law constant inlbf

2 Pa mN

m skg

2 2:= =

HD Heat input hrBtu

W sJ

skg m

3

2:= =

h Height ft or in. mh Head loss, pressure drop ft or in. m

h Specific enthalpy lbmBtu kg

Jsm2

2

=

ht Molar specific enthalpy lb moleBtu

molJ

hD Specific enthalpy change lbmBtu kg

Jsm2

2

=

hvapD Heat of vaporization lbmBtu

kgJ

sm2

2

=

HTU Height of a transfer unit ft or in. mj Colburn Factor dimensionless

jA Molar flux of component A per area ft hrlb mole-2 m s

mol2 :

K Distribution coefficient for phase equilibrium dimensionless

k Mass transfer coefficient hrft

sm

kc Convective mass transfer coefficient hrft

sm

L Liquid flow (for a flash, in a column, stripper, or absorber) hrlb mole

smol

LS Liquid flow rate, solute-free basis hrlb mole

smol

l Length, distance ft or in. m

m Mass lbm kgm General phase equilibrium coefficient dimensionlessm Slope of the operating line or slope of the equilibrium line dimensionless

MW Molecular weight lb molelbm

molkg

N Number of stages dimensionlessn Number of moles lb mole mol

Chapter 5: Mass Transfer

NCEES 179


no Molar flow per area ft hrlb mole-2 m s

mol2 :

NTU Number of transfer units dimensionless

P Pressure inlbf

2 Pa mN

m skg

2 2:= =

Pc Critical pressure inlbf

2 Pa mN

m skg

2 2:= =

Pr Reduced pressure dimensionless

P* Three-phase equilibrium pressure inlbf

2 Pa mN

m skg

2 2:= =

p Partial pressure inlbf

2 Pa mN

m skg

2 2:= =

psat Saturation pressure, or vapor pressure inlbf

2 Pa mN

m skg

2 2:= =

/ Poynting correction factor dimensionless

q Ratio of liquid phase flow to feed flow dimensionless

Qo Heat duty hrBtu W s

Js

kg m3

2:= =

q Ratio of liquid phase flow to feed flow (fraction not vaporized) dimensionless

R Reflux ratio dimensionless

R Universal gas constant lb mole RBtu

-c mol KJ:

S Boil-up ratio dimensionlessS Stripping factor dimensionlessT Temperature °R or °F K or °CTc Critical temperature °R or °F K or °CTr Reduced temperature dimensionless

u Velocity secft s

m

V Volume ft3 m3

V Vapor flow (for a flash, in a column, stripper, or absorber) hrlb mole

smol

vt Molar volume lb moleft3

molm3

v Specific volume lbmft3

kgm3

vD Specific volume change during phase change lb moleft3

molm3

X Mole ratio in liquid phase (solute-free basis) dimensionlessx Mole fraction in liquid phase dimensionlessY Mole ratio in vapor phase (solute-free basis) dimensionless


180 NCEES


y Mole fraction in vapor phase dimensionlessZ Compressibility factor dimensionlessz Mole fraction in the feed dimensionlessz Distance or length ft or in. m

a Interfacial area per unit volumeftft3

2

mm

3

2

aij Relative volatility for components i and j dimensionless

d Film thickness ft or in. mg Activity coefficient dimensionless

g Surface tension inlbf m

Nskg2=

e Void fraction dimensionless

m Dynamic viscosity seccP ftlbmor - Pa s m s

kg: :=

r Density ftlbm

3 mkg

3

zFugacity coefficient of a pure component in the vapor phase dimensionless

ztFugacity coefficient of a component in a mixture in the vapor phase dimensionless

dz Volume fraction of the dispersed phase (holdup) dimensionless

5.2 Phase Equilibria

5.2.1 Phase Equilibrium Applications

5.2.1.1 Distribution of Components Between Phases in a Vapor/Liquid EquilibriumAssume Dalton’s Law and Raoult’s Law apply. The distribution coefficient is defined as:

K xy

Pp sat

i ii i= =

where Ki = distribution coefficient for component i

The relative volatility is defined as:

KK

y xy x

ij j

ij i

i ja = =

where aij = relative volatility for components i and j

For a binary system, the following expressions may be derived:

( ) ( )y xx

K x K KK x

1 111 12

1 12

2 1 1 2

1 1aa= + − = + −

( ) ( )x yy

K y K KK y

111 1 1

1

1 1 2 1

2 1

2 2a a= + − = + −


NCEES 181

5.2.1.2 Dew PointThe dew point is defined as the point where the vapor reaches saturation and the liquid phase begins to form. It may be determined by iterative calculations from one of the following three relationships, given the vapor composition and either pressure or temperature:

or orx Ky

x py P

P

py1 1 1

i

n n n

sat

n

ni i

i

ii

i i

i

i

isati

i1 1 1 1

1

= = = = == = = =

= f p/ / / /

/

If ,Ky

1>n

i

i

i 1=/ increase temperature or decrease total pressure.

If ,Ky

1<n

i

i

i 1=/ decrease temperature or increase total pressure.

5.2.1.3 Bubble PointSimilarly, the bubble point is defined as the temperature/pressure combination in which the first bubble of vapor is formed in a liquid. It may be determined by iterative calculations from one of the following three relationships, given the liquid composition and either pressure or temperature:

or ory K x y Px p

P x p1 1,,

n n nsat

n

sat

n

ii

i ii

ii

i i

ii i

i1 1 1 1 1= = = = =

= = = = =/ / / / /

If ,K x 1>

n

i ii 1=/ decrease temperature or increase total pressure.

If ,K x 1<n

i ii 1=/ increase temperature or decrease total pressure.

5.2.1.4 Single-Stage FlashA single-stage flash determines the distribution of components between the liquid and vapor phase. It may be determined by iterative calculations from one of the following two relationships, given the feed composition, the relative proportions of vapor and liquid resulting from the flash, and either pressure or temperature:

( ) ( )orx f Kz

y f Kz K

1 1 1 1 1 1n n n n

ii i

i

ii

i i

i i

i1 1 1 1= + − = = + − =

= = = =/ / / /

where

zi = mole fraction of component in the feed

f = ratio of vapor phase flow to the feed flow

The lever rule may be applied to binary single-stage flash calculations as follows:

FV f y x

z x

FL f y x

y z1

i i

i i

i i

i i

= = −−

= − = −−

F, zi, fi

L, xi

V, yi

T, Ptot


182 NCEES

5.2.2 Diffusion

5.2.2.1 Fick’s Law of Diffusion: Molar Flux j D dz

dcA AB

A= −

Mass transport due to diffusion and bulk flow:

( )n n x j n n x c D dzdx

A A A A B A ABA= + = + −o o o o

( )n n x j n n x c D dzdx

B B B A B B BAB= + = + −o o o o

where

nAo = molar flow of species A

no = bulk flow

Rules of Thumb for Diffusion Coefficients at 25°C

secftDAB

2c msmDAB

2c mIn GasesAir 0.43 × 10–4 – 2.4 × 10–4 0.4 × 10–5 – 2.2 × 10–5

Hydrogen 1.8 × 10–4 – 8.1 × 10–4 1.7 × 10–5 – 7.5 × 10–5

Carbon dioxide 0.32 × 10–4 – 1.7 × 10–4 0.3 × 10–5 – 1.6 × 10–5

In LiquidsGases in water 0.75 × 10–8 – 2.2 × 10–8 0.7 × 10–9 – 2.0 × 10–9

Acids in water 1.3 × 10–8 – 3.2 × 10–8 1.2 × 10–9 – 3.0 × 10–9

Organics in water 0.43 × 10–8 – 1.5 × 10–8 0.4 × 10–9 – 1.5 × 10–9

In organic solvents 1.6 × 10–8 – 3.2 × 10–8 1.5 × 10–9 – 3.0 × 10–9

5.2.2.2 Integrated Forms of Fick’s Law of Diffusion

Steady-State Equimolar Counterdiffusion of Two Components (No Bulk Flow, DAB = DBA, Ideal Gas):

( ) ( )n

Dc c

c Dx x, ,A

ABA A i

ABA A id d

= − = −o

For an ideal gas:

( ) ( )n RTD

p p RTD P

y y, ,AAB

A A iAB

A A id d= − = −o

where

i = conditions at the interface

d = film thickness

Steady-State Diffusion of A Through a Stagnant Film (n 0B =o )

lnn

c Dxx

11

,A

AB

A i

Ad

= −−

o f p


NCEES 183

where

xA,i = concentration of A at the interface

xA = concentration of A at distance z from the interface

Concentration profile:

ln lnxx z

xx

11

11

, ,

,

A i

A

A i

A bd−

−= −

−f fp pwhere

xA,b = concentration of A in the bulk fluid

z = distance from the interface

For an ideal gas:

lnn RTD P

yy

RTD P

yy y

11

,

,A

AB

A i

A ABlm

A A i

d d= −

−=

−o f p

ln lny

yy

y yp

P pP p

p p

11

,

,

,

,lm

A i

A

A A ilm

A i

A

A A i=

−−−

=

−−

−` `j j

where

ylm = logarithmic mean of the mole fractions in the gas phase and at the interface

plm = logarithmic mean of the partial pressures in the gas phase and at the interface

For diffusion of one component through a multicomponent mixture, the equation above with an effective diffusion coefficient can be used:

DDy

y1,A mix

Aj

jj A

A=−

!/

Definitions of the Mass-Transfer CoefficientSystem Mole Fraction Concentration Pressure

Equimolar counter-diffusion, liquidn k x

kc D

A A

AB

x

x d

D=

=

o n k c

kD

A A

AB

c

c d

D=

=

o

Equimolar counter-diffusion, ideal gasn k y

k RTD P

A A

AB

y

y d

D=

=

o n k c

kD

A A

AB

c

c d

D=

=

o n k p

k RTD

A G A

GABd

D=

=

o

Diffusion through a stagnant film, liquidn k x

k cc D

A A

lm

AB

x

x d

D=

=

l

l

o n k c

k cD

A A

lm

AB

c

c d

D=

=

l

l

o

Diffusion through a stagnant film, ideal gasn k y

k RT yD P

A A

lm

AB

y

y d

D=

=

l

l

o n k c

k cD

A A

lm

AB

c

c d

D=

=

o n k p

k RT pD

A A

lm

AB

G

G d

D=

=

l

l

o

Diffusion through a stagnant film, ideal gas, mass-basis

m k y

k RT yD P MW

A A

lm

AB A

y

y d

D=

=

l

l

o


184 NCEES

where ln

cc cc c

c clm

A Ai

Ao Ai

Ao A=

−−

−

kc = mass-transfer coefficient for liquid (concentration basis)

kG = mass-transfer coefficient for gas (pressure basis)

kx = mass-transfer coefficient for liquid (mole fraction basis)

ky = mass-transfer coefficient for gas (mole fraction basis)

kc' = mass-transfer coefficient for liquid (concentration basis), corrected for inert component

kG' = mass-transfer coefficient for gas (concentration basis), corrected for inert component

kx' = mass-transfer coefficient for liquid (mole fraction basis), corrected for inert component

ky' = mass-transfer coefficient for gas (mole fraction basis), corrected for inert component

5.2.2.3 Convective Mass TransferReynolds analogy between momentum, heat, and mass transfer with Colburn correction:

j Gk

D

j c Gh

kc

/

/

MM

G

AB

Hp

p

2 3

2 3

tn

n

=

=

d

d n

n

For flow through straight tubes and across plane surfaces:

j jf8M H= =

For turbulent flow around cylinders:

j jf8M H #=

where

f = Darcy friction factor

G = mass velocity in ft hrlbm-2

or m skg2 :

GM = molar mass velocity (same as nAo )

h = heat-transfer coefficient in hr ft FBtu- -o2 or

m KW2 :

jH = Colburn heat-transfer factor

jM = Colburn mass-transfer factor

k = thermal conductivity in hr ft FBtu- -o or m K

W:

kG = gas-phase mass-transfer coefficient


NCEES 185

Other correlations for the mass-transfer coefficient:

Mass Transfer1 for Simple SituationsFluid Motion Range of Conditions Equation

Inside circular pipes

Re = 4000–60,000 Sc = 0.6–3000

jM = 0.023 Re–0.17 Sh = 0.023 Re0.83 Sc1/3

Re = 10,000–400,000 Sc > 100

jM = 0.0149 Re–0.12 Sh = 0.0149 Re0.88 Sc1/3

Unconfined flow parallel to flat plates2

Transfer begins at leading edge Rex < 50,000

jM = 0.664 Rex–0.5

Rex = 5 × 105–3 × 107

Pr = 0.7–380 . Pr PrPrNu Re0 037 . .

.

xi

0 800 43 0

0 25= e o

Rex = 2 × 104–5 × 105

Pr = 0.7–380

Between above equation and

. Pr PrPr

Nu Re0 0027 ..

xi

00 43 0

0 25= e o

Confined gas flow parallel to a flat plate in a duct Ree = 2600–22,000 jM = 0.11 Ree

–0.29

Liquid film in wetted-wall tower, transfer between liquid and gas

4nC = 0–1200

ripples suppressedSee note 4.

4nC = 1300–8300 ( . )Sh Sc1 76 10 4 .

.51 506

0 5# nC= − c m

Perpendicular to single cylinders

Re = 400–25,000 Sc = 0.6–2.6 .G

k PSc Re0 281. .

M

G 0 56 0 4= l^ hRel = 0.1–105 Pr = 0.7–1500 . . . PrNu Re Re0 35 0 34 0 15. . .0 5 0 58 0 3= + +l l^ ^h h8 B

Past single spheres Re Sc .0 5ll = 1.8–600,000 Sc = 0.6–3200

.Sh Sh Re Sc0 347 . .0

0 5 0 62= + ll_ i

. . ( ). . ( )

Sh Gr Sc Sc Gr ScGr Sc Gr Sc

2 0 0 0254 102 0 0 569 10<

. .

.

M M

M M0 0 333 0 244 8

0 250 8

2=

++* 4

Through fixed beds of pellets3

Rell = 90–4000 Sc = 0.6

.j j Re2 06 .M H

0 575f= = −

ll^ h

Rell = 5000–10,300 Sc = 0.6

. .j j Re0 95 20 4 .M H

0 815f= = −

ll^ h

Rell =0.0016–55 Sc = 168–70,600

.j Re1 09 /M

2 3f= −

ll^ h

Rell = 5–1500 Sc = 168–70,600

.j Re0 250 .M

0 31f= −

ll^ h

1. Average mass-transfer coefficients throughout, for constant solute concentrations at the phase surface. Generally, fluid properties are evaluated at the average conditions between the phase surface and the bulk fluid. The heat-mass-transfer analogy is valid throughout.

2. Mass-transfer data for this case scatter badly but are reasonably well represented by setting jM = jH.


186 NCEES

3. For fixed beds, the relation between e and dp is –

a d6 1

p

f=^ h

, where a is the specific solid surface, surface per volume of bed. For mixed sizes:

d

n d

n dp

i pii

i piin

n

2

1

3

1=

=

=

/

/

4. For small rates of flow or long contact times:

.Dk

Sh 3 41,

AB

L avav .

d=

For large Reynold numbers of short contact times:

k l

D6,l av

AB21

rtdC= e o

Sh l Re Sc23

av21

rd= c m

Total absorption rate from the average kL:

N lu

c c k c c, , , ,A avy

A l A L av A i A M0d

= − = −r

r r` `j j

ln

c c

c c

c c

c c c c,

, ,

,

, , ,A i A M

A i A l

A i A

A i A A i A l

0

0− =

−

−

− − −r

r

r` `

``

`j jjj

jR

T

SSSSSSS

V

X

WWWWWWWwhere

a = specific surface of a fixed bed of pellets, pellet surface/volume of bed

cA,i = concentration of A at the interface

cA0 = concentration of A at the approach, or initial, value

c A = bulk-average concentration of A

c ,A l = bulk-average concentration of A across length l

DAB = molecular diffusivity of A in B

dc = diameter of a cylinder

de = equivalent diameter of a noncircular duct = 4 (cross-sectional area)/perimeter

dp = diameter of a sphere; for a nonspherical particle, diameter of a sphere of the same surface as the particle

G = mass velocity

GrM = Grashof number for mass transfer gl3 2

ttntD d n

k = mass-transfer coefficient

kl,av = average mass-transfer coefficient across length l

l = length


NCEES 187

NA,av = average mass-transfer flux of A at, and relative to, a phase boundary

ni = a number, demensionless

Nu = Nusselt number khd

Pr = Prandtl number k

cpn

Pr0 = Prandtl number at the approach, or initial, value

Pri = Prandtl number at the interface

Re = Reynolds number dGn or lGn

Re' = Reynolds number for flow outside a cylinder d Gcn

Re'' = Reynolds number for flow past a sphere d Gpn

Ree = Reynolds number for flow in a noncircular duct d Gen

Rex = Reynolds number with x as the length dimension xGn

Sc = Schmidt number DABtn

Sh = Sherwood number Dk lAB

Sh0 = Sherwood number at the approach, or initial, value

Shi = Sherwood number at the interface

u y = bulk average velocity in the y direction (parallel to the direction of flow)

C = mass flow rate per unit width

d = thickness of a layer

e = void fraction

Source: Treybal, Robert, Mass Transfer Operations, New York: McGraw-Hill, 1987, pp. 74–75.

5.2.2.4 Mass Transfer with ReactionConsider a reaction between a dissolving gas A and a liquid phase reactant B, with q moles of B reacting per mole of A, so that:

A B Productsn m "+

q nm=

where

q = number of moles of B reacting per mole of A

CAL and CBL = molar concentrations of A and B, respectively, in the liquid


188 NCEES

The rate of reaction of A, JL, is then given by

J k C CL nm ALn

BLm=

where knm = reaction velocity constant, in mol

mm n3 1+ −

d nJL has units, moles/sec/unit volume of liquid. Alternatively,

J k C Cnm ALn

BLm

Lf=

JL is the rate of reaction and has units of s mmol

3:, n and m are the orders of reaction in A and B, and Lf is the liquid

hold-up fraction. A "reaction time" tR can be defined as

( )nt

k C C21

( )Rnm AL

nBLm1=

+−

The mass transfer of A in the liquid is given by

( )J k a C C*L AL AL= −

where

J = reaction rate in moles/sec/unit volume of reactor

C*AL = dissolved gas concentration in liquid bulk in

mmol3

kL = interphase mass-transfer coefficient in sm

a = gas-liquid interphase surface area/unit dispersion volume in m1

J is the rate of reaction and has units of s mmol

3:. A mass-transfer "diffusion time," tD, can be defined as

tkD

DL

AL2=

where DAL = diffusivity of A in the liquid

If a fast reaction is occurring near the interface within the "diffusion film," it will enhance the mass-transfer rate and the equation for the mass transfer of A into liquid, above, becomes

( )J k a C C* *L AL AL= −

( )n

k D k C C C1

2** ( )

LAL nm AL AL

nBLm1 2

1

=+− −

= Gwhere k*L = enhanced liquid-film mass-transfer coefficient in s

m


NCEES 189

Various Gas-Liquid Reaction Regimes and Parameters of ImportanceRegime Conditions Important Variables Concentration Profiles

I Kinetic control

Slow reaction

.tt

0 02RD 1

Rate \ Le \ knm

\ C*AL

n` j \ C*

BLm` j

Independent of a (if a is adequate) Independent of kL

GAS

LIQUID

FILM BULKCBL

CAL

CAL*

II Diffusion control

Moderately fast reaction in bulk of liquid, C 0AL .

. tt

0 02 2RD1 1

Design so that

a kD

100L

L

AL2e

Rate \ a \ kL

\ C*AL

Independent of knm Independent of Le (if Le is adequate)

CBL

CAL

CAL*

III Fast reaction

Reaction in film, C 0AL . (pseudo first order in A' )

tt

qCC

2 *RD

AL

BL1 1

C C*BL AL22

Rate \ a

\ knm

\ C*AL

n21+

` cj m

Independent of kL Independent of Le

CBL

CAL

CAL*

IV Very fast reaction

General case of III tt

2RD1

C C*BL AL+

Rate \ a

depends on

k k C C*L nm AL BL

Independent of Le

CBL

CAL

CAL*

V Instantaneous reaction

Reaction at interface; controlled by transfer of B to interface from bulk, J k aL\

tt

qCC

*RD

AL

BL22

Rate \ a \ kL

Independent of C*AL

Independent of knm Independent of Le

CBL

CAL

CAL*

5.2.2.5 Mass Transfer Between Phases for Dilute Systems( ) ( ) ( ) ( )n k x x k y y k c c k p pA L i G i L i G i= − = − = − = −l lo

andk k k k PL L L G Gt= =l lr

yi

y

xi

x

T, ptot

MASS TRANSFER BETWEEN PHASES:LIQUID PHASE INTERFACE VAPOR PHASE

x xy y

kk

k Pk

G HTUL HTU

i

i

G

L

G

L L

M L

M Gt−−

= = =ll r

where

kL = liquid-phase mass-transfer coefficient (mole fraction basis)


190 NCEES

Lkl = liquid-phase mass-transfer coefficient (concentration basis)

kG = gas-phase mass-transfer coefficient (mole fraction basis)

k Gl = gas-phase mass-transfer coefficient (partial pressure basis)

LM = molar-liquid mass velocity, in moles/time/area

GM = molar-gas mass velocity, in moles/time/area

HTUL = height of a transfer unit based on liquid phase resistance

HTUG = height of a transfer unit based on vapor phase resistance

pi = partial pressure

Ltr = average molar density of liquid phase

In most types of separation equipment, the interfacial area for mass transfer cannot be accurately determined and transfer coefficients based on volume of the device are used:

andK a k a k am

K a mk a k a1 1 1 1 1G G L L G L

= + = +

where

a = effective interfacial mass-transfer area per unit volume, in ftft or

mm

3

2

3

2

KG = overall gas-phase mass-transfer coefficient

KL = overall liquid-phase mass-transfer coefficient

m = slope of equilibrium line

Overall Mass Transfer Coefficients KL and KG for Dilute Systems

( ) ( )n K x x K y yA L

eqG

eq= − = −o

where

xeq = liquid mole fraction in equilibrium with vapor phase

yeq = vapor mole fraction in equilibrium with liquid phase

Overall Mass-Transfer Coefficients for Dilute SystemsGas Phase Liquid Phase

Equilibrium: y = m • x K k km1 1

G G L= + K mk k

1 1 1L G L

= +

Use for: High solubility, low m; gas-phase resistance is controlling

Low solubility, high m; liquid-phase resistance is controlling


NCEES 191

5.2.2.6 Mass Transfer Between Phases for Concentrated Systems ( ) ( ) ( ) ( )n x

k x xy

k y yx

K x xy

K y yA BM

L iBM

G i

BMeq

Leq

BMeq

Geq

=−

=−

=−

=−

ot t t t

( ) ( )

lnx

xx

x x

11

1 1BM

i

i

=

−−

− − −

__ i

j

( ) ( )

lnx

xx

x x

11

1 1BMeq

eq

eq=

−−

− − −

__ i

i ( ) ( )

lny

yy

y y

11

1 1BM

i

i

=

−

−− − −

`` j

j

( ) ( )

lny

y

yy y

1

11 1

BMeq

eq

eq=

−

−− − −

`` j

j k k y k P yG G BM G BM= = lt

Lk k x k P xL L BM L BM= = lt

x xy y

kk

k xk y

G HTU xL HTU y

i

i

G

L

G BM

L BM

M L BM

M G BM−−

= = =t

t

where

kGt = gas-phase mass-transfer coefficient for concentrated systems

KGt = overall gas-phase mass-transfer coefficient for concentrated systems

kLt = liquid-phase mass-transfer coefficient for concentrated systems

KLt = overall liquid-phase mass-transfer coefficient for concentrated systems

xBM = logarithmic-mean solvent concentration between bulk and interface

yBM = logarithmic-mean gas concentration between bulk and interface

LM = molar-liquid mass velocity, in moles/time/area

GM = molar-gas mass velocity, in moles/time/area

HTUL = height of a transfer unit based on liquid-phase resistance

HTUG = height of a transfer unit based on vapor-phase resistance

Overall Mass-Transfer Coefficients KLt and KG

t for Concentrated Systems

( )( )

K yy

k yx

k x xy y1 1 1

G BMeqBM

G BMeqBM

L i

eqi= + −

−t t t

( )( )

K xx

k xy

k y yx x1 1 1

L BMeqBM

L BMeqBM

G i

ieq

= + −−

t t t


192 NCEES

5.2.2.7 Height of a Transfer Unit HTU k a y

Gk aG

GG BM

M

G

M= = t

HTU k a x

Lk aL

L BM

M

L

ML = = t

HTU K a yG

K aG

yy

HTU LmG

yx

HTUOGG BM

eqM

G

M

BMeqBM

G M

M

BMeqBM

L= = = +t

HTU K a xL

K aL

xx

HTU mGL

xy

HTUOLL BM

eqM

L

M

BMeqBM

LM

M

BMeqBM

G= = = +t

where

HTUG = height of a transfer unit based on vapor-phase resistance

HTUOG = height of a overall vapor-phase mass-transfer unit

HTUL = height of a transfer unit based on liquid-phase resistance

HTUOL = height of a overall liquid-phase mass-transfer unit

Height Equivalent to One Theoretical Plate (HETP)

If equilibrium line and operating line are parallel L

mG1

M

M =e o, then:

HETP = HTU

If equilibrium line and operating line are straight, but not parallel, then:

lnHETPHTU

LmGLmG

1OG

M

M

M

M

=−

e o

5.3 Continuous Vapor-Liquid Contactors

5.3.1 Material and Energy Balances for Trayed and Packed Units

5.3.1.1 Theoretical StageAn ideal theoretical stage has the following characteristics:

1. It operates in steady state and has a liquid product and a vapor product.2. All vapor and liquid entering the stage are intimately contacted and perfectly mixed.3. Total vapor leaving the stage is in equilibrium with total liquid leaving the stage.

For a single binary distillation stage, the following balances and equilibrium relationships apply.


NCEES 193

Overall mass balance:

Fn STAGE n(zn)

(yn)

(xn)

ΔHn

(yn+1)

(xn–1)

Vn+1

Vn

Ln

Ln–1F V L V Ln n n n n1 1+ + = ++ −

Component mass balance:

z F y V x L y V x Ln n n n n n n n n n1 1 1 1+ + = ++ + − −

Energy balance:

h F h V h L H h V h L, , , , ,f n n V n n L n n n V n n L n n1 1 1 1 D+ + + = ++ + − −t t t o t t

where

ht = molar specific enthalpy

Fn = feed flow to stage n

Vn = vapor flow leaving stage n

Ln = liquid flow leaving stage n

HnD o = heat input to stage n

Phase equilibrium:

y K xn n=

For binary system with relative volatility a12:

yx

x1 1n

n

n

12

12

a

a=+ −_ i

5.3.1.2 Constant Molal OverflowWhen the molar heats of vaporization of the components are nearly equal, the molar flow rates of the vapor and liquid are nearly constant in each section of the column.

In the rectifying section, the following assumptions then apply:

andL L L L V V Vn n0 1 1= = = = =

And in the stripping section, the following assumptions then apply:

andL L L V V VN m N m= = = =l l

where

L = liquid flow in the rectifying section

V = vapor flow in the rectifying section

Ll = liquid flow in the stripping section

V l = vapor flow in the stripping section

N = total number of stages

m = stage in stripping section

n = stage in rectifying section


194 NCEES

5.3.1.3 Column Material Balance

Stage Model for Distillation

V1

V1

V2

Vn

Vn+1

Vf+1

VM+1

VN+1

STAGE N

STAGE M

STAGE f (FEED)

STAGE n

STAGE 1

STAGE MODELFOR DISTILLATION

RECT

IFYI

NG S

ECTI

ONST

RIPP

ING

SECT

ION

CONDENSERSTAGE 0

VfzF

F

VM

VN

L0

Qc

L0 D

Ln-1

Lf-1

LM-1

LN-1

REBOILERSTAGE N+1

LN

LN

B

LM

Lf

Ln

L1

XD

•

QR

XB

•


NCEES 195

Overall mass balance:

F = D + B

Component mass balance:

z F x D x BF D B= +

Ratios:

FD

x xz xD B

F B= −−

FB

x xx zD B

D F= −−

For the rectifying section, the following balances apply:

D V L V L0 n n1 1= − = −+

x D y V x L y V x LD n n n n1 1 0 0 1 1= − = −+ +

For the stripping section, the following balances apply:

B L V L VN N m m1 1= − = −− +

x B x L y V x L y VB N N N N m m m m1 1 1 1= − = −− − + +

To calculate the composition on each stage (for constants L, Ll, V, and V l), for the

Rectifying section: y V

L x Vx D

L DL x L D

x DRR x R

x1 1n n

Dn

Dn

D1 = + = + + + = + + ++

Stripping section: y V

L x Vx B

L BL x L B

x BSS x S

x

BLBL

xBLx1

1 1m m

Bm

Bm

Bm

B1 = − = − − − = + − =

−−

−+ l

ll l

ll l

l

l

Reflux ratio (also called external reflux ratio):

R DL

DV D= = −

Boil-up ratio:

S BV

BL 1= = −l l

Slope of the operating line, for the

Rectifying section: slope VL

RR1= = +

Stripping section: slope VL

SS

BLBL

11

= = + =−l

ll

l


196 NCEES

5.3.1.4 Graphical Solution for Binary Distillation (McCabe-Thiele Diagram)

McCabe-Thiele Diagram for Binary Distillation With Constant Molal Overflow and Constant Relative Volatility

xNxB

y1

y = x

y - INTERCEPT (x = 0)

x - INTERCEPT (y = 1)

xD

zF

xI

yI

q LINE

EQUILIBRIUM CURVE

yN+1

yNy = M

OLE

FRAC

TION

IN V

APOR

x = MOLE FRACTION IN LIQUID

STRIPPINGOPERATING LINE

RECTIFYING OPERATING LINE

C

D

AE

B

00

1

1

Equations for the McCabe-Thiele DiagramName Equations

Equilibrium Line ( )y xx

1 1aa= + −

Operating Line for the Rectifying Section

A

y VL x V

x DL DL x L D

x DRR x R

x1 1n n

Dn

Dn

D1 = + = + + + = + + ++

Slope: VL

RR

1= +y-Intercept (x = 0):

y Rx

L Dx D

1D D

x 0 = + = +=

Reflux Ratio:

R yx

1xD0

= −=

Operating Line for the Stripping Section

B

y V

L x Vx B

L BL x L B

x BSS x S

x

BLBL

xBLx1

1 1m m

Bm

Bm

Bm

B1 = − = − − − = + − =

−−

−+ l

ll l

ll l

l

l

BL f R f x x

x x1 1

D F

F B= − + + − −−l ` `j j

Slope:

VL

SS 1= +

ll

x-Intercept (y = 1):

xBL

x BL 1B

y 1 =+ −

= l

lBoil-up Ratio:

S xx x1 y

y B

1

1= −−

=

=


NCEES 197

Equations for the McCabe-Thiele Diagram (cont'd)Name Equations

Feed Line

Cy f

fx fz

qqx q

z11 1

F F=−

+ = − − −

Slope:

ff

qq1

1−

= −

Intercept:

For x f1F $ -

x fz

qz

1yF F

0 = − ==

For x f1F # -

y fz f

qq z1

1xF F

1 =+ −

= −−

=

Feed Quality:

For y = 0 intercept:

f xz

q xz

1yF

yF

0 0= − =

= =

For x = 1 intercept

f yz

q yz y

11

1x

F

x

F x

1 1

1= −−

= −−

= =

=

Intersection of Feed Line/ Operating Lines

D

x f

zRx

R ff R

1 11

IF D= − + + −

+e ô h

y f

zfz

Rx

R ff R

1 11 1

IF F D= + − + + −

− +e ` ô j h

Intersection of Feed Line/ Equilibrium Line

E

For constant a:

x f

zff

fz

ff

fz

21

11

1 1 1 41

11

1 1 1 1 1F F F

2

a a

aa a

a

a=− − + − −

− −+ − + − −

− −−

− −_ ` _ ` _ ì j i j i j> >H H

y x ff

fz1 F= − +e o

Operating Line for Total Reflux y x=

Operating Line for Minimum Reflux R y x

x ymin

F F

D F= −−

Circled A, B, C, D, and E in table above refer to the previous graph, "Binary Distillation With Constant Molal Overflow."


198 NCEES

5.3.1.5 Feed ConditionsThe feed condition is defined by

q = mole fraction liquid in feed

= molar enthalpy of vaporizationm lar enthalpy to c nvert feed to saturated vap rq q q

f = mole fraction vapor in feed

q + f = 1

L L q F L f F1= + = + −l ` j

V V q F V f F1= + − = +l l` j

Feed ConditionsFeed Condition Values for f and q Flows at Feed Location Feed Line in McCabe-Thiele

Subcooled Liquid f < 0( )

f hc T T

vap

pL b F

D= −

−

q > 1( )

q hc T T

1vap

pL b F

D= +

−

F

L V

V 'L '

Bubble Point (Saturated Liquid)

f = 0

q = 1F

L V

V 'L '

Partially Vaporized 0 < f < 1

0 < q < 1

F

L

V 'L '

V


NCEES 199

Feed Conditions (cont'd)Feed Condition Values for f and q Flows at Feed Location Feed Line in McCabe-Thiele

Dew Point (Saturated Vapor)

f = 1

q = 0

F

L V

V 'L '

Superheated Vapor f > 1( )

f hc T T

1vap

pV F d

D= +

−

q < 0 ( )

q hc T T

vap

pV F d

D= −

−

F

LV

V 'L '

where

cpL = heat capacity of the liquid

cpV = heat capacity of the vapor

TF = temperature of the feed

Tb = bubble point temperature of the liquid

Td = dew point temperature of the vapor


200 NCEES

5.3.1.6 Condensers

Types of CondensersTotal Condenser Partial Condenser

A total condenser does not represent a theo-retical stage.

A partial condenser represents a theoretical stage.

L1

V1

V1 y1

y1

x0

L0x0

x1

NOT A THEORETICAL STAGE

“STAGE” 0

STAGE 1

D

L1

V1

V1

V2

V2

y2

y2

y0 x0=

x1

A THEORETICAL STAGE

STAGE 1

STAGE 2 D

x N–1

y

yN

x N

ab

c

x

The triangle indicated by abc represents the top stage of the distillation column.

y

yN

yN+1

x N+1

ba

d c

e

x N–1x Nx

The triangle indicated by cde represents the top stage of the distillation column and the triangle indicated by abc represents the partial condenser.

Heat Duty: ( )Q V h D R h1TC vap vap1D D= = +o Heat Duty: Q L h D R hPC vap vap1D D= =o

For subcooled reflux:

If the reflux is subcooled, a portion of the vapor entering the top stage of the column will condense, providing heat to increase the liquid temperature to the bubble point. The additional amount of liquid that is condensed inside the column is determined by:

L hL c T T

vap

ER pR R1D

D=

−_ i


NCEES 201

Effective reflux ratio (also called internal reflux ratio) for the stages in the column:

DL

DL L

D

L c hT T

1ER

ER pRvap

R1

D D=

+=

+−_ i> H

The temperature of the top stage in the column, T1, may be estimated as equal to the bubble point of the external reflux.

where

T1 = temperature of top stage

TR = temperature of the reflux

LER = external reflux (LER = RD)

DL = rate of liquid condensed on top stage of the column

cpR = heat capacity of the reflux

5.3.1.7 Reboilers

Types of ReboilersReboiler Without Mixing Reboiler With Mixing

If the vapor effluent from the reboiler is in equili-brium with the bottom product, then the reboiler represents a theoretical stage. Other examples: kettle reboiler, internal heating coil.

If liquid effluent from the reboiler mixes with the liquid from the bottom stage of the column, the reboiler does not represent a theoretical stage.

THEORETICALSTAGE

Vap

BOTTOMPRODUCT

HOTSTREAM

STAGEN+1

LNXN

LN+1XN+1

LNXN

VN+1YN+1

Liq

NOT ATHEORETICAL

STAGEVap

LIQUIDFROMTRAYS

BOTTOMPRODUCT

HOTSTREAM

Liq

Heat Duty: Q V h S B hR N vap vap1D D= =+o Heat Duty: Q V h S B hR R vap vapD D= =o

Heat Duty: Q B R f x xx x

f h1RD F

F BvapD= + − −

−−o ` j= G


202 NCEES

5.3.1.8 Minimum Flow Rates and Reflux

Underwood Method With No Distributed Nonkey Components

The Underwood method assumes constant relative volatilities and constant molal overflows, and it requires a trial-and-error solution.

First, by trial-and-error, find a value for φ that is between the relative volatilities of the light key and heavy key components. The relative volatilities are based on a characteristic temperature for the column, such as the bubble-point temperature of the distillate or the flashed feed temperature at the column pressure. The heavy key is the reference component j for the relative volatilities of each component i.

qz

f1 F

ij

ij ii/a {

a− = − =/

Second, calculate the value of φ from:

Rx

1minD

ij

ij ia {

a+ = −/

where

zfi = concentration of component i in the feed

q = moles of feed to stripping section per mole of feed

aij = relative volatility between components i and j

φ = adjustable parameter, which has no physical significance

fi = fraction of component i in the feed that is vaporized

5.3.1.9 Minimum and Theoretical Stages

Minimum Theoretical Stages: Fenske Equation

The Fenske equation applies when the relative volatility is constant across the column. If the relative volatility varies across the column, a geometric mean of the range of values for the relative volatility may be used as an approximation. For example:

/top botij

1 2a a a= ` j

or/

top mid botij1 3

a a a a= ` jFor a binary separation, the Fenske equation for the number of stages (including any theoretical stages represented by the condenser and reboiler) at total reflux is

N

ln

ln xx

xx

11

,min

D

DBB

1 2a=

−−= G

For a multicomponent separation —where 1 and 2 are the two components with the light key indicated by i and the heavy key indicated by j—the Fenske equation is

N

ln xxxx

minDD

B

B

ij

ji

i

j

a=> H

where Nmin = minimum number of stages, including any theoretical stages represented by the condenser and reboiler


NCEES 203

Estimated Number of Theoretical Stages: Gilliland Correlation

Gilliland Correlation

1.0

1.0

0.80.60.4

0.2

0.2

0.10.080.06

0.6

0.04

0.40.04

R – RminR + 1

0.02

0.020.01

0.100.01

N –

N min

N +

1

Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed, New York: McGraw-Hill, 1993, p. 609.

Estimated Number of Theoretical Stages: Underwood Correlation

The Underwood correlation can be used for constant volatility and partial reflux.

Underwood CorrelationRectifying Section (Top) Stripping Section (Bottom)

,K K0 1 11 2 2# # ,K K0 0 11 21 # #

LV

RR 1= +

LV R f x x

x xf1

D F

F B= + − −−

−` j

b Rx1

D= +b

R f x xx x

f

x

1D F

F B

B=+ − −

−−` j

K b LV L

Vb LV L

V b LV

21

11

41

11

1,1 212

12

12

12

2

12!

a

a

a

aa

=− − −−

− −− − −f fp p

Intersection of feed line with operating lines: x fx

Rx

R ff R

1 11

IF D= − + + −

+e ^o h

lnNx K K xx K K x

RI D

D I

1 2

1 2=− −

− −__ _

_ii i

i lnNx K K xx K K x

SB I

I B

1 2

1 2=− −

− −__

__ii

ii


204 NCEES

where

K1 , K2 = distribution coefficients of components 1 and 2

b = intercept of the operating line with the vertical axis

NR = number of stages in the rectifying section

NS = number of stages in the stripping section

5.3.1.10 Multicomponent Distillation

Key and Nonkey Components

Key components are the two components in a mixture that characterize the degree of separation or that may provide the basis for a separation to be achieved.

Light key: The more volatile of the two key components. Present in both the distillate and bottoms product, and recovered predominantly in the distillate product.

Heavy key: The less volatile of the two key components. Present in both the distillate and bottoms product, and recovered predominantly in the bottoms product.

Nonkey: Other components in the mixture to be separated.

Light nonkey: Components more volatile than the light key component. Present almost completely in the distillate product.

Heavy nonkey: Components less volatile than the heavy key component. Present almost completely in the bottoms product.

Distributed key: Components having volatility between that of the light key and heavy key. Present in both the distillate and bottoms product. Also called intermediate key.

5.3.1.11 Absorption and StrippingFor dilute solutions ( )x 1solvent . , use solute-free basis for the concentrations (X, Y) and the flow rates (GS, LS):

Y yy

P pp

1AA

A

tot A

A= − = − X xx

1AA

A= −

G G y

YG1

1S AA

= − =+

` _j i L L xXL1

1S AA

= − =+

_ _i i


NCEES 205

Absorption and StrippingAbsorber Stripper

Feed Yin

For fresh solvent: Xin = 0

LS, Xout

GS, Yout LS, Xin

GS, Yin

Feed Xin

For fresh stripping gas: Yin = 0

Material Balance

andY Y GL X X X X G

L Y Yout inS

Sout in out in

S

Sout in= − − = − −` `j j

Equilibrium Line (EQ): y = m x

orYX mm X X

m Y mY

1 1 1EQ EQ=+ −

=+ −_ _i i

Operating Line (OL)

Y GLX Y G

LX

S

Sin

S

Sout= + −

Operating Line (OL)

Y GLX Y G

LX

S

Sout

S

Sin= + −

Minimum Flow

L

m Y mY

X

G Y Y

1,minS

in

inin

S in out=

+ −−

−`

_ i

jMinimum Flow

G

m X mm X

Y

L X X

1,minS

in

inin

S in out=

+ −−

−`

_ i

j

Diagram

Yout

Gs

Ls, min

TOP

BOTTOM

OLEQ

Yin

Xout X eqXin in(Y )

Diagram

LsGs, min

TOP

BOTTOM

OL

EQ

Xin

Xin( )

Yout

Yin

Xout

Y eq

Absorption Factors: Equilibrium Equations: Stripping Factors:

A mGL= General: y = m x S L

mG=

A KGL= Vapor/Liquid: y = K x S L

KG=

A H GP Ltot= Henry’s Law: y P

H xtot

= S P LH Gtot

=

A H Gp Lsat

= Raoult’s Law: y Pp

xtot

sat= S p L

H Gsat=


206 NCEES

Absorption and Stripping (cont'd)Absorber Stripper

Efficiency

Ey y xy y

GLGL

EA

A A1

min

ineq

in

in out

act

N

N

1

1

=−

−=

=−−

+

+

_c

cim

m

Efficiency

Ex x xx x

LGLG

ES

S S1

min

ineq

in

in out

act

N

N

1

1

=−

−=

=−−

+

+

_c

cim

m

Theoretical Stages

ln

ln

for

N AA AEA E

N EE A1 1

A

A

=−+

= + =

c mTheoretical Stages

ln

ln

for

N SS S ES E

N EE S1 1

S

S

=−+

= + =

d n

NTU (Number of Transfer Units)

ln

NTU YY Y

Y

Y Y XY Y X

Y Y X Y Y X

OYlm

in out

lm

outeq

in

ineq

out

ineq

out outeq

in

D

D

=−

=

−−

− − −___

_iii

i8

>8B

HB

NTU (Number of Transfer Units)

ln

NTU XX X

X

X X YX X Y

X X Y X X Y

OXlm

in out

lm

outeq

in

ineq

out

ineq

out outeq

in

D

D

=−

=

−−

− − −___

_iii

i8

>8B

HB

where

DYlm = log mean concentration difference in the vapor phase (solute-free basis)

DXlm = log mean concentration difference in the liquid phase (solute-free basis)

NTUOY = overall number of transfer units based on the gas phase

NTUOX = overall number of transfer units based on the liquid phase

5.3.2 Design Parameters for Trayed Units

5.3.2.1 Primary Tray Unit Design Parameters• Number of passes• Tray spacing• Tray type• Outlet weir type and height• Downcomer type and area• Clearance under downcomer• Hole size, valve size, or bubble cap size and style• Fractional hole area for sieve and valve trays• Tray pressure drop• Tray efficiency• Tray capacity• Tray hydraulics (flooding)


NCEES 207

Starting Dimensions for Cross-Flow Sieve TraysDimension (units) Vacuum Atmospheric Pressure

Tray spacing (in.) 24 24 24Downcomer area (% column) 5 10 15Active area (% column) 90 80 70Hole area (% active) 12 10 8Weir height (in.) 1 2 2Hole diameter (in.) 0.25 0.25 0.25Downcomer clearance (in.) 0.5 1.0 1.5

Source: Albright, Lyle F., Editor, Albright's Chemical Engineering Handbook, Chapter 12, "Distillation," by James R. Fair, Boca Raton, FL: CRC Press, 2009, p. 1027.

5.3.2.2 Tray Selection

Criteria for Selecting a Distillation Column DeviceCriterion Details

Vapor-Handling Capacity Entrainment flooding. At incipient flooding, the minimum column diameter is fixed.Liquid-Handling Capacity Fixes the size of downcomers. Downcomer backup can lead to flooding.

Mass-Transfer Efficiency Sets required height for a given number of theoretical stages. Efficiency can be a function of column diameter.

Flexibility Of concern when the column must be operated under a wide range of feed rates or when future capacity needs must be considered in the initial design.

Pressure Drop Low pressure drop is critical for vacuum columns, especially when a low bottoms temperature must be maintained.

Cost Consider total cost of the system, including auxiliary equipment; a more expensive device may lead to lower operating costs.

Design Limitations Device should be proven commercially. Also, the user needs to understand how the device was designed (if by a vendor).

Special Concerns Fouling, corrosion, ease of installation or removal, potential foaming problems, adequate residence time for reactions, special heat-transfer needs.

Source: Albright, Lyle F., Editor, Albright's Chemical Engineering Handbook, Chapter 12, "Distillation," by James R. Fair, Boca Raton, FL: CRC Press, 2009, p. 1008.


208 NCEES

5.3.2.3 Common Types of Distillation Trays

Bubble Cap Tray (left) and Various Caps (right)

Sieve Tray (left) and Dual-Flow Tray (right)

Bubble Cap Trays


NCEES 209

Sieve Trays

Valve Trays

5.3.2.4 Comparison of Common Types of Distillation Trays

Comparison of the Common Tray TypesFeature Sieve Trays Valve Trays Bubble-Cap Trays Dual-Flow Trays

Capacity High High to very high Moderately high Very highEfficiency High High Moderately high Lower than other types

Turndown

About 2:1; not gener-ally suitable for operation under variable loads

About 4–5:1; some special designs achieve (or claim) 10:1 or more

Excellent; better than valve trays; good at extremely low liquid rates

Low; even lower than sieve trays; unsuitable for variable load operation

Entrainment Moderate ModerateHigh; about 3 times higher than sieve trays

Low to moderate

Pressure Drop Moderate

Moderate; early designs somewhat higher; recent designs same as sieve trays

High Low to moderate

Cost Low About 20 percent higher than sieve trays

High; about 2–3 times the cost of sieve trays

Low

Maintenance Low Low to moderate Relatively high Low

Fouling Tendency Low Low to moderate High; tends to col-lect solids

Extremely low; suitable where fouling is extensive and for slurry handling

Effects of Corrosion Low Low to moderate High Very low


210 NCEES

Comparison of the Common Tray Types (cont'd)Feature Sieve Trays Valve Trays Bubble-Cap Trays Dual-Flow Trays

Availability of Design Information Well-known Proprietary, but infor-

mation readily available Well-known Some information available

Other Instability sometimes occurs in large diameter (> 8 ft) columns

Main Applications

Most columns when turn-down is not critical

Most columns, services where turndown is important

Extremely low-flow conditions; where leakage must be minimized

Capacity revamps where ef-ficiency and turndown can be sacrificed; highly fouling and corrosive services

Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, pp. 266–267.

5.3.2.5 Tray EfficiencyThe point efficiency is the ratio of the change of composition at a point to the change that would occur on a theoretical stage:

E y yy y

intOG

n n

n n

po1

1eq= −−

−

−f p The Murphree tray efficiency applies to an entire tray instead of to a single point on a tray:

E y yy y

MVneq

n

n n

tray1

1= −−

−

−f p Overall column efficiency:

E NN

OC a

t=

The overall column efficiency is related to the Murphree efficiency by:

lnln

withEE

m LV1 1

OCMV

m

mm=

+ −=

_ i8 B

where

EOC = overall column efficiency

EOG = point efficiency for a tray

EMV = Murphree tray efficiency

Nt = number of theoretical stages in a column

Na = number of actual stages in a column

yneq = vapor mole fraction in equilibrium with the liquid

l = ratio of slope of equilibrium curve to operating line


NCEES 211

5.3.2.6 Hydraulic Model for Trays

The Hydraulic Model for Trays

LIQUID AND GAS

FROTH

LIQUID WITH BUBBLES

TRAY BELOW

TRAY ABOVE

AB

AN

ADB

ADT

hwhcl

Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992. As shown in Green, Don W., and Robert H. Perry, Perry's Chemical Engineers'

Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-27.

Tray Area DefinitionsTray Area Symbol Definition

Total tower cross-sectional area AT The inside cross-section area of the empty tower without downcomers or trays

Net area AN

Total cross-section area minus the area at top of the downcomer; also referred to as free area; represents smallest area available for vapor flow in the intertray spacing

Bubbling area AB

Total tower cross-section area minus total downcomer area, downcomer seal area, and any other nonperforated regions; also referred to as the active area (Aa); represents the area available to vapor flow near the tray floor

Hole area Ah Total area of perforations on the tray; smallest area available for vapor passage

Slot area AS

Total vertical curtain area for all valves through which vapor passes in a hori-zontal direction as it leaves the valves, based on the narrowest opening of the valves; smallest area available for vapor flow on a valve tray

Open slot area ASo Slot area when all valves are fully opened

Fractional hole area AfRatio of hole area to bubbling area (in sieve trays) or slot area to bubbling area (in valve trays)

Downcomer top area ADT Area at top of downcomerDowncomer bottom area ADB Area at bottom of downcomer


212 NCEES

5.3.2.7 Definitions of Vapor LoadSeveral different parameters are used for characterization of the vapor load.

The vapor load (Vload), in sft or s

m3 3, is

V CFSloadL G

Gt tt= −

where

CFS = vapor flow rate at conditions, in secft or s

m3 3

rL, rG = densities of the liquid and gas phases, respectively

The F-factor for gas loading, in

sec ftlbft or

s mkgft

. .

3

0 5

3

0 5d en o

, is

F u Gt=

where u = superficial linear gas velocity

The C-factor for gas loading, in secft or s

m , is

C uL G

Gt tt= −

In practice, the F-factor and the C-factor may be based on bubbling area AB, net area AN, or some other area, depending on the source of data and correlations. Care must be taken to use the correct area basis, depending on the source.

These terms are related as follows:

C AV Fload

L Gt t= =

−

5.3.2.8 Definitions of Liquid Load The tray liquid load QL, in in.

gpmor hr m

m3

: , isgpm

Q LL W=

where

gpm = liquid volumetric flow rate, in mingal

or sm3

LW = outlet weir length, in inches or meters

The downcomer liquid load QD, in in.gpm

or secft or s

m , isgpm

Q ADDT

=


NCEES 213

5.3.2.9 Flow Regimes on Trays

Flow Regimes

SPRAY

FROTH

EMULSION

FLOODING

Cs, V

APOR

LOAD

/A, ft

/sBUBBLE

LIQUID FLOW RATE PER WEIR LENGTH

Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992. As shown in Green, Don W., and Robert H. Perry, Perry's Chemical Engineers'

Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-29.

Tray Performance Diagram

AREA OFSATISFACTORY OPERATION

EXCE

SSIVE

ENTR

AINMEN

T

VAPO

R FL

OW R

ATE

ENTRAINMENT FLOODING

DOWNCOMER FLOODING

DUMP POINT

LIQUID FLOW RATE

EXCESSIVE WEEPING

WEEP POINT

Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, pp. 266–269.


214 NCEES

5.3.2.10 Flooding

Effect of Design Parameters on FloodingDesign Parameters That

Lower Flooding PointSpray Entrainment

FloodingFroth Entrainment

FloodingDowncomer Backup

FloodingDowncomer Choke

FloodingLow bubbling area X X XLow fractional hole area (< 8%) X X X

Low tray spacing X X XHigh weirs (> 4 in) X XSmall weir length X XSmall clearance under downcomer X

Small downcomer top area X

Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 274.

Entrainment Flooding

The correlations for entrainment given below are based on C-factors, specifically the Souders and Brown constant

CSB at the entrainment flood point, in secft or s

m .

C u, ,SB flood S floodL G

Gt tt= −

where uS,flood = superficial gas velocity at the entrainment flood point

Fair’s Entrainment Flooding Correlation

C u 20

, ,

. .

SB flood N floodL G

G0 2 0 5

v t tt= −c em o

where uN,flood = superficial gas velocity at the entrainment flood point based on the net area AN.

CSB,flood and uN,flood are based on the net area AN. The correlation is applicable to sieve trays, valve trays, and

bubble cap trays.

These restrictions apply:

1. System is nonfoaming or low-foaming.2. Weir height is less than 15 percent of tray spacing.3. Sieve-tray perforations are 13 mm (1/2 in.) or less in diameter.4. Ratio of slot (bubble cap), perforation (sieve), or full valve opening (valve plate) area Ah to active area Aa

is 0.1 or greater. Otherwise the value of uN,flood should be corrected using the table below:

AAa

h uN,flood Correction Factor

0.10 1.000.08 0.900.06 0.80


NCEES 215

Fair's Entrainment Flooding Correlation

0.7

1.0 2.00.7

0.60.5

0.50.5

0.5, ft

/s0.2

20 σ

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0.07

0.07

0.060.05

0.05

0.04

0.030.020.01 0.03

LG

C

gl

F

g

gl

=

=Unf

–

lv

sbflo

od,

_

PLATE SPACING36"

24"

18"

12"

9"6"

PLATE SPACING36"

24"

18"

12"

9"6"

ρ

ρ

ρ

ρρ


Kister and Haas Entrainment Flooding Correlation

.C d

hS0 144

. . .

SBLH

LG

ct

2 0 125 0 1 0 5

tc

tt= e d do n n

where

dH = hole diameter

hct = clear liquid height at transition from froth to spray regime

g = surface tension

S = tray spacing

CSB and uflood are based on the net area AN. For surface tensions greater than 25 cmdyne

, use the value of 25 cmdyne

. The correlation applies to nonfoaming systems.


216 NCEES

Recommended Range of Application: The Kister and Haas Entrainment Flood Correlation

Criteria Applicability NotesFlooding mechanism Entrainment (jet) flood onlyTray types Sieve or valve trays onlyPressure 1.5–500 psia 1

Gas velocity 1.5–13 secft

Liquid load 0.5–12 in.gpm

of outlet weir 2, 3, 5

Gas density 0.03–10 ftlb3

1

Liquid density 20–75 ftlb3

Surface tension 5–80 cmdyne

Liquid viscosity 0.05–2.0 cPTray spacing 14–36 in. 4, 5Hole diameter 1/8–1 in.Fractional hole area 0.06–0.20 5Weir height 0–3 in.

1. At pressures above 150 psia, downcomer flood is often the capacity limitation. This limitation is not predicted by the correlation. Caution is required.

2. At high liquid loads (above 7–10 in.gpm

), downcomer flood is often the capacity limitation. This limitation is not predicted by the correlation. Caution is required.

3. Equation does not apply for liquid loads lower than 0.5 in.gpm

of weir. For this reason, this correlation must not be extended to lower liquid rates.

4. At lower tray spacing, entrainment flooding may be related to lifting of the froth envelope and to froth height rather than to spray height. This correlation must not be extended to lower tray spacing.

5. The correlation does not apply when the following three conditions occur simultaneously: (a) ratio of flow-path length to tray spacing is high, > 3; (b) liquid rate is high, < 6 in.

gpm of

weir; and (c) fractional hole area is high, > 11%. Under these conditions, entrainment flooding is related to vapor channeling and vapor cross-flow rather than to spray height.

5.3.2.11 Downcomer Backup FloodingThe downcomer backup is determined by a pressure balance for the downcomer:

hdc = ht + hw + how + hhg + hda


NCEES 217

where

hdc = height of clear liquid in downcomer, in inch liquid or mm liquid

ht = total tray pressure drop

hw = height of weir at tray outlet

how = height of liquid crest over weir

hhg = liquid hydraulic gradient across tray

hda = head loss due to liquid flow under downcomer apron

The height of aerated liquid in the downcomer is determined by:

hh

dcdc

dcz

=l

where

h dcl = height of aerated liquid in downcomer

dcz = relative froth density (froth density to liquid density)

To prevent downcomer backup flooding, the following criterion must be met:

h S hdc W1 +l

Criteria for Downcomer Aeration FactorsFoaming Tendency

Bolles's Criteria1 Glitsch's Criteria2 Fair et al.'s Criteria3

Examples dcz Examples dcz Examples dcz

Low Low molecular weight hydrocar-bons4 and alcohols 0.6 .

ftlb1 0<G 3t 0.6

Rapid bubble rise systems, such as low gas density, low liquid viscosity systems

0.5

Moderate Distillation of medium molecular weight hydrocarbons 0.5 . .

ftlb1 0 3 0< <G 3t 0.5

High Mineral oil absorbers 0.4 .ftlb3 0>G 3t 0.4

Very high Amines, glycols 0.3

Slow bubble rise systems, such as high gas density, high liquid viscosity, foam-ing systems

0.2–0.3

Notes:1. "Distillation Theory and Practice: an Intensive Course," University of New South Wales/

University of Sydney, August 9–11, 1977.2. Glitsch, Inc. Ballast Tray Design Manual, 6th ed., Wichita, KS: Koch-Glitsch LP, 1993.3. Perry, R.H. and D.W. Green (eds). Perry's Chemical Engineers' Handbook, 7th ed., New

York: McGraw-Hill, 1997.4. The author believes that "low molecular weight hydrocarbons" refers to light hydrocarbons

at near atmospheric pressure or under vacuum. The foam stability of light hydrocarbon distillation at medium and high pressure is best inferred from the Glitsch criterion.

Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992.


218 NCEES

5.3.2.12 Downcomer Choke Flooding

Glitsch Correlation

The maximum clear liquid velocity at the downcomer entrance to avoid downcomer choke flooding is the lowest of the three following correlations:

.

Q SFQ SF

Q S SF

250

41

7 5

,

,

,

max

max

max

D

D L G

D L G

1

2

3

t t

t t

=

= −

= −

``` `

jjj j

where

S = tray spacing

SF = system factor

QD,max = maximum downcomer liquid load, in ftgpm

or sft or s

m2

Koch and Nutter Correlations

The maximum downcomer velocity is calculated from:

.Q tS SF S448 8 12 30,maxD R

#= d nwhere tR = apparent residence time, or the ratio of downcomer volume to the clear liquid flow in the downcomer, in seconds

Koch and Nutter Correlations14

12

10

8

6

4

2

00 10 20 30 40

5.13 SEC

4 SEC

†R FOR THEKOCH CORRELATION (8)

†R FOR THENUTTER CORRELATION (9)

5.13 sec

4 sec

†R FOR THEKOCH CORRELATION

†R FOR THENUTTER CORRELATION

lb/ft3

KOCH AND NUTTER CORRELATIONS

,GLρ ρ–

RESI

DENC

E TI

ME

, se

c† R

70 80



NCEES 219

Generalized Criteria for Maximum Downcomer Velocity

Maximum Downcomer Velocities

Foaming Tendency Example

Clear Liquid Velocity in Downcomer, secft

18-in. Spacing

24-in. Spacing

30-in. Spacing

Low Low-pressure (< 100 psia) light hydrocarbons, stabilizers, air-water simulators 0.4–0.5 0.5–0.6 0.5–0.6

Medium Oil systems, crude oil distillation, absorbers, midpressure (100–300 psia) hydrocarbons 0.3–0.4 0.4–0.5 0.4–0.5

High Amines, glycerine, glycols, high-pressure (> 300 psia) light hydrocarbons 0.2–0.25 0.2–0.25 0.2–0.3

Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992.

Recommended Minimum Residence Time in the DowncomerFoaming Tendency Examples Residence

Time, secLow Low molecular weight hydrocarbons, alcohols 3Medium Medium molecular weight hydrocarbons 4High Mineral oil absorbers 5Very high Amines and glycols 7

Source: Bolles, W.L., Monsanto Company: private communication, 1977.

System Factors

Capacity Discount Factors for Foaming SystemsSystem Type Examples Factor

Nonfoaming 1.00Fluorine systems Freon, BF3 0.90Moderate foaming Oil absorbers, amine, and glycol regenerators 0.85Heavy foaming Amine and glycol absorbers 0.73Severe foaming MEK units 0.60Foam-stable Caustic regenerators 0.30

Source: Glitsch Inc., Ballast Tray Design Manual, Bulletin 4900, 1961, p. 13.


220 NCEES

5.3.2.13 Tray Hydraulic Parameters

Hydraulic Parameters

SIEVE TRAY

hhg

hhg

how

P2

P1P1 P– =2 hd

hhg

hhgh +

+

+

+

–d hw

hw

hw

12

–1hda

2hβ ( )ow

+ how

hhgh ++++ dah t how

how

hw

hw

Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-39.

where

hd = dry tray pressure drop, in inch liquid or mm liquid

hda = head loss due to liquid flow under downcomer apron, in inch liquid or mm liquid

hhg = liquid hydraulic gradient across tray, in inch liquid or mm liquid

how = height of liquid crest over weir, in inch liquid or mm liquid

ht = total tray pressure drop, in inch liquid or mm liquid

hw = height of weir at tray outlet, in inch liquid or mm liquid

b = tray aeration factor in pressure drop equation, dimensionless

5.3.2.14 Tray Pressure DropThe total pressure drop across a tray, ht:

ht = hd + hl

where hl = pressure drop through the aerated liquid on the tray, in inch liquid or mm liquid

Dry tray pressure drop:

h K ud LG

h2

tt=

where

K = dry-tray pressure drop coefficient, in secftin or

smmm

2 2c cm m


NCEES 221

uh = gas velocity through the perforations, in sec

ft or sm

For sieve trays:.KC0 186

v2=

where Cv = orifice coefficient for dry tray pressure drop correlation

Orifice Coefficient for Dry Tray Pressure Drop

0.90

0.80

0.70

0.600.05 0.10 0.15 0.20

TRAY THICKNESS

HOTE DIAMETER

1.2

1.0

0.8

0.6

0.2

0.1 AND LESS

TRAY THICKNESS

HOLE DIAMETER

1.2

1.0

0.8

0.6

0.2

0.1 AND LESS

HOLE AREA ACTIVE AREA

ORIFICE COEFFICIENT FOR DRY TRAY PRESSURE DROP

= AhAa

DISC

HARG

E CO

EFFI

CIEN

T C v


K Values (Pressure Drop Coefficients) for Valve TraysValve

Position Valve Thickness Flat Valve Venturi Orifice Valves

Closed --- 6.154 3.077Open 10 gauge (0.134 in.) 0.821 0.448Open 12 gauge (0.104 in.) 0.931 0.448Open 14 gauge (0.074 in.) 1.104 0.448

Pressure drop through the aerated liquid is

hl = b hc

where

b = tray aeration factor

hc = clear liquid height on tray


222 NCEES

Aeration Factor β for Sieve Trays

FROT

H DE

NSIT

Y OR

AER

ATIO

N FA

CTOR

AERATION FACTOR β

RELATIVE FROTH DENSITY

1.0

0.8

0.6

0.4

0.2

2.01.51.00.50 2.50

†Φ

Fga = Uo (ρg)1/2


Aeration Factor β for Valve Trays

3689

413

710

HYDROCARBONHYDROCARBONAIR-WATERAIR-WATER

HYDROCARBONHYDROCARBONHYDROCARBONHYDROCARBON

REFERENCE REFERENCESYMBOL SYMBOLSYSTEM SYSTEM

1.0

0.8

0.6

0.4

0.2

0

FROT

H DE

NSIT

Y,

OR

AERA

TION

FACT

OR

0 0.5 1.0

F B= ft/s lb / ft3u vva ,1.5 2.0 2.5

ρ

β

AERATION FACTOR β FOR VALVE TRAYS



NCEES 223

Clear liquid height on the tray is

h h hh2c w owhg= + +

Height of the liquid crest over the weir is

.h F Q0 48ow w L 32

= _ iwhere

QL = tray liquid load, in in.gpm

or h mm3

:

hc = clear liquid height on tray, in inch liquid or mm liquid

Fw = weir correction factor, dimensionless

Weir Correction Factor FW for Segmental Downcomers in Calculation of Liquid Head Over the Weir

1.30

1.20

1.10

1.000.2 0.4 0.7 1 2 4

(LIQUID LOAD, GPM) / (WEIR LENGTH, FT.)2.57 10 20 40 70 100 200

WEI

R CO

RREC

TION

FACT

OR, F

w

1.0

0.9

0.8

0.7

0.60.5

RATIO WEIR LENGTHTO TOWER DIAMETER

RECOMMENDEDLIMIT



224 NCEES

The hydraulic gradient is

h g Rf u L12

hg h

f f=

where

f = friction factor

uf = velocity of the aerated liquid across the tray, in secft or s

m

Lf = length of flow path across the tray, in feet or meters

g = acceleration due to gravity

Rh = hydraulic radius, in feet or meters

Rh, the hydraulic radius of the aerated mass, is

R h D

h D

hh

DD L

2 12

2

hf f

f f

f tl

fT W

{

= +

=

=+

where

LW = outlet weir length

h1 = pressure drop through the aerated liquid on the tray, in inches or millimeters of liquid

hf = froth height on tray, in inches or millimeters

Df = average of tower diameter and weir length, in inches or millimeters

DT = tower diameter, in inches or millimeters

jt = froth density on tray

The velocity of the aerated mass across the tray uf is also equal to the velocity of the clear liquid across the tray:

.u hQ

DL

37 41

fl

L

f

w=

The friction factor is correlated with the Reynold number:

ReR u

h lh f Lnt=

where ml = viscosity of the liquid


NCEES 225

Friction Factor for Froth Cross-Flow on Sieve Trays0.5

0.2

0.1

0.05

0.02 0.4 0.7 1.0 1.50.4 0.7 1.0 1.5

0.01103

μ

104

REYNOLDS MODULUS =

hw , in.

l

105

FRIC

TION

FAC

TOR,

f

Rh Uf lρ


For a segmental downcomer, the head loss is

.h Agpm

0 03 100dada

= e owhere Ada = area under the downcomer apron, in ft2 or m2

5.3.2.15 General Considerations for Column SizingTray sizing calculations are performed at points where the column loading is expected to be the highest and lowest in each section. Typically, these are

• The top tray• Above every feed, product draw-off, and point of heat addition or removal• Below every feed, product drawoff, and point of heat addition or removal• The bottom tray• At any point in the column where the calculated vapor or liquid loading peaks

5.3.3 Nontrayed Continuous Contact Columns (Packed Towers)

5.3.3.1 Primary Packed-Tower Design Parameters• Type of tower separation• Packing height• Packing type and packing factors• Tower pressure drop• Flooding velocity calculation


226 NCEES

5.3.3.2 Gas Absorption With Countercurrent Flow

Gas Absorption With Countercurrent Flow

Li , XAi

Gi , YAi

PACKING

G, YA L, XA

Lo , XAo

Go , YAo

h = o

h=h

dh

Operating Line Above Equilibrium Line

(YAo / m) XAo MAX= ( )

YA

YAo

YAi

XAo

XA

BOTTOMOF TOWER

PINCH POINT

OPERATING LINE

EQUILIBRIUMLINE (SLOPE = m)

SLOPE =MIN

LG

SLOPE = LG


NCEES 227

where

G = mass velocity of gas phase

L = mass velocity of liquid phase

XA = mass fraction A in liquid phase

YA = mass fraction A in gas phase

h = height of packing

i = dilute end

o = rich end

s = interface

5.3.3.3 Desorption or Stripping With Countercurrent Flow

Desorption or Stripping With Countercurrent Flow

Lo , XAo

Go , YAo

PACKING

G, YA L, XA

L i , XA i

Gi , YAi

h = o

h = h

d h


228 NCEES

Operating Line Below Equilibrium Line

YAo

YAo (MAX)

MYAo

YAi XAi XAo

XA

YA TOP OF TOWER

PINCHPOINT

OPERATING LINE FORMINIMUM GAS FLOW

OPERATING LINE

EQUILIBRIUM LINE

SLOPE =MAX

LG

5.3.3.4 Gas Absorption With Concurrent Flow

Gas Absorption With Concurrent Flow

L0, XA0

G0, YA0

G, YA L, L, XA

Li , XAi

Gi , YAi

h = o

h = h

dh


NCEES 229

Absorption Operation With Concurrent Flow

YA

YAo

YAi

(YAi ) MAX

XAo XAi

XA

TOP OF TOWEROPERATING LINE

EQUILIBRIUM LINE

MINLG

SLOPE = LG

5.3.3.5 Desorption or Stripping With Concurrent Flow

Desorption or Stripping With Concurrent Flow

Li , XAi

Go, YAo

L , XAoo

Gi , YAi

h = o

h = h

dh


230 NCEES

Desorption or Stripping Operation With Concurrent Flow

YAYAo

YAi

(YAi ) MAX XAoXAi

XA

OPERATING LINE

EQUILIBRIUMLINE

MINLG

5.3.3.6 Mass Transfer Between Phases

Mass-Transfer Coefficients

NA = ky (yA – yAs)

NA = kx (xAs – xA)

NA = Kx (xA* – xA)

NA = Ky (yA – yA*)

where

NA = molar flux of A

kx, ky = individual mass-transfer coefficients

Kx, Ky = overall mass-transfer coefficients

xAs, yAs = solute mole fraction at interface in liquid and gas phase, respectively

xA* = mole fraction of solute in the liquid phase at equilibrium

yA* = mole fraction of solute in the gas phase at equilibrium

(NA)AVG Ai = (ky)AVG (yA – yAs) Ai

where Ai = total interfacial area

Ai =a A h


NCEES 231

where

a = interfacial area per unit volume, in ft2

A = cross-sectional area, in ft2

h = height of packing, in ft

Operating Line

The equation for the operating line is

( )orG y Gy L x Lx y GL x G Gy L x1

o Ao A o Ao A A A Ao o Ao− = − = + −

Packing Height of Transfer Unit

The height of packing is

( ) ( )( )

h H y y yy dy

11

GA A As

A lm Ay

Ai

Ao= − −−

y# and h = nG HG

where

nG = number of gas phase transfer units

lm = log mean

The number of gas-phase transfer units is

( ) ( )( )

n y y yy dy

11

GA A As

A lm Ay

Ai

Ao= − −−

y#

where ( )( ) ( )

yy y

1 21 1

A lmA As− =

− + − as an approximation

For dilute solutions, assume L, G, and slope m are constant.

H H LmG H L

mG HOG G L OL= + =

where HOG and HOL = height of overall transfer units in gas and liquid phases, respectively

mGL A= = absorption factor, which ranges from 1.0 to 1.4

1A S= = stripping factor

m P

H= l

where

P = absolute pressure

H l= Henry's constant

HHAOGOL=

andny yy y

nx xx x

* *OGA A lm

Ao AiOL

A A lm

Ao Ai=−−

=−−

` `j j


232 NCEES

where

ln

y y

y y

y y

y y y y*

*

*

* *

A A lm

i

o

A A o A A i

A A

A A

− =

−

−

− − −` `

``

`j jjj

jR

T

SSSSSSS

V

X

WWWWWWW

and similarly for x x*A A lm

-` jFor dilute solutions:

nx xx x

*OLlm

Ao Ai

A A

=−−

` j

5.3.3.7 Packing HETPFor gas absorption: h = nOG HOG

For gas stripping: h = nOL HOL

Also, h = NTP HETP

where

NTP = number of theoretical plates

HETP = height of an equivalent theoretical plate

ln

ln

NHGpL

y pH

pLHG y p

Hx

pLHG

1

TP

A

AA

1

01

=−

− −+

d dn nR

T

SSSSSSSSSS

V

X

WWWWWWWWWW

mGL m p

HHGpL

A A= = =

pLHG1S A

= =

ln

lnN

y mxy mx

1

1

S

S S

TPA A

A A

1 1

0 1

=− −

−+_ e

c

i

m

o> H

where

A = absorption factor

S = stripping factor

Note: For absorption and stripping, calculations for tower height are the same, although the operating line slope will differ.


NCEES 233

5.3.3.8 Height of Overall Transfer Unit

( )H K a yG1OG

y A lm= −

u

where ( )

( ) ( )

lny

yy

y y1

11

1 1*

*

A lm

A

A

A A− =

−−

− − −

f p

( )H K a xL1OL

x A lm= −

u

where ( )

( ) ( )

lnx

xx

x x1

11

1 1

*

*

A lm

A

A

A A− =

−−

− − −

f p

5.3.3.9 Number of Gas Phase Transfer Units n

y y y

ydy

11

*OGA A A

A lmAy

y

A

A

1

0=− −

−

```jj

j# Using the log mean average:

. lnn yy

y ydy

0 5 11

*OGAo

Ai A

A Ay

y

Ai

Ao= −−

+−` j#

In dilute solutions:

ny yy y

*OGA lm

Ao Ai

A

=−−

` j

where

ln

y y

y y

y y

y y y y*

*

*

* *

A lm

A top

A bottom

A bottom A topA

A

A

A A− =

−

−

− − −`

```

`j

jjj

j

5.3.3.10 Number of Liquid Phase Transfer Units n

x x xx

dx1

1*OL

A A A

A lmAx

x

Ai

Ao=− −

−

__`ii

j#

. lnn xx

x xdx

0 5 11

*OLAi

Ao

A A

Ax

x

Ai

Ao= −−

+−

#

5.3.3.11 Absorption With ReactionDissolved solute reacts with solvent in liquid phase if irreversible reaction:

lnn yy

OG AiAo=


234 NCEES

5.3.3.12 Correlations for Mass-Transfer CoefficientsFor insoluble gases that do not react chemically with the liquid:

H GD

1x x

xx vx

xa n t

n=h

d n

where

Hx = individual liquid-phase HTU

Gx = mass velocity of liquid

mx = viscosity of liquid

Dvx = diffusivity of liquid

rx = liquid density

a and h = constants given in the table below

Values of a and h in Equations1 for Various Packing Materials at 77°F

Packing Type Packing Size (in.) a hRings 2

1.5

1

0.5

0.375

80

90

100

280

550

0.22

0.22

0.22

0.35

0.46Saddles 1.5

1

0.5

160

170

150

0.28

0.28

0.28Tile 3 110 0.28

1. All quantities in equations must be expressed in fps units if these values of a are used.

Source: McCabe and Smith, Unit Operation of Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976, p. 735.

The temperature effect of liquids on the HTU can be evaluated as:

H H e . ( )x xo

T T0 013 o= − −

where

Hx = HTU at T °F

Hxo = HTU at To °F

T = final temperature in °F

To = initial temperature in °F


NCEES 235

Henry's Law: y* = m x

x* = my

where m = Henry's Law Constant/Total Pressure

5.3.3.13 Packing SelectionSelection of packing is based primarily on packing factors and avoidance of flooding.

Packing FactorsPACKING FACTORS**(WET AND DUMP PACKED)

TYPE OF PACKING MAT’L.NOMINAL PACKING SIZE (INCHES)

¼ ¼⅜ ½ ½ ½⅝ ¾ 1

60CERAMIC

PLASTIC

CERAMIC

METAL

PLASTIC

METAL

CERAMIC

CERAMIC

METAL

METAL

SUPER INTALOX

RASCHIG RINGS

RASCHIG RINGS

1/32”

1/16” WALL

WALL

SUPER INTALOX

INTALOX SADDLES

HY-PAK RINGS

PALL RINGS

PALL RINGS

BERL SADDLES

RASCHIG RINGS

30

2 3 31 1

33 1621

98 52 2240725 330 200 145

42 1518

52 4097 25 16

164870 2028

110900 240

700

1/8”

3/16”

1/4”

3/8”

EXTRAPOLATED

1/32” WALL

1/16” WALL

3/32” WALL

WALL

WALL

WALL

WALL

390 300 170 155 115

325783110137

3

220290

F OBTAINED IN 16" AND 30" I.D. TOWER

DATA BY LEVA

410

1600 1000 580 380 255 155 125 95 65 37

170 4565

Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).


236 NCEES

Packing Factors: Stacked Packings & Grids

PACK

ING

FACT

OR– F

1000800600

400

200

1008060

40

20

101''

NOMINAL PACKING SIZE – INCHES

CROSS PARTITION DIAMOND PITCHSQUARE PITCH

DIAMOND PITCHSQUARE PITCH

CROSS PARTITIONRINGS (SQUARE PITCH)

RASCHIG RINGS(CERAMIC)


RASCHIG RINGS

METAL GRID WOOD GRIDS

5/16'' WALL

3/8'' WALL

(METAL 1/8'' WALL)

4'' x 4'' x 1/2''(1'' x 1'' x 1/16'')

1'' x 2'' x 1/4''

1'' x 1'' x 1/4''

11/2'' x 11/2'' x 3/16''

2'' x 2'' x 3/8''

1/4'' WALL3/16'' WALL

SINGLE SPIRAL RINGS (

GRID TILE (CERAMIC)

CHECKER BRICK, 55% FREE SPACE CROSS PARTITION DIAMOND PITCH

SQUARE PITCHDIAMOND PITCHSQUARE PITCH

CROSS PARTITIONRINGS (SQUARE PITCH)



RASCHIG RINGS

METAL GRID WOOD GRIDS

2'' 3'' 4''

5/16'' WALL

3/8'' WALL

(METAL 1/8'' WALL)

4'' x 4'' x 1/2''(1'' x 1'' x 1/16'')

1'' x 2'' x 1/4''

1'' x 1'' x 1/4''

11/2'' x 11/2'' x 3/16''

2'' x 2'' x 3/8''

1/4'' WALL3/16'' WALL

SINGLE SPIRAL RINGS

GRID TILE (CERAMIC)

CHECKER BRICK, 55% FREE SPACE


Packing Factors: Screen Packing & Random Dumped Packing

PACK

ING

F

NOMINAL PACKING SIZE - INCHES

ACTO

R– F

1000800600

400

200

1008060

40

20

101''

FROM MANUFACTURERS DATAEXCEPT AS NOTED

TELLERETTESMAS PAC FN-200 PANAPAK

CROSS PARTITIONRINGS

GOODLOE

MAS PACFN-90

QUARTZ ROCK 2'' SIZECANNON

STEDMAN

FROM MANUFACTURERS DATAEXCEPT AS NOTED

TELLERETTESMAS PAC FN-200 PANAPAK

CROSS PARTITIONRINGS

GOODLOE

MAS PACFN-90

QUARTZ ROCK 2'' SIZECANNON

STEDMAN

2'' 3'' 4''



NCEES 237

5.3.3.14 Flooding and Pressure Drop

Packed Tower Pressure Drop

Generalized Pressure Drop Correlation

0.60

0.40

0.20

0.10

.060

.040

.020

.010

.006

.004

.002

.001.01

L = LIQUID RATE, LBS./SEC., SQ. FT.G = GAS RATE, LBS./SEC., SQ. FT.ρL = LIQUID DENSITY, LBS./CU. FT.ρG = GAS DENSITY, LBS./CU. FT.F = PACKING FACTORg C = GRAVITATIONAL CONSTANT, 32.2

12

.02 .04 .06 0.1 0.2 0.4LG

0.6 1.0 2.0 4.0 6.0 10.0

GENERALIZED PRESSURE DROPCORRELATION

PARAMETER OF CURVES IS PRESSUREDROP IN INCHES OF WATER/FOOTOF PACKED HEIGHT1.50

1.00

0.50

0.25

0.10

0.05

1.501.00

0.50

0.25

0.10

0.05

ρL ρG

ρG

Gg

()

F0.1

2 ρ Gρ

ρ ρC

GL

GENERALIZED PRESSURE DROPCORRELATION

PARAMETER OF CURVES IS PRESSURE IN INCHES OF TER/FOOT

OF PACKED HEIGHTDROP WA


Determination of column diameter D:

D GG4 A

r= c dm n

where GA = actual gas flow rate of the packed column


238 NCEES

Pressure Drop Versus Gas Rate

4.0

2.0

1.00.8

0.6

0.4

0.2

0.1100 2 3 4 500 1000 2000

F = 190L =

10,00

0

L = 12

,000L =

15,00

0

L = 20

,000

L = 25

,000

L = 30

,000

L = 8,

000

L = 4,

000

L = 2,

000

L = 6,

000

DRY

5/8 RASCHIG RINGS (METAL) (1/32" WALL) COLUMN DIA. = 15 in.

PACKING HEIGHT = 5.1 ft.

F = 190L =

10,00

0

L = 12

,000L =

15,00

0

L = 20

,000

L = 25

,000

L = 30

,000

L = 80

00L =

4000

L = 20

00L =

6000

DRY

5000

5/8 RASCHIG RINGS (METAL) (1/32" WALL) COLUMN DIA. = 15 in.


∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING

LIQUID RATE lb/ft2, hrAS PARAMETER

AIR MASS VELOCITY ~ lb/ft2, hr


4.0

2.0

1.00.8

0.6

0.4

0.2

0.120 40 60 80 100 200 400

L = 10

,000

L = 5,

000

L = 3,

000

L = 1,

000

L = 10

0DR

Y

L = 10

,000

L = 50

00L =

3000

L = 10

00L =

100

DRY

F = 725

LIQUID RATE lbs./ft2,hr.AS PARAMETER

1/4-in. INTALOX SADDLES (CERAMIC) COLUMN DIA. = 8 in.


F = 725

AS PARAMETER

600 1000

1/4-in. INTALOX SADDLES (CERAMIC) COLUMN DIA. = 8 in.


∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING


LIQUID RATE lb/ft2, hr



NCEES 239

Pressure Drop Versus Gas Rate (cont'd)

2.0

1.00.8

0.6

0.4

0.2

0.150030020010050 1000 2000

COLUMN DIA. = 8''PACKING HEIGHT = 4.4'F= 330

L = 8,

000

L = 5,

000

L = 3,

000 L =

2,00

0

L = 1,

000 L =

500

DRY

L = 6,

000

3/8 INTALOX SADDLES (PORCELAIN)

COLUMN DIA. = 8 in.PACKING HEIGHT = 4.4 ftF = 330

L = 80

0 0

L = 50

00L =

3000

L = 20

00

L = 10

00L =

500

DRY

L = 60

00

3/8 INTALOX SADDLES (PORCELAIN)

∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING




4.

2.

1.0.8

0.6

0.4

0.2

0.1100 2 3 4 500 1000 2000 5000

F= 18

COLUMN DIA. = 30 in.PACKING HEIGHT = 10 ft.NO.2 HY-PAK (METAL)

L = 10

,000

L = 20

,000

L = 30

,000

L = 40

,000

L = 50

,000

L = 60

,000

L = 5,

000

DRY

F = 18

COLUMN DIA. = 30 in.PACKING HEIGHT = 10 ft.NO.2 HY-PAK (METAL)

L = 10

,000

L = 20

,000

L = 30

,000

L = 40

,000

L = 50

,000

L = 60

,000

L = 50

00DR

Y

∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING





240 NCEES


2.0

4.0

1.00.8

0.6

0.4

0.2

0.1500432100 1000 2000

L = 35

,000

L = 30

,000

L = 25

,000

L = 20

,000

L = 15

,000

L = 12

,000

L = 9,

000

L = 6,

000 L =

4,50

0L =

1,50

0DR

Y

L = 35

,000

L = 30

,000

L = 25

,000

L = 20

,000

L = 15

,000

L = 12

,000

L = 90

00L =

600 0

L = 45

00 L = 15

0 0DR

Y

3" X 3" CROSS PARTITION RINGS – DUMPED (CERAMIC)

3" X 3" CROSS PARTITION RINGS – DUMPED (CERAMIC)

∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING



F = 78


1000 20005432100

4.0

2.0

1.0

0.6

0.4

0.2

0.15000

COLUMN DIA. = 16 in.PACKING HEIGHT = 6.0 ft.CO-CURRENT FLOW

L = 70

,000

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY L

INE

2 in. RASCHIG RINGS (CARBON STEEL)


L = 70

,000

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY L

INE

2 in. RASCHIG RINGS (CARBON STEEL)

∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING



F = 57



NCEES 241


1000 2000 5000500432100

4.0

2.0

1.0

0.6

0.4

0.2

0.110,000

L = 60,000L = 70,000L = 80,000

L = 50,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

L = 5,

000

DRY

COLUMN DIA. = 16 in.PACKING HEIGHT = 6.2 ft.

"CO-CURRENT" FLOW

1-1/2" INTALOX SADDLES (PORCELAIN)

L = 60,000L = 70,000L = 80,000

L = 50,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

L = 50

00

DRY

COLUMN DIA. = 16 in.PACKING HEIGHT = 6.2 ft.

"CO-CURRENT" FLOW

1-1/2" INTALOX SADDLES (PORCELAIN)

∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING




1000 20005432100

4.0

2.0

1.0

0.6

0.4

0.2

0.15000

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY L

INE

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY L

INE


1 in. INTALOX SADDLES (POLYPROPYLENE)

COLUMN DIA. = 16 in.PACKING HEIGHT = 6.0 ftCO-CURRENT FLOW


∆P~I

NCHE

S W

ATER

/ FT.

PAC

KING



F = 57



242 NCEES


1000 20005432100

4.0

2.0

1.0

0.6

0.4

0.2

0.15000


F = 21LIQUID RATE LBS./FT.2, HR.AS PARAMETER

F = 21LIQUID RATE lb/ft2, hrAS PARAMETER

L = 50

,000L =

100,0

00L =

90,00

0L =

80,00

0L =

70,00

0L =

60,00

0L =

40,00

0L =

30,00

0L =

20,00

0L =

10,00

0DR

Y LIN

EL = 50

,000L =

100,0

00L =

90,00

0L =

80,00

0L =

70,00

0L =

60,00

0L =

40,00

0L =

30,00

0L =

20,00

0L =

10,00

0DR

Y LIN

E

∆P~I

NCHE

S W

ATER

/ FT.

PACK

ING






2.0

4.0

1.0

0.6

0.4

0.2

0.11000 20005432100 5000


F=28

COLUMN DIA. = 16 in.PACKING HEIGHT =6.0 ft."CO-CURRENT" FLOW

L = 70,000

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY L

INE

F = 28

COLUMN DIA. = 16 in.PACKING HEIGHT = 6.0 ft."CO-CURRENT" FLOW

L = 70,000

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY L

INE

∆P~I

NCHE

S W

ATER

/ FT.

PACK

ING

1-1/2 in. PALL RINGS (CARBON STEEL)1-1/2 in. PALL RINGS (CARBON STEEL)

LIQUID RATE LBS./FT.2,- HR.AS PARAMETER




NCEES 243


2.0

4.0

1.0

0.6

0.4

0.2

0.11000 2000500432100 5000 10,000


LIQUID RATE LBS./FT.2,HR. AS PARAMETER


L = 70,000

L = 80,000

L = 90,000L = 100,000L = 110,000L = 120,000

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY

2 in. PALL RINGS (POLYPROPYLENE)



L = 70,000

L = 80,000

L = 90,000L = 100,000L = 110,000L = 120,000

L = 60

,000

L = 50

,000

L = 40

,000

L = 30

,000

L = 20

,000

L = 10

,000

DRY

∆P~I

NCHE

S W

ATER

/ FT.

PACK

ING

2 in. PALL RINGS (POLYPROPYLENE)



244 NCEES

5.3.3.15 Flooding Velocities

Flooding in Gas Absorption Packed Towers

0.01

1.0

0.1

0.01

.001

.0001

.000010.10 1.0 10 100

Ggc

ap

L

LG

30.2

G

L

G2 μL

where

ap = packing area, in ftft3

2

e = void fraction in packing

mL = viscosity of liquid in centipoise

gc = gravitational constant, 32.2

rG = density of gas phase, in ftlb3

rL = density of liquid phase, in ftlb3


NCEES 245

5.4 Miscellaneous Mass Transfer Processes (Continuous, Batch, and Semicontinuous)

5.4.1 Membrane Separation Processes

5.4.1.1 General Background

Fluid Stream SchematicPERMEATE OR FILTRATETMP

FEEDFEED CHANNEL

RETENTATE

ΔP

Normal flow filtration (NFF) refers to the situation in which retentate flow is zero and all the feed stream flows to the membrane surface are normal.

Tangential flow filtration (TFF) refers to the situation in which the feed stream flows are tangential to the membrane surface and exit the module as a retentate stream, creating a velocity gradient at the membrane surface.

Permeation flux J in ft dayft2

3 or m smol2 indicates the productivity of a membrane:

membrane areavolumetric permeate flow rate

J =

Permeability L indicates the sensitivity of productivity or flux to transmembrane pressure (TMP):

transmembrane pressurefluxL =

TMP may refer to a module average. Pure-component permeability (e.g., water permeability) refers to membrane properties, while the more industrially relevant process permeability includes fouling and polarization effects.

The recovery or conversion ratio CR indicates the efficiency of a membrane module:

feed flow ratepermeate flow rate

CR =

Solutes entrained by the permeate flow are retained by the membrane. They accumulate on the membrane surface and form a region of high concentration called the polarization boundary layer. A steady state is reached between back transport away from the membrane surface, tangential convective transport along the membrane surface, and normal convective flow towards the membrane.

The local transmission or sieving coefficient S indicates the passage of a single component through a membrane. The concentrations may change within a module:

( )( )locallocal

S ccf

p=

The observed passage Sobs indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream entering a module. The observed passage characterizes the module:

))ule

ule((modmod

S cc

obsf

p=


246 NCEES

The intrinsic passage Sint indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream at the membrane wall. The intrinsic passage characterizes the membrane:

S cc

int w

p=

where

cf = concentration in feed

cp = concentration in permeate

cw = concentration at wall of membrane

The retention or rejection R is the complement to the transmission coefficient or passage:

R = 1 – S

The multiple-component separation factor aij defines the selectivity for component separation:

cccc

SS

ijj

i

jf

jp

if

ip

a = =f

f p

p where

cif = concentration of component i in feed

cip = concentration of component i in permeate

Component transport through membranes can be considered as mass transfer in series:

1. Transport through a polarization layer above the membrane that may include static or dynamic cake layers2. Partitioning between the upstream polarization layer and membrane phases at the membrane surface3. Transport through the membrane4. Partitioning between the membrane and the downstream fluid

A simplified model of polarization can be used as the basis for analysis:

Polarization in Tangential Flow Filtration

REGIONS: CONCENTRATIONS: FLOW VECTORS:

TANGENTIAL FLOW

PERMEATENORMAL FLOW

PERMEATE

Cb

Cw

Cp

POLARIZATIONBOUNDARYLAYER

BULK SOLUTIONS



NCEES 247

5.4.1.2 Gas SeparationThe flux for permeation is

J z p p, ,ii

i feed i permeatet= −c `m j

where:

Ji = permeation flux of component i, in ft hrft2

3 or m smol2

ri = permeability of component i, in

ft hr psift ft2

3 or m sPamol2

z = membrane thickness

pi = partial pressure of component i

Stage cut q is defined by

feed volume flow ratepermeate volume flow rate

LV

i = =

where

V = molar permeate flow rate, in hrlb mole or s

mol

L = molar feed flow rate, in hrlb mole or s

mol

Selectivity is

xxyy

ij

ji

ji

a =e

e o

o

where

aij = separation factor

xi = mole fraction of component i in the feed or reject

yi = mole fraction of component i in the permeate

The pressure ratio U is

PPpermeate

feedU =

The ratio of permeation flux for two components i and j is

JJ

xy

x y

j

iij

jj

ii

a

U

U=

−

−

e

d n

o

R

T

SSSSSSSSSSS

V

X

WWWWWWWWWWW

At stage cut 0U = , the permeate composition as a function of feed composition is

y x x x

21

11 1

11

14

i i ii

2

a a a

aUU U U

= + + − − + + − −−

c c c _m m m i> H For membrane modules, the partial pressure driving force is a point function dependent on the partial pressures at a point on the membrane and is not constant. To take this into account, the equation may be used in iterative calcula-tions for approximating the performance of membrane modules.


248 NCEES

The limiting case for a >> F is

y x PP

xi i permeate

feedi, U=

The limiting case for a << F is

yxx

1 1ii

i,a

a

+ −_ i

Flow Paths in Gas PermeatorsPERMEATE

MEMBRANE

FEED

FEED

FEED

SPIRAL WOUND MODULES(a)

HOLLOW-FIBER MODULES WITH COUNTERCURRENT FLOW

(HOLLOW-FIBER WALL)MEMBRANE

PERMEATE

(b)

HOLLOW-FIBER MODULES WITH CROSS FLOW(c)

FEED (HOLLOW-FIBER WALL)MEMBRANE

PERMEATE

5.4.1.3 Material Balances for Membrane Modules

MEMBRANE MODULE

MEMBRANE

REJECT

PERMEATE

INCREMENT

FEEDL0 x0 PF LN xN PF

VN yN PP

n-1 n

Overall and component balances for a module are

L0 = LN + VN

x0 L0 = xN LN + yN VN

Overall and component balances for an increment of module area are

Ln–1 + Vn–1 = Ln + Vn

xn–1 Ln–1 + yn–1 Vn–1 = xn Ln + yn Vn

These may be expressed as

V V V y xL x x

n n nn n

n n n1

1 1D = − =

−−

−− −_ i


NCEES 249

where y y y

V V Vy V y V y V

21

n n n

n n

n n n n nn

1

1

1 1/

D

D

= +

= −−

−

−

− −

` j

At any point along the membrane, the permeate composition is

yV y Vn nN1 D=/

and the permeate composition for the overall module is

y V y VN N n nN1 D=/

Area for Membrane Modules

Based on a stepwise incremental solution, the membrane area is

A A J

y VN n

N

i av

n nN

g1 1

D= = _ i> H/ /

where J z x P y P x P y P z x x P y y P21

21

i avi

n F n P n F n Pi

n n F n n Pg 1 1 1 1t t= − + − = + − +− − − −_ c c ` ` c c _ `i m m j j m m i j9 9C C

The overall module area can be approximated as

A Jy V

Ni av

n n

g

= _ i

where J z x P y P x P y P z x x P y y P2

121

i avi

F P N F n Pi

n F n Pg 0 0 0 0t t= − + − = + − +_ c c ` ` c c _ `i m m j j m m j j9 9C C

Procedure for Incremental Calculation

Given aij, PF, PP, L0, and x0:

1. Select increment Dx2. For the initial point 0, calculate y0 and (Ji)0

3. Determine xn

4. Calculate yn and y n

5. Calculate DVn and Vn

6. Calculate y Vn nD

7. Calculate Ln

8. Calculate (Ji)n, (Ji)avg, and An

9. After the final increment, calculate (Ji)N and AN


250 NCEES

5.4.1.4 Membrane Separation Processes—Reverse Osmosis

Osmotic Pressure

The osmotic pressure ps of a solution is

ps = Fs is cs R T

where

ps = osmotic pressure in psi or Pa

Fs = osmotic coefficient

is = number of ions formed by solute molecules

cs = concentration of the solute in ft

lb mole3 or

mmol3

R = universal gas constant

T = absolute temperature in °R or K

Concentration Gradients

FEEDF

POROUSSUPPORT

SKIN

c wi

c wF

c si

c sP

c sm

c sP

awF

awP c wP=

PERMEATEP

Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993, p. 872.

where

aw = activity of water

cs = concentration of solute


NCEES 251

Flux Across Membrane

The flux of solvent JW (water, for example) is

J RTc D v

zP

ww w w rD D= −c m

where

J = permeation flux in ft hrft2

3 or m sm2

3

c = concentration in ft

lb mole3 or

mmol3

D = effective diffusivity in hrft2 or s

m2

v = partial specific volume in lbmft3 or kg

m3

DP = friction losses in psi or Pa

z = membrane thickness in ft or m

Dp = differential osmotic pressure in psi or Pa

The flux of solute is

J D S zc

s s ssD= c m

where:

Ss = distribution coefficient of the solute

Polarization Factor

The polarization factor is the relative concentration difference across the polarization boundary layer and is

cc c

kJ f

ssi s

c

wC =−

=

where

f = fraction of solute rejected

kc = mass transfer coefficient based on concentration, in hrft or s

m

Pressure Drop

The internal flow in a hollow-fiber membrane is laminar, and the internal pressure drop DPf with one closed end is

PDJ L128

2fw3

2nD =

where

L = length

D = diameter

m = viscosity


252 NCEES

5.4.2 Liquid-Liquid Extraction

5.4.2.1 Partition Ratio The equilibrium partition ratio in mole fraction units is

K xyo

extract

raffinate

i ii

i

ic

c= =

where

yi = mole fraction of solute i in the extract phase

xi = mole fraction of solute i in the raffinate phase

gi = activity coefficient of solute i in the indicated phase

The equilibrium partition ratio in mass ratio units Kil is

K XY

mm

mm

feed solventsoluteraffinate

extraction solventsoluteextract

ii

i= =ll

le

e o

o

where

Yi l = ratio of mass solute i to mass extract solvent in extract phase

Xil = ratio of mass solute i to mass extract solvent in raffinate phase

m = mass flow rate, in hrlbm or s

kg

The advantage of using the solute-free basis is that the feed solvent and extraction solvent flows do not change during the extraction.

5.4.2.2 Extraction Factor On a McCabe-Thiele type of diagram, E is the slope of the equilibrium line divided by the slope of the operating

line SF .

m FSE i i=

where

E i = extraction factor

mi = local slope of the equilibrium line

S = mass flow rate of the solvent phase, in hrlbm or s

kg

F = mass flow rate of the feed phase, in hrlbm or s

kg

For dilute systems with straight equilibrium lines, the slope of the equilibrium line is equal to the partition ratio:

m Ki i= l


NCEES 253

5.4.2.3 Separation FactorThe separation factor indicates the relative enrichment of a given component in the extract phase after one theoretical stage of extraction.

XXYY

XYXY

KK

raffinate

extractij

j

i

j

i

j

j

i

i

j

ia = = =l

l

l

l

l

l

l

l

l

l

l

f

f

f

f

p

p p

p

where ija l = separation factor for solute i with respect to solute j (mass ratio basis)

Equilibrium Lines

Plotting equilibrium data in terms of mass ratios on logarithmic scales often gives a straight line.

Hand-Type Ternary Diagram for Water + Acetic Acid + MIBK at 25oC

WATER LAYER

PLAIT POINT

864

2

2

.8

.8

1

1

.6

.6

.4

.4

.2

WT.

ACET

IC A

CID

WT.

MIBK

.2

.08

.08

.1

.1.01.01

.06

.06

.04

.04

.02

.02

Y

X

MIBK LAYER

LIQUID - L

IQUID EQUILIBRIUM

LIQUID - L

IQUID EQUILIBRIUM

WT. ACETIC ACIDWT. WATER



254 NCEES

5.4.2.4 Liquid-Liquid Extraction: Process Calculations

Countercurrent Extraction Cascade

2

n

Y2

Y1YE ' oreXF ' f

XR ' r YS ' s

X1

X n–1

Xr–1

r –1

r

Yn+1

Yr

Yn

Xn

1FEED STAGE

RAFFINATE STAGE


Theoretical (Equilibrium) Stage Calculations With McCabe-Thiele Method

McCabe-Thiele Graphical Stage Calculation Using Bancroft Coordinates

PARTIAL STAGEX

X

Yr s

'

'

X Yf e'

SLOPE =

WT. SOLUTEWT. FEED-SOLVENT

2

1

3

4

20

2

0r

OPERATING LINE

EQUILIBRIUM LIN

E

F 'S '

Y 'W

T. SO

LUTE

WT.

EXTR

ACTI

ON-S

OLVE

NT



NCEES 255

For immiscible feed and extraction solvents, the operating line for the feed end (stage 1 to stage n) is

Y SF X S

E Y F Xn n

e f1 = +

−+l l

l ll

l l l l

where

fX l = mass ratio of solute in feed

eY l = mass ratio of solute in extract

El = mass flow rate of extraction solvent only

F l = mass flow rate of feed solvent only

Sl = mass flow rate of extraction solvent only

For immiscible feed and extraction solvents, the operating line for the raffinate end (stage n to stage r) is

Y S

F X SS Y R X

n ns r

1= +−

−llll

ll l l l

where

Xrl= mass ratio of solute in raffinate

Ysl= mass ratio of solute in solvent

Rl= mass flow rate of raffinate solvent only

The overall material balance is

Y E

F X S Y R Xe

f s r=+ −

ll

l l l l l l

Kremser-Souders-Brown (KSB) Theoretical Stage Equation

For straight equilibrium and operating lines, the number of theoretical stages N is approximated by:

//

,ln

lnforN

X Y mX Y m

m FS

1 1 1

1E

E EE E

r s

f s

=−−

− += =

l l l

l l l

lll Y

f cp m

where

N = number of theoretical stages

ml = local slope of equilibrium line in mass ratio units

Sl= mass flow rate of the solvent only (solute-free basis), in hrlbm or s

kg

F l= mass flow rate of the feed solvent (solute-free basis), in hrlbm or s

kg


256 NCEES

An alternate form is

//

// forX Y m

X Y m1 1

1 1EE E E

r s

f sN

−−

= −− =

l l l

l l lY

//

forX Y mX Y m

N 1 1Er s

f s−−

= + =l l l

l l l

Graphical solutions to the KSB equation are shown below. Note that the term for the abscissa is the inverse of the term used in the KSB equation.

Graphical Solutions to the KSB Equation

1.00.80.60.4

0.2

.001.0008.0006.0004

.0002

.01.008.006.004

.002

0.1.08.06.04

.02

.0001

.00001

.00008

.00006

.00004

.00002

N = 1

2

3

4

6

8

1 2 4 6 8 10ε, EXTRACTION FACTOR

10

15

X

–

Y/m

sr X

–

Y/m

sf



NCEES 257

In general, these equations are valid for any concentration range in which equilibrium can be represented by a linear relationship Y = m X + b (written here in general form for any system of units). For applications that involve dilute feeds, the section of the equilibrium line of interest is a straight line that extends through the origin where Yi = 0 at Xi = 0. In this case, b = 0 and the slope of the equilibrium line is equal to the partition ratio where m = K.

The KSB equation also may be used to represent a linear segment of the equilibrium curve at higher solute concen-trations. In this case, the linear segment is represented by a straight line that does not extend through the origin, and m is the local slope of the equilibrium line, so .andb m K0= =Y Y

Furthermore, a series of KSB equations may be used to model a highly curved equilibrium line by dividing the analysis into linear segments and matching concentrations where the segments meet. For equilibrium lines with moderate curvature, an approximate average slope of the equilibrium line may be obtained from the geometric mean of the slopes at low and high solute concentrations:

m m m maverage geometric mean low high. =

Stage Efficiency

(%) actual stages

theoretical stages100o #p =

c cc c

,*

, ,md

d n d

d n d n

1

1p =

−−

+

+

(%)

[ ( )]ln

ln 1 1100E

Eo

md #pp=

+ −

where

op = overall stage efficiency

mdp = Murphree stage efficiency based on the dispersed phase

Mass Transfer Between Phases

( ) ( )( ) ( )

n k y y n k y yn k x x n k x x

int

int

y y

x x

= − = −

= − = −

*

*

o o

o o where

no = molar flow per area

xint = mole fraction of solute i in the raffinate phase at the interface

x* = mole fraction of solute i in the raffinate phase in equilibrium with the extract phase

yint = mole faction solute i in the extract phase at the interface

y* = mole fraction of solute i in the extract phase in equilibrium with the raffinate phase

( ) ( )( )

NTU y y yy dy

11

intG

my

y 1

s

e= − −−#


258 NCEES

For dilute solutions:

( )NTU

x xx x

*OLm

r

1=

−−f

where

xf = mole fraction of solute i in the feed

xr = mole fraction of solute i in the raffinate

NTUG = number of transfer units based on gas phase

NTUOL = number of trasnsfer units based on liquid phase

( )lm = log mean

Rate-Based Calculations With Mass-Transfer Units

In most cases, the dominant mass-transfer resistance resides in the feed (raffinate) phase, because the slope of the equilibrium line usually is greater than one. In that case, the overall mass-transfer coefficient based on the raffinate phase may be written:

k k m k1 1 1or r er

vole

= +

where

ke = extract phase mass-transfer coefficient, in hrft or s

m

kr = raffinate phase mass-transfer coefficient, in hrft or s

m

kor = overall mass-transfer coefficient based on the raffinate phase, in hrft or s

m

mervol = local slope of equilibrium line (volumetric concentration basis)

The required contacting height of an extraction column is related to the height of a transfer unit and the number of transfer units by:

Z k aV

X XdX HTU NTUt

or

req

x

x

or orout

in

= − =#

where

Zt = total height of extractor

Vr = liquid velocity of raffinate phase, in secft or s

m

a = interfacial area per unit volume, in ftft or

mm

3

2

3

2

Xeq = mass ratio in equilibrium with composition of extract phase

HTUor = height of overall transfer units (based on raffinate phase)

NTUor = number of transfer units (based on raffinate phase)


NCEES 259

For straight equilibrium and operating lines, the number of transfer units is approximated by the Colburn equation:

ln

NTUX m

YX m

Y

1 1

1 1 1

E

E E

or

r

f

s

s

=−

−

−− +

ll

l

ll

lJ

L

KKKKKKKKKcN

P

OOOOOOOOOm

where

,m FS 1E E= =lll

Y

An alternate form is

exp

X mY

X mY NTU

1 1

1 1 1

E

E E

r

f or

s

s

−

−=

−

− −

ll

l

ll

l c m< F

The height of a transfer unit is

HTU HTU

HTUEor r

e= +

HTU A k a

Qr

col r

r=

HTU A k a

Qe

col e

e=

where

HTUr = height of a transfer unit due to resistance in the raffinate phase, in ft or m

HTUe = height of a transfer unit due to resistance in the extract phase, in ft or m

Acol = column cross-sectional area, in ft2 or m2

Qr = volumetric flow rate of the raffinate phase, in minft or s

m3 3

Qe = volumetric flow rate of the extract phase, in minft or s

m3 3

The relation between overall raffinate phase transfer units from the Colburn equation and the number of theoretical stages from the KSB equation is

ln for

for

NTU N

NTU NX m

YX m

Y

1 1 1

1 1

E

E E

E

or

or

r

f

s

s

#=−

=

= =−

−− =

ll

l

ll

l

Y


260 NCEES

Extraction Factor

The solute reduction factor FR, or extraction factor, is an indication of process performance.

For a single-stage batch process or for one theoretical stage of a continuous process, the extraction factor is

forF X

XN

1 1

1

1E

E ER out

in= =−

−=

c

c m

m

The required solvent-to-feed ratio is approximated by

forFS

KF

N1

1R=−

=

where K = distribution coefficient for phase equilibrium

For any extraction configuration, the concentration of solute in the extract is

forY

FSX

F Y1 1 0outin

R in= − =cdm

n For cross-flow extraction, in which the raffinate phase for each stage is contacted with fresh solvent, the extraction factor is

F N1 ER

No= +

p

c m

FS

KNF 1R

N1o= −pc m

For multi-stage countercurrent extraction, the extraction factor is

F

1 1

1

E

E ER

No

=−

−pc

c m

m

For countercurrent extraction without discrete stages, the extraction factor is

expF

NTU

1 1

1 1 1

E

E ER

or=

−

− −c m< F


NCEES 261

5.4.2.5 Liquid-Liquid Extraction Equipment: Static Extraction Columns

Column Configurations

HEAVIERLIQUID

HEAVIER LIQUID

HEAVIERLIQUID

HEAVIERLIQUID

HEAVIERLIQUID

LIGHTERLIQUID

LIGHTERLIQUID

LIGHTERLIQUID

LIQUID – LIQUID EXTRACTION (2 CONFIGURATIONS)

LIGHTER LIQUID

LIGHTERLIQUID

Static extraction columns include spray-type, packed, and trayed columns.

Schematic of Common Static Extractors: (a) Spray Column, (b) Packed Column, and (c) Sieve Tray Column

LIGHT LIQUID OUTLIGHT LIQUID OUT

LIGHT LIQUID OUT

LIGHTLIQUID IN

RAGREMOVAL

LARGE-DIAMETER ELGIN HEAD

REDISTRIBUTORPERFORATED PLATE

DOWNCOMER

COALESCEDDISPERSED

INTERFACE

PACKING

LIGHT–PHASEDISTRIBUTOR

HEAVY LIQUID OUTHEAVY LIQUID OUT HEAVY LIQUID OUT

LIGHT LIQUID IN

LIGHT LIQUID IN

(a) (b) (c)

COLUMNINTERFACE

OPERATINGINTERFACE

HEAVYLIQUID IN

HEAVYLIQUID IN

HEAVYLIQUID IN



262 NCEES

5.4.2.6 Liquid-Liquid Extraction Equipment: Spray Columns

Liquid Dispersion

For liquid distributors, the liquid should issue from the hole as a jet that breaks up into drops. As a general guide-line, the maximum recommended design velocity corresponds to a Weber number (We) of about 12. The minimum Weber number that ensures jetting in all the holes is about 2. It is common practice to specify a Weber number between 8 and 12 for a new design.

u dWe

,maxoo d

. tc

where

uo,max = maximum velocity through an orifice or nozzle

We = Weber number

g = surface tension

do = orifice or nozzle diameter

rd = density of the dispersed phase

Drop Size, Dispersed-Phase Holdup, and Interfacial Area

For the general case where the dispersed phase travels through the column as drops, an average liquid-liquid inter-facial area can be calculated from the Sauter mean drop diameter and dispersed-phase holdup.

The drop diameter is

.d g1 15P htcD

=

where

dp = Sauter mean drop diameter

Dr = density difference between the raffinate and the extract

h = parameter, specifically:

h = 1.0 for no mass transfer

h = 1.0 for transfer from continuous to dispersed phase

h = 1.4 for transfer from dispersed to continuous phase

The dispersed-phase holdup is

,exp

cos

uu

u a d

61

42d

sod

d

c

dp p

2

z

f rz

f z

rg

g=− −

−

=

−

d

c

`n

m

j>

= G

H

where

dz = volume fraction of the dispersed phase (holdup)

z = tortuosity factor

ud = liquid velocity of the dispersed phase


NCEES 263

uc = liquid velocity of the continuous phase

uso = slip velocity at low dispersed-phase flow rate

e = void fraction

aP = interfacial area

The interfacial area is

a d6

pp

dfz=

Drop Velocity

The average velocity of a dispersed drop udrop is

uu

dropd

dfz

=

Interstitial Velocity of Continuous Phase

The interstitial velocity of the continuous phase uic is

uu1ic

d

c

f z=

−` jSlip Velocity and Characteristic Slip Velocity

The relative velocity between the counterflowing phases is referred to as the slip velocity us:

u u us drop ic= +

The characteristic slip velocity uso obtained at low dispersed-phase flow rate is

Re

g d18Stokes

c

c P2

3

n

t tD=

where

Re = Reynolds Number

rc = density of the continuous phase

Dr = density difference between the two phases

mc = viscosity of the continuous phase

For ReStokes < 2:

u

g d18so

c

p2

ntD

=

For ReStokes > 2:Re

u dsop c

ctn=

where

. . .ReP

H H0 94 0 857 59 3..

0 1490 757 #= −

. . .ReP

H H3 42 0 857 59 3..

0 1490 441 2= −


264 NCEES

P

gcc

4

2 3

n t

t c

D=

H d g P

34 .

.pcw

2 0 140 149

ctnnD= f dp n

P , H = dimensionless groups

mw = reference viscosity equal to 0.9c P or 9 #10-4Pa s

g = surface tension in in.lbf

The slip velocity at higher holdup is estimated from:

u u 1s so d. z-` j

Flooding Velocity

It is generally recommended that flow velocities be limited to 50 percent of the calculated flooding velocities.

.

.u

uu

u

1 0 925

0 178cf

cfdf

so=+ d n

where

ucf = continuous phase flooding velocity

udf = dispersed phase flooding velocity

Drop Coalescence Rate

Problems with coalescence are most likely when the superficial dispersed-phase flooding velocity udf is greater than about 12 percent of the characteristic slip velocity.

Mass Transfer Coefficients and Efficiency

.k a m k a

D m D

g

0 081

1

/ /

/

oc dcvol

od

c c

cdc d d

d

d dc

1 2 1 2

2

3 3 1 4

#

tn

tn

z zct

tD

= =+

−

e

`

d

f

eo

j

n

p

o

where

Dc = solute diffusion coefficient for the continuous phase

Dd = solute diffusion coefficient for the dispersed phase

koc = overall mass-transfer coefficient based on the continuous phase

kod = overall mass-transfer coefficient based on the dispersed phase

mdc = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase concentration


NCEES 265

mdcvol = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase

concentration on volumetric concentration basis

γ = interfacial tension

μc = viscosity of continuous phase

μd = viscosity of dispersed phase

rc = density of continuous phase

rd = density of dispersed phase

φd = volume fraction of dispersed phase (holdup)

With the height of one transfer unit (based on the continuous phase):

HTU k auoc

cc =q

5.4.2.7 Liquid-Liquid Extraction Equipment: Packed Columns

Liquid Redistribution

Little benefit is gained from a packed height greater than 10 ft (3 m). Redistributing the dispersed phase about every 5 to 10 ft (1.5 to 3 m) is recommended to generate new droplets and constrain backmixing.

Minimum Packing Size

For a given application, a minimum packing size or dimension exists below which random packing is too small for good extraction performance. The critical packing dimension dc is

.d g2 4c tvD

=

Packing Holdup

For standard commercial packings of 0.5 in (1.27 cm) and larger, φd varies linearly with the liquid velocity of the dispersed phase (ud) up to values of φd = 0.10 (for low values of ud). As ud increases further, φd increases sharply up to a “lower transition point” resembling loading in gas-liquid contact. At still higher values of ud, an upper transition point occurs, the drops of dispersed phase tend to coalesce, and ud can increase without a corresponding increase in φd. This regime ends in flooding. Below the upper transition point, the dispersed-phase holdup is

u uu1 1

d

d

d

cso dz z

f z+ − = −` j

Packing Flooding: Siebert, Reeves, and Fair Correlation

.

.

cos

u

uu

u a d

1 0 9254

10 178

2cf

cfdf

so p p

2rg

fg=

+

=

d cn m= G

Z

[

\

]]]]]]]]

_

`

a

bbbbbbbb


266 NCEES

Packing Flooding: Modified Crawford-Wilke Correlation

Flooding Velocities104

64

2

64

2

64

2

21 4 6 10 2 4 6

Dα

αα

CV

lV V

VV

V

= ft./hr. (SUPERFICIAL VELOCITY)= CONTINUOUS PHASE= DISPERSE PHASE= sq. ft. AREA OF PACKING/ c ft.= DIFFERENCE= VOID FRACTION IN PACKING

VISCOSITY IN (CENTIPOISE)= DENSITY (POUNDS PER / CUBIC FOOT)

μ'c =

'

γ =

γ

F = PACKING FACTOR (DIMENSIONLESS)

LIQUID – LIQUID PACKED TOWERS

A MODIFIED CRAWFORD-WILKE CORRELATION

10 22

22

0.50.5

0.5 0.5=

++

1.50.2c

cD

DC

CC

c F

4 6 10

103

32

102

10

CC

C

INTERFACIAL SURFACE TENSION (DYNES / cm)

Pressure Drop

In general, the pressure drop through a packed extractor is due to the hydrostatic head pressure. The resistance to flow caused by the packing itself normally is negligible; typical packings are large and flooding velocities are much lower than those needed to develop significant DP from resistance to flow between the packing elements.

Mass Transfer Coefficients

D

1d

cd

d d

d 21

z

nn

tn

=+

e

d

o

n For φd < 6:

.k

u

1

0 00375d

cd

s

nn

=+d n


NCEES 267

For φd > 6:

.k u D0 023d sd d

d 21

tn=

−

e o

.Dk d

Dd u

0 698 1c

c p

c c

c

c

p s cd

52

21

tn

nt

z= −e e `o o j

k k km1 1

od d c

dcvol

= +

where

kc = continuous-phase mass-transfer coefficient

kd = dispersed-phase mass-transfer coefficient

Packing Data

Random and Structured Packings Used in Packed Extractors

Packing Surface Area ap1 mm3

2Void Fraction1 (e)

Metal Random PackingKoch-Glitsch IMTP® 25 Koch-Glitsch IMTP® 40 Koch-Glitsch IMTP® 50 Koch-Glitsch IMTP® 60 Sulzer I-Ring #25 Sulzer I-Ring #40 Sulzer I-Ring #50 Nutter Ring® NR 0.7 Nutter Ring® NR 1 Nutter Ring® NR 1.5 Nutter Ring® NR 2 Nutter Ring® NR 2.5 HY-PAK® #1 in. HY-PAK® #1-1/2 in. HY-PAK® #2 in. FLEXIRING® 1 in. FLEXIRING® 1-1/2 in. FLEXIRING® 2 in. CMR® 1 CMR® 2 CMR® 3 BETARING® #1 BETARING® #2 FLEXIMAX® 200 FLEXIMAX® 300 FLEXIMAX® 400

224 151 102 84 224 151 102 226 168 124 96 83 172 118 84 200 128 97 246 157 102 186 136 189 148 92

0.964 0.980 0.979 0.983 0.964 0.980 0.979 0.977 0.977 0.976 0.982 0.984 0.965 0.976 0.979 0.959 0.974 0.975 0.973 0.970 0.980 0.963 0.973 0.973 0.979 0.983


268 NCEES

Random and Structured Packings Used in Packed Extractors (cont'd)

Packing Surface Area ap1 mm3

2Void Fraction1 (e)

Plastic Random PackingSuper INTALOX® Saddles #1 Super INTALOX® Saddles #2 BETARING® #1 BETARING® #2 SNOWFLAKE® FLEXIRING® 1 in. FLEXIRING® 1-1/2 in. FLEXIRING® 2 in.

204 105 167 114 93 205 119 99

0.896 0.934 0.942 0.940 0.949 0.922 0.925 0.932

Ceramic Random PackingINTALOX® Saddles 1 in. INTALOX® Saddles 1-1/2 in. INTALOX® Saddles 2 in.

256 195 118

0.730 0.750 0.760

Ceramic Structured PackingFLEXERAMIC® 28 FLEXERAMIC® 48 FLEXERAMIC® 88

282 157 102

0.720 0.770 0.850

Metal Structured Packing2

Koch-Glitsch SMV-8 Koch-Glitsch SMV-10 Koch-Glitsch SMV-16 Koch-Glitsch SMV-32 Sulzer SMV 2Y Sulzer SMV 250Y Sulzer SMV 350Y INTALOX® 2T INTALOX® 3T INTALOX® 4T

417 292 223 112 205 256 353 214 170 133

0.978 0.985 0.989 0.989 0.990 0.988 0.983 0.989 0.989 0.987

Plastic Structured Packing2

Koch-Glitsch SMV-8 Koch-Glitsch SMV-16 Koch-Glitsch SMV-32 Sulzer SMV 250Y

330 209 93 256

0.802 0.875 0.944 0.875

1. Typical value for standard wall thickness. Values will vary depending upon thickness.2. SMV structured packings also are available with horizontal dual-flow perforated plates

installed between elements (typically designated SMVP packing). These plates generally reduce backmixing and improve mass-transfer performance at the expense of a reduction in the open cross-sectional area and somewhat reduced capacity.



NCEES 269

5.4.2.8 Liquid-Liquid Extraction Equipment: Sieve Tray Columns

Sieve Tray Perforated Area

Perforations usually are in the range of 0.125 to 0.25 in (0.32 to 0.64 cm) in diameter, set 0.5 to 0.75 in (1.27 to 1.81 cm) apart, on square or triangular pitch. Hole size appears to have relatively little effect on the mass-transfer rate except that, in systems of high interfacial tension, smaller holes produce somewhat better mass transfer. The entire hole area is normally set at 15 to 25 percent of the column cross-section, although adjustments may be need-ed. It is common practice to set the velocity of liquid exiting the holes to correspond to a Weber number between 8 and 12. This normally gives velocities in the range of 0.5 to 1.0 sec

ft (15 to 30 scm ).

The velocity of the continuous phase in the downcomer (or upcomer) udow, which sets the downcomer cross- sectional area, should be set lower than the terminal velocity of some arbitrarily small droplet of dispersed phase, such as a diameter of 1/32 or 1/16 in (0.08 or 0.16 cm). Otherwise, recirculation of entrained dispersed phase around a tray will result in flooding. The terminal velocity ut of these small drops can be calculated using Stokes’ Law:

ug d18t

c

p2

ntD

=

Downcomer area typically is in the range of 5 to 20 percent of the total cross-sectional area, depending upon the ratio of continuous- to dispersed-phase volumetric flow rates.

For large columns, tray spacing between 18 and 24 in. (45 and 60 cm) is generally recommended.

The height of the coalesced layer at each tray, h, is

hg

P P g L1 d

o dow d

z t

z t

D

D D D=−

+ −` j

where

DPo = orifice pressure drop

DPdow = pressure drop for flow through a downcomer (or upcomer)

L = downcomer (or upcomer) length

The orifice pressure drop DPo is

. .log ReforP Re u d g

du d

21 1 0 71 3 2

.

o d oo

o do o d

22

2 0 2

tvt v

nt

D D= − + =−

d dn nwhere do = diameter of orifice in ft

The pressure drop through the downcomer is

.P

u2

4 5dow

dow c2 t

D =

where udow = velocity in downcomer (or upcomer)

For large columns, the design should specify that the height of the coalesced layer is at least 1 in. (2.5 cm) to en-sure that all holes are adequately covered.


270 NCEES

For segmental downcomers, the area of the downcomer is

A SH H S6 3 42 2= +_ i

where

A = area of segmental downcomer (or upcomer)

H = height of segmental downcomer (or upcomer)

S = chord length of segmental downcomer (or upcomer)

Chord length S is

S H D H8 2 2col

21

= −d n= Gwhere Dcol = column diameter

Sieve Tray Flooding Velocity

Velocity of the continuous phase at the flood point is

u

B uu C

L A.

cf

cfdf

2

0 5

=+

−

d n

R

T

SSSSSSSS

V

X

WWWWWWWW

where

A d g6o tcD

= .

Bg f1 11

ha

d2t

t

D=

.C

g f22 7

da

c2t

t

D=

where

fha = fractional hole area

fda = fractional downcomer area

The cross-flow velocity of the continuous phase uc flow is

u z hL

ucflowfp

c. -

where

Lfp = length of flow path

z = sieve tray spacing

Sieve Tray Efficiency

The sieve tray efficiency is approximated by

. d

zuu0 21 .

. .

oo c

d0 35

0 5 0 42

pv

= f dp n


NCEES 271

5.4.3 Adsorption

5.4.3.1 Adsorption EquilibriumFor a single adsorbate in a gas stream, the equilibrium capacit of the adsorbent may be related to the concentration of the adsorbate in the bulk stream by the Freundlich equation:

W = a pn

where

W = unit mass of adsorbentmass f ads rbateq q

p = partial pressure of adsorbate in the bulk gas stream

a, n = empirical coefficients derived from log-log plot of data for W vs. p

Both coefficients are a function of temperature.

The Freundlich equation can be used for liquid-solid adsorption by entering concentration instead of partial pressure.

Typical Adsorption IsothermsTYPICAL ADSORPTION ISOTHERMS

INCREASINGTEMPERATURE

LOG PARTIAL PRESSURE OF ADSORBATE

MASS

ADS

ORBA

TE/M

ASS

ADSO

RBAN

T

5.4.3.2 Adsorption OperationAdsorption in typical commercial operations is conducted by passing the gas or liquid stream through a usually vertical fixed bed of adsorbent particles. Adsorption beds are usually oriented vertically.

Adsorption beds have three zones that characterize the operation:

1. Equilibrium zone where adsorbate is in equilibrium with inlet concentration2. Mass transfer zone where adsorbate is diffusing into adsorbent3. Active zone where no adsorption has occurred

The length of the mass transfer zone (MTZ) is a function of the fluid velocity along with adsorbent porosity and uniformity of pore size.


272 NCEES

Adsorption Concentration Profiles Across Bed

EQUILIBRIUMZONE

MASSTRANSFER

ZONE

LOy OUT

y IN

ACTIVEZONE

CONCENTRATION PROFILE AT A GIVEN TIME DURING ADSORPTION OPERATION

BED LENGTH

VAPO

R PH

ASE

CONC

ENTR

ATIO

N

Three performance regimes for adsorption beds characterize the operation. Considering a given point in a bed:

1. Dry, when the mass transfer zone is below the point in the bed and the concentration has a low value2. Break-through,when the mass transfer zone reaches the point in the bed and the concentration increases3. Saturated, when the concentration at the point in the bed increases to the value of the inlet concentration

Adsorption Outlet Composition Versus Time

DRY BREAK-THROUGH

TIME0

SATURATED

y OUT

y IN

CONCENTRATION PROFILE AS A FUNCTION OF TIME AT A GIVEN POINT IN THE BED. ADSORPTION STEP.

VAPO

R PH

ASE

CONC

ENTR

ATIO

N


NCEES 273

5.4.3.3 Adsorption RegenerationAdsorption processes can be nonregenerative or regenerative. Nonregenerative adsorption is a batch process. For regenerative adsorption, adsorbent beds are cycled between adsorption and desorption (regeneration) modes and multiple beds are required for continuous operation.

During regeneration, stripping the adsorbate is accomplished by passing a pure fluid through the bed at a lower pressure for pressure swing adsorption (PSA) or at a higher temperature for temperature swing adsorption (TSA). For TSA, the pressure may be slightly lowered in addition to the temperature increase. Often a split stream from the fluid exiting the adsorbing bed is used as the pure fluid for regenerating adsorption beds.

The regeneration of adsorption beds leaves a residual concentration of adsorbate in the adsorbent. This reduces the working capacity of regenerated adsorbent in comparison with the capacity of fresh adsorbent.

Working capacity W W Wsat regen= −l

where

Wsat = amount adsorbed on the bed at break-through

Wregen = amount of adsorbate remaining on the bed after regeneration

5.4.3.4 Characteristics of Typical Adsorption Systems

Adsorption System Characteristics

System Type:TSA PSA

Gas Phase Liquid Phase Gas PhaseConfiguration of systemNumber of beds 2 to 4 2 to 4 2 to 16Time on adsorption 4 to 8 hours 4 to 8 hours Minutes to hoursFlow direction on adsorption Down Up Up

Flow direction on regeneration Up Down; treated vaporized liquid when feasible Down

Common adsorbents

Hydrophobic Activated carbons for removing VOCs from gas

Activated carbons for water purification

Activated carbon for air separations; heavy hydrocarbons from light hydrocarbons

Hydrophilic Silica gel, activated alumina, mol sieve for dehydration and removing slightly polar organics

5.4.4 Leaching

5.4.4.1 Single-Stage LeachingLeaching is the removal of a soluble substance from an insoluble solid via liquid extraction. The desired compo-nent diffuses into the solvent by mass transfer.

Two common methods of leaching are:

• Percolation of liquids through stationary solid beds• Dispersion of solids in each leaching stage by mechanical agitation


274 NCEES

5.4.4.2 Multistage LeachingFor multistage leaching processes, the most common setup is continuous countercurrent leaching, where a liquid solvent overflows from stage to stage in a direction opposite to the flow of the solid. The stages are numbered in the direction of flow of the solid.

• The flow rates of contained liquid in the solid slurry streams are shown as L-values.• The concentrations of solute in the solid slurries are shown as x-values.• Feed solid slurries enter at stage 1, containing a liquid flow of La with a solute concentration of Xa.• Leached solid slurries exit at stage N, containing a liquid flow of Lb with a solute concentration of Xb.• It is assumed that the solids flow rate is constant from stage to stage.• The flow rates of overflow solvent from each stage are shown as V-values.• The concentrations of solute in the solvent streams are shown as y-values.• Lean solvent enters the process at stage N, at a mass flow rate of Vb and a solute concentration of yb.• The concentrated solvent, or leachate, exits at a mass flow rate of Va and a solute concentration of Ya.

Multistage Leaching Diagram

Va VbVNYa

V2 Vn Vn+1 Vn+2

xa xbxN-1

NnONE

STAGELEACHATE LEAN

SOLVENT

FEEDSOLIDS

LEACHEDSOLIDS

STAGE STAGE STAGE

x1 xn-1 xn xn+1n+1La LbLN-1L1 Ln-1 Ln Ln+1

YbYNY2 Yn Yn+1 Yn+2

Leaching Calculations

Inputs = Outputs:

La + Vn+1= Va + Ln

Component balance:

( ) ( ) ( ) ( )L x V y V y L xa a n n a a n n1 1+ = ++ +

Leaching Operating Line

Y V

LX V

V Y L Xn n

nn n

a a a a1 1 1= +

−+

+ +

Note: If the density of liquid Ln is constant from stage to stage, then the overflow and underflow rates are both con-stant and the operating line is straight.

Calculation of the Number of Required Stages in Leaching With Constant Overflow

The equilibrium line for leaching is

Xe = Ye


NCEES 275

The first stage of the leaching process is calculated initially as a mass balance to set up the flow of slurried solids through the rest of the stages. Therefore, the following calculation determines the total number of stages N, in the format of N–1:

ln

lnN

x xy yy xy x

1

b a

b a

a a

b b

− =

−−

−−e

e o

o

5.4.5 Batch Distillation

5.4.5.1 Rayleigh Equation

lnndn

nn

y xdxf

n

n

x

x

0

f f

0 0

= = −# #where

nf = moles in still at end of run

n0 = initial moles in still

xf = mole fraction in liquid phase at end of run

x0 = initial mole fraction in liquid phase in still

5.4.5.2 Relative Volatility Equation

xyxy

11ija =

−−d

c m

n

where

aij = relative volatility

y = mole fraction of light component in vapor phase

Rearranging:

( )y xx

1 1aa= + −

Therefore,

ln lnnn

nn

AA

AB BB

0 0a=

where

nx = moles of liquid "x" left in the still at any time

0 = time zero

aAB = relative volatility


276 NCEES

5.4.5.3 Operating Line for Batch Distillation With Reflux y R

Rx R

x1 1n

D

Dn

D

D1 = + + ++

where

RD = reflux ratio based on the distillate rate

x = liquid composition

5.4.5.4 Batch Distillation Apparatus

Batch Distillation Apparatus

N

N-1

N-2

COLUMN

DISTILLATEACCUMULATOR

CONDENSER

REBOILER

QR•

QC•

1

2

3


NCEES 277

5.4.6 Crystallization

5.4.6.1 Saturation and Supersaturation

The Solubility-Supersolubility Diagram

LABILE

TEMPERATURE

STABLEMETASTABLE

CONC

ENTR

ATIO

N

C"B"

C'

B'

B

D CA

Diagram regions:

• Stable (unsaturated) zone, where crystallization is impossible.• Metastable (supersaturated) zone, between the solubility and supersolubility curves, where spontaneous crys-

tallization is improbable. However, if a crystal seed were placed in such a metastable solution, growth would occur on it.

• Unstable or Labile (supersaturated) zone, where spontaneous crystallization is probable, but not inevitable.

5.4.6.2 Expressions of SupersaturationDc = c – c*

where

c = concentration

c* = saturation concentration

Dc = driving-force concentration


278 NCEES

*S cc=

where

S = supersaturation ratio

s *cc S 1D= = −

where s = relative supersaturation (100s is % supersaturation)

5.4.6.3 Expression of SupercoolingDq = q* – q

where

q = temperature of the solution

q* = saturation temperature of the solution

The supersaturation and supercooling are related by the local slope of the solubility curve *dd ci

by*c d

d ci iD D= c m

5.4.6.4 Nucleation

Diagram of NucleationNUCLEATION

PRIMARY

HOMOGENEOUS(SPONTANEOUS)

HETEROGENEOUS(INDUCED BY FOREIGN PARTICLES)

SECONDARY(INDUCED BY CRYSTALS)

Gibbs Energy of Nucleation

G

r3

4crit

c2rc

D =

where

Gr3

4crit

c2rc

D = = Gibbs free energy for the critical radius of a stable nucleus

g = interfacial tension between the developing crystal surface and the supersaturated solution

rc = critical radius of a stable nucleus


NCEES 279

Homogeneous Nucleation Rate (Arrhenius Form)

( )lnJ A

k T Sv

316

EXP 3 3 2

3 2rc= −> H where

J = nucleation rate

A = rate constant

k = Boltzmann constant (k NRc= , where N is Avogadro's number)

v = number of moles of ions produced from one mole of electrolyte (for non electrolytes, v = 1)


S = supersaturation ratio

Heterogenous Nucleation Rate

J k cmaxnnD=

where

J = nucleation rate

kn = nucleation rate constant

Dcmax = maximum allowable metastable zone width

n = the observed order of the nucleation (a fitting parameter)

5.4.6.5 Crystal GrowthR K c A dt

dm G dtdL

dtdr v1 3 3 6 6

G Gg

c c c cbat

bat

bat

batD= = = = = = r

where

RG = mass deposition rate, in m skg2 :

KG = mass-transfer coefficient with units that are dependent on g (if g = 1), in sm

g = the order (a fitting parameter)

Dcg = concentration driving force for mass transfer, in mkg3

A = b L2 = particle area, in m2

m = a rc L3 = particle mass, in kg

t = time, in s

a = volume shape factor

b = surface shape factor

G = overall linear growth rate, in sm

rc = crystal density, in mkg3


280 NCEES

L = some characteristic size of the crystal, in m

r = radius corresponding to the equivalent sphere, in m

vr = mean linear velocity of growth, in sm

Some Mean Overall Crystal Growth Rates Expressed as a Linear Velocity1

Crystallizing Substance Cc S smvr b l

( ) ( )NH SO Al SO H O244 2 4 2 4 3 2: : 15 30 30 40

1.03 1.03 1.09 1.08

1.1 × 10–8* 1.3 × 10–8* 1.0 × 10–7* 1.2 × 10–7*

NH4NO3 40 1.05 8.5 × 10–7

( )NH SO4 2 4 30 60 90

1.05 1.05 1.01

2.5 × 10–7* 4.0 × 10–7 3.0 × 10–8

NH4H2PO4 20 30 30 40

1.06 1.02 1.05 1.02

6.5 × 10–8 3.0 × 10–8 1.1 × 10–7 7.0 × 10–8

MgSO H O74 2: 20 30 30

1.02 1.01 1.02

4.5 × 10–8*

8.0 × 10–8* 1.5 × 10–7*

( )NiSO NH SO H O64 4 2 4 2: : 25 25 25

1.03 1.09 1.20

5.2 × 10–9

2.6 × 10–8

4.0 × 10–8 ( )K SO Al SO H O242 4 2 4 3 2: : 15

30 30 40

1.04 1.04 1.09 1.03

1.4 × 10–8*

2.8 × 10–8*

1.4 × 10–7*

5.6 × 10–8*KCl 20

401.02 1.01

2.0 × 10–7

6.0 × 10–7

KNO3 20 40

1.05 1.05

4.5 × 10–8

1.5 × 10–7

K2SO4 20 20 30 50 50

1.09 1.18 1.07 1.06 1.12

2.8 × 10–8* 1.4 × 10–7* 4.2 × 10–8* 7.0 × 10–8* 3.2 × 10–7*

KH2PO4 30 30 40 40

1.07 1.21 1.06 1.18

3.0 × 10–8

2.9 × 10–7

5.0 × 10–8

4.8 × 10–7

NaCl 50 50 70 70

1.002 1.003 1.002 1.003

2.5 × 10–8

6.5 × 10–8

9.0 × 10–8

1.5 × 10–7

Na S O H O52 2 3 2: 30 30

1.02 1.08

1.1 × 10–7 5.0 × 10–7


NCEES 281

Some Mean Overall Crystal Growth Rates Expressed as a Linear Velocity1 (cont'd)

Crystallizing Substance Cc S smvr b l

Citric acid monohydrate 25 30 30

1.05 1.01 1.05

3.0 × 10–8 1.0 × 10–8 4.0 × 10–8

Sucrose 30 30 70 70

1.13 1.27 1.09 1.15

1.1 × 10–8* 2.1 × 10–8* 9.5 × 10–8 1.5 × 10–7

1 The supersaturation is expressed by S cc=l with c and c' as kg of crystallizing substance per kg of free water. The

significance of the mean linear growth velocity, v G21=rc m, is explained by equation 6.61 and the values recorded

here refer to crystals in the approximate size range 0.5–1 mm growing in the presence of other crystals.

* Denotes that the growth rate is probably size-dependent.

Source: Mullin, J.W., Crystallization, 4th ed., Woburn, MA: Reed Educational and Professional Publishing Ltd., 2001, p. 237.

5.4.7 FiltrationTypes of filters:

1. Discontinuous pressure filters2. Continuous filters3. Centrifugal filters4. Cartridge filters5. Bag filters

5.4.7.1 Factors for Selection of Filter MediaThe filter media in any process filter need to meet the following requirements to be of value in a chemical process:

• The septum must obviously be able to retain the solids to be filtered, producing a reasonably clear filtrate• The removed solids must not plug off the media upon initial or subsequent use.• The media must be chemically resistant to the chemicals in the filtrate and the filter cake.• The septum must be strong enough physically to withstand the operating conditions.• The media must allow the cake to be discharged cleanly and completely.• The cost of the media must be reasonable enough not to add significantly to the overall plant or production

cost.


282 NCEES

5.4.7.2 Filtration EquationsTotal pressure drop:

( ) ( )p p p p p p p p pa b a b c mD D D− = − = − + − = − −l l

where

- Dp = overall pressure drop

pa = filter inlet pressure

p' = septum inlet pressure

pb = filter outlet pressure

- Dpc = pressure drop over cake

- Dpm = pressure drop over medium

Therefore, P p pb aD = −

Filter cake pressure drop:

( )( )

dLdp

g Du150 1

c s p2 3

2

z f

n f=−

where

dLdp

= pressure gradient at thickness L

µ = viscosity of filtrate

u = linear velocity of filtrate, based on filter area

e = porosity of cake

gc = gravitational conversion factor

Dp = nominal diameter of solid particles

D sv6

s p p

pz = for nonspherical particles

1sz = for spherical particles

or

. ( )

dLdp

g

u vs

4 17 1

c

p

p

3

22

f

n f

=− f p

where

sp = surface of single particle

vp = volume of single particle

Filter medium resistance:

R u

p p gup g

mb c m c

n nD=

−=

−l` j


NCEES 283

5.4.8 Drying of Solids

5.4.8.1 Moisture (Solvent) Percentage ContentTypically calculated on a dry solid/dry air basis:

X = % moisture in solid = mmsw

where

X = moisture (solvent) content in solid, moisture mass/dry solid mass

mw = moisture (solvent) content, mass of water or solvent, in lbm

ms = mass of dry solid, in lbm

Y = % moisture in air = m

maw

where

Y = moisture (solvent) content in air, moisture mass/dry air mass

mw = moisture (solvent) content, mass of water or solvent, in lbm

ma = mass of dry air, in lbm

5.4.8.2 Rate of DryingRate of drying is dictated by the state of the solvent, such as:

• "Free" solvent on surface of solids• "Bound" solvent, which must reach the surface through diffusion or capillary action• "Solvated" solvent, which is chemically bound to the solids (sometimes labile to removal, sometimes not) that

are not generally considered in drying analyses


284 NCEES

Drying Curve

FALLINGRATE II

N, D

RYIN

G RA

TEFALLINGRATE I

CONSTANT RATE

X * XC

X, MOISTURE (SOLVENT) CONTENT lb/lb DRY SOLID

where

X* = equilibrium moisture content: the moisture content of the solid when it reaches equilibrium with the surrounding air; depending upon the specific conditions of the surrounding air

Xc = critical moisture content: the moisture content that marks the instant when the liquid content on the surface of the solid is no longer sufficient to maintain a continuous liquid film on the surface

Constant Rate: Rate of drying independent of moisture content. During this period the solid is so wet that the entire surface of the solid is covered with a continuous film of liquid.

Falling Rate I: Only part of the solid surface is saturated as the entire solid surface can no longer be main-tained at saturation conditions by the movement of moisture within the solid. The rate of drying is linear with regard to X.

Falling Rate II: The entire solid surface is unsaturated and the drying rate is limited by the rate of internal moisture movement.

5.4.8.3 Specific Drying ApplicationsDrying of slab using gas from one side only:*

1. For drying during the constant rate periodRate of drying can be determined based on the balance between the heat transfer to the material and the rate of vapor removal from the surface.

Nh A T

k A pCt

gmD

D= =

* Source: McCabe, Warren L., and Julian C. Smith, Unit Operations in Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976.


NCEES 285

where

DT = gas dry bulb temperature—temperature at surface of solid

Dp = vapor pressure of water at surface temperature—partial pressure of water vapor in the gas

A = surface area, in ft2

kg = mass-transfer coefficient, in hr ft atmlbm- -2

Nc = constant drying rate, in ft hrlbm-2

l = latent heat of evaporation, in lbmBtu

ht = total heat-transfer coefficient, in hr ft FBtu- -2 c

When the air is flowing parallel to the surface:

ht = 0.0128 G0.8

When the air is flowing perpendicular to the surface, the equation is

ht = 0.37 G0.37

where G = mass velocity, in ft hrlbm-2

( )t ANm X X

C

s 1 2=−

where

t = drying time

X1 = moisture content in solid at time 1

X2 = moisture content in solid at time 2

2. For falling rate period I

( )( ) lnt A N N

m X XNNs

1 2

1 22

1= −−> H

where

N1 = drying rate at time 1, in ft hrlb-2

N2 = drying rate at time 2, in ft hrlb-2

ms = mass of dry solids, in lb

3. For falling rate period II, rate curve must be integrated: t A

mNdXs

x

x

2

1= d n #


286 NCEES

5.4.8.4 Dryer Design and Performance1. Tray dryers

To determine the tray area for a specific production rate:

( )A L

P t tT

d=+

where

P = production rate, in mass of dry solids per hour

t = drying time

td = downtimefor loading and unloading trays

LT = tray loading in mass of dry solids per square area of tray, in ftlbm2

( )t k T TW d

12 f a s

s p2m t

= −

where

dp = drop diameter, in ft

W = moisture content in the drop, in lbm dry solidlbm

kf = thermal conductivity of the gas film, in hr ft FBtu- -c

Ta –Ts = temperature difference between drop and gas, in °F

l = latent heat of evaporation, in lbmBtu

rs = density of dry particle, in ftlbm3

2. Continuous through-circulation dryersTo determine required conveyor length:

Required dryer holding capacity C in pounds is

C = P t

where

P = production rate, in hrlbm dry solid

t = drying time, in hr


NCEES 287

A LP t=

where

A = conveyor area, in ft2

L = bed loading, in ft c nvey r arealbm dry s lid2 q q

q

B WA=

where

B = effective dryer length, in ft

W = conveyor width, in ft

3. Rotary dryersThe residence time can be determined empirically using:

for countercurrent flow, sign in the expression below is positive

for concurrent flow, sign in the expression below is negative

. .tSN D

LF

D LG0 23 0 65

.

.p

0 9

0 5

!=−

where

t = retention time, in min

D = diameter of shell, in ft

Dp = weighted average particle size of material, in micrometers

N = speed, in minrev

S = slope of shell, in ftft

G = air mass velocity in hr ftlbm- 2

F = feed rate in hr-ft f dryer cr ss-sectional area

lbm dry material2 q q


288 NCEES

4. Spray dryersAn estimate of the drying time can be found using: t

K T TW d

12 f a s

s p2m t

=−` j

where

t = drying time, in min

dp = drop diameter in ft

W = moisture content in the drop in lbm dry solidlbm

Kf = thermal conductivity of the gas film in hr ft FBtu- -c

Ta – Ts = temperature difference between drop and gas in °F

rs = density of the solid

5.4.8.5 Typical Critical Moisture Content of Various Materials

Approximate Critical Moisture Contents Obtained on the Air Drying of Various Materials, Expressed as Percentage Water on the Dry Basis1,2

Material Thickness (in.) Critical Moisture (% Water)

Barium nitrate crystals, on trays 1.0 7Beaverboard 0.17 Above 120Brick clay 0.62 14Carbon pigment 1 40Celotex 0.44 160Chrome leather 0.04 125Copper carbonate, on trays 1–1.5 60English china clay 1 16Flint clay refractory brick mix 2.0 13Gelatin, initially 400% water 0.1–0.2 (wet) 300Iron blue pigment, on trays 0.25–0.75 110Kaolin 14Lithol red 1 50Lithopone press cake, in trays 0.25 6.4

0.50 8.00.75 12.01.0 16.0

Niter cake fines, on trays Above 16Paper, white eggshell 0.0075 41 Fine book 0.005 33 Coated 0.004 34 Newsprint 60–70Plastic clay brick mix 2.0 19


NCEES 289

Approximate Critical Moisture Contents Obtained on the Air Drying of Various Materials, Expressed as Percentage Water on the Dry Basis1,2 (cont'd)

Material Thickness (in.) Critical Moisture (% Water)

Poplar wood 0.165 120Prussian blue 40Rock salt, in trays 1.0 7Sand, 50–150 mesh 2.0 5 200–325 mesh 2.0 10 through 325 mesh 2.0 21Sea sand, on trays 0.25 3

0.50 4.70.75 5.51.0 5.92.0 6.0

Silica brick mix 2.0 8Sole leather 0.25 Above 90Stannic tetrachloride sludge 1 180Subsoil, clay fraction 55.4% 21Subsoil, much higher clay content 35Sulfite pulp 0.25–0.75 60–80Sulfite pulp (pulp lap) 0.039 110White lead 11Whiting 0.25–1.5 6.9Wool fabric, worsted 31Wool, undyed serge 8

Sources: 1 Perry, Robert H., and Cecil H. Chilton, Perry's Chemical Engineers' Handbook, 6th ed.

2 Schweitzer, Philip A., Handbook of Separation Techniques for Chemical Engineers, 2nd ed.


290 NCEES

5.4.9 Adiabatic Humidification and Cooling

Adiabatic Humidification and CoolingLENGTH OR HEIGHT

Z

GAS INTERFACE

ADRIABATICSAT'N

TG1

Y '2

Y '2

Y 'as

Y 'as

Y '

T – dT

Y 'as

Y '1

L'1 L'2L' L'+ dL'

Y'1 Y ' Y ' dY '+G's1

ds = adz

G 's1G 's1

G 's1

Y '1

Y '2

TG

TG TG2G

dTG

TG1

TG2 TG1

TG2

Tas

Tas Tas Tas

TasTas

Tas

BULK GAS

BULK GAS

ABS

HUMI

DITY

ABS

HUMI

DITY

TEMP

ERAT

URE

SENSIBLE RATE OF TRANSFER

RATE OF MASS TRANSFER

TEMPERATURE

zO

O

dz

dY '

MATERIAL BALANCE

INTERFACIAL SERVICE

SAT'N HUMIDITY

dZ

PSYCHOMETRIC RELATIONS

SENSIBLE HEAT TRANSFER

MASS TRANSFER

FLOW MODEL

INTERFACE AND BULK LIQUID

L'2 – L'1 = G 's (Y '2 – Y '1)

G'sdY '1 = kYa (Y 'as – Y ')dz

dL' = G'sdY'

G's Cs1 dTG = hg a (TG – Tas) dz


NCEES 291

where

Ll = solute-free liquid flow rate

G sl = dry-gas mass flow rate

Y 1l = initial humidity

Y 2l = final humidity

Y asl = saturation humidity at liquid-gas interface

TG = temperature of bulk gas

Tas = temperature at liquid-gas interface

CS1 = specific heat capacity at the liquid-gas interface

hg = gas heat-transfer coefficient

Since Y asl is constant:

ln Y YY Y

Gk a z

as

as

s

y

2

1−−

=l ll l

lf p

where

ky = overall mass-transfer coefficient

a = interstitial surface per unit volume, in ftft3

2

z = height, in ft

G Y Y k a Z Ys y lm2 1 D− =l l l l_ ^i h

where Y lmD l^ h = logarithmic mean of humidity difference

or

lnlmNTU YY Y

Y YY Y

tGas

as2 1

2

1

D=

−= −

−l

l ll ll l

^ h > H and

HTU k aG

NTUz

tGy

s

tG= =l

where

NTUtG = number of gas-phase transfer units

HTUtG = height of transfer unit

5.4.9.1 Air-Water Systems Y y29

18A A= r

where YA = molal humidity


292 NCEES

AY yy1AA=

−rr

where yAr = mole fraction of water vapor

Y yy

2918 1

AAA= −rre o

Relative humidity = 100 APP

A

where AP = partial pressure of water at a given temperature

PA = vapor pressure of water at a given temperature

A

AY PP Y P

P1 1A AS

A

A=−

= −

where Yas = saturation humidity

% saturation = A

A( )Y

YP PP P

10011

100as

A

A

A=−

−

^_ i

h at total pressure of one atmosphere

Humid heat CPH = 0.24 + 0.46YA

CPH = CPy (1 + YA)

where CPy = specific heat of water vapor at constant pressure

CPH = humid heat capacity

5.4.9.2 Adiabatic Saturation Temperature t t C Y YAS y

PH

RAS A0 0

m= − −` j

where

tAS = adiabatic saturation temperature

ty0 = initial inlet temperature

lR = heat of vaporization at reference temperature

YA0 = initial inlet humidity

CPH = humid heat capacity

YAS = humidity at saturation

t t C Y YWB y

PH

RWB A

m= − −` j

where

YWB = humidity at wet bulb temperature

tWB = wet bulb temperature


NCEES 293

Humidity Chart for the Air-Water System at One Atmosphere

12

25

0.22 0.24

140° ADRIABATIC SITUATION LINES

SATURATED VOLUME VS. TEMPERATURE

SPECIFIC VOLUME VS TEMPERATURE

HUMI

D HE

AT V

S HU

MIDI

TY

PERC

ENT

SATU

RATIO

N 135°

130°

125°

120°

115°

110°105°

100°95°

90°85°

80°75°

70°65°60°55°50°45°

140° ADRIABATIC SITUATION LINES

SATURATED VOLUME VS. TEMPERATURE

SPECIFIC VOLUME VS TEMPERATURE

HUMI

D HE

AT V

S HU

MIDI

TY

PERC

ENT

SATU

RATIO

N

0.26 0.28 0.15

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0

0.30

100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

135°

130°

125°

120°

115°

110°105°

100°95°

90°85°

80°75°

70°65°60°55°50°45°

40 60 80 100 120 140TEMPERATURE, F°

160 180 200 220 240 250

13

14

15

16

17

12

19

20

21

22

HUMI

DITY

, LB

WAT

ER V

APOR

/LB D

RY A

IR

VOLU

ME,C

U FT

/LB D

RY A

IRHUMID HEAT, BTU/LB DRY AIR (°F)

Source: G.G. Brown et al., Unit Operations, New York: John Wiley & Sons, Inc., 1950, p. 545.

Cooling Tower Operating Diagram

80

60Hy vs tx

txHY

11

CpxLGB

Hy8 vs t4

tx0

Hy0

SLOPE =

TOP OF TOWER

BOTTOM OFTOWER

CpxLmaxGB

Hy vs tx

txHY

11

CpxLGB

Hy8 vs t4

tx0

Hy0

40

20

050 60

SLOPE =

70 80

TOP OF TOWER

BOTTOM OFTOWER

90t, °F

H, B

TU/LB

DRY

AIR

100 110

CpxLmaxGB


294 NCEES

H GC L t H G

C L tyB

Pxx y0

B

Pxx0= + −e eo o

where

Hy = enthalpy of vapor phase

CPx = specific of liquid phase

L = liquid phase mass velocity

GB = dry air mass velocity

tx = liquid phase temperature

Hy0 = initial enthalpy of vapor phase

tx0 = liquid phase inlet temperature

295

6 PLANT DESIGN AND OPERATION

6.1 Terms and Definitions

DefinitionsTerm Description

Boiling point The temperature at which the vapor pressure of a liquid equals the atmospheric pressure of 14.7 pounds per square inch (psia), 101 kPa, or 760 mm of mercury. For purposes of this classification, when an accurate boiling point is not available for a material or when a mixture does not have a constant boiling point, use the 20%-evaporated point of a distillation performed in accordance with ASTM D 86. Boiling point is commonly expressed in °F or °C.

Combustible dust

A finely divided solid material that is 420 microns or less in diameter and that, when dispersed in air in the proper proportions, can be ignited by a flame, spark, or other source of ignition. Will pass through a U.S. No. 40 standard sieve.

Combustible liquid

A liquid having a closed-cup flash point at or above 100°F (38°C). Subdivided into:

Class II: Closed-cup flash point at or above 100°F (38°C) and below 140°F (60°C)

Class IIIA: Closed-cup flash point at or above 140°F (60°C) and below 200°F (93°C)

Class IIIB: Closed-cup flash point at or above 200°F (93°C)

This category does not include compressed gases or cryogenic fluids.Deflagration An exothermic reaction, such as the extremely rapid oxidation of a flammable dust or vapor in air, in

which the reaction progresses through the unburned material at a rate less than the velocity of sound. A deflagration can have an explosive effect.

Detonation An exothermic reaction characterized by the presence of a shock wave in the material that establishes and maintains the reaction. The reaction zone progresses through the material at a rate greater than the velocity of sound. The principal heating mechanism is one of shock compression. A detonation has an explosive effect.


296 NCEES

Definitions (cont'd)Term Description

Explosion An effect produced by the sudden, violent expansion of gases, which may be accompanied by a shock wave, a disruption of enclosing materials or structures, or both. An explosion could result from:

• Chemical changes such as rapid oxidation, deflagration or detonation, decomposition of molecules, or runaway polymerization (usually detonations)

• Physical changes such as pressure tank ruptures• Atomic changes such as nuclear fission or fusion

Flammable gas

A material that is a gas at 68°F (20°C) or less at 14.7 psia (101 kPa) of pressure—therefore a material that has a boiling point of 68°F (20°C) or less at 14.7 psia (101 kPa)—and which either:

• Ignites at 14.7 psia (101 kPa) when in a mixture of 13% or less by volume with air• Has a flammable range mixed in air at 14.7 psia (101 kPa) and 63°F (20°C)

These levels shall be determined at the specified pressure and temperature in accordance with ASTM E 681.

Flammable liquefied gas

A liquefied compressed gas that, under a charged pressure, is partially liquid at a temperature of 68°F (20°C) and that is flammable.

Flammable liquid

A liquid having a closed-cup flash point below 100°F (38°C). Flammable liquids are further catego-rized into a group known as Class I liquids and subdivided into:

Class IA: Closed-cup flash point below 73°F (23°C) and boiling point below 100°F (38°C)

Class IB: Closed-cup flash point below 73°F (23°C) and boiling point at or above 100°F (38°C)

Class IC: Closed-cup flash point at or above 73°F (23°C) and boiling point below 100°F (38°C). The category of flammable liquids does not include compressed gases or cryogenic fluids.

Flammable material

A material capable of being readily ignited from a common source of heat or at a temperature of 600°F (316°C).

Flammable solid

A solid, other than a blasting agent or explosive, that:

Is capable of causing fire through friction, absorption or moisture, spontaneous chemical change, or retained heat from manufacturing or processing

or

Has an ignition temperature below 212°F (100°C)

or

Burns so vigorously and persistently when ignited as to create a serious hazard

A chemical shall be considered a flammable solid in accordance with the test method of CPSC 16 CFR: Part 1500.44 if it ignites and burns with a self-sustained flame at a rate greater than 0.1 inch (2.5 mm) per second along its major axis.

Flammable vapors or fumes

The concentration of flammable constituents in air that exceeds 25% of their lower flammable limit (LFL).

Flash point The minimum temperature in degrees Fahrenheit (or Centigrade) at which a liquid will give off suf-ficient vapors to form an ignitable mixture with air near the surface or in the container, but will not sustain combustion. The flash point of a liquid shall be determined by appropriate test procedure and apparatus as specified in ASTM D 56, ASTM D 93, or ASTM D 3278.

Chapter 6: Plant Design and Operation

NCEES 297


Highly toxic A material that produces a lethal dose or lethal concentration that falls within any of these categories:

• A chemical that has a median lethal dose (LD50) of 50 milligrams or less per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each

• A chemical that has a median lethal dose (LD50) of 200 milligrams or less per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each

• A chemical that has a median lethal concentration (LC50) in air of 200 parts per million by vol-ume or less of gas or vapor, or 2 milligrams per liter or less of mist, fume, or dust when admin-istered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each

Mixtures of these materials with ordinary materials, such as water, may not warrant classification as highly toxic.

Immediately dangerous to life and health (IDLH)

The concentration of air-borne contaminants that poses a threat of death, immediate or delayed per-manent adverse health effects, or effects that could prevent escape from such an environment. This concentration level of contaminants is established by the National Institute for Occupational Safety and Health (NIOSH) based on both toxicity and flammability. Generally it is expressed in parts per-million by volume (ppm/v) or milligrams per cubic meter (mg/m3).

Organic peroxide

An organic compound that contains the bivalent -O-O- structure and that may be considered a struc-tural derivative of hydrogen peroxide in which one or both of the hydrogen atoms have been replaced by an organic radical. Organic peroxides can pose an explosion hazard (detonation or deflagration) or can be shock sensitive. They also can decompose into various unstable compounds over an extended period of time.

Class I: Formulations that are capable of deflagration but not detonation

Class II: Formulations that burn very rapidly and pose a moderate reactivity hazard

Class III: Formulations that burn rapidly and pose a moderate reactivity hazard

Class IV: Formulations that burn in the same manner as ordinary combustibles and pose a mini-mal reactivity hazard

Class V: Formulations that burn with less intensity than ordinary combustibles or do not sustain combustion and pose no reactivity hazard

Unclassified detonable: Organic peroxides that are capable of detonation. These pose an extremely high explosion hazard through rapid explosive decomposition.


298 NCEES


Oxidizer A material that readily yields oxygen or other oxidizing gas or that readily reacts to promote or initi-ate combustion of combustible materials and, if heated or contaminated, can result in vigorous self-sustained decomposition.

Class 4: An oxidizer that can undergo an explosive reaction due to contamination or exposure to thermal or physical shock and that causes a severe increase in the burning rate of combustible materials with which it comes into contact. Additionally, the oxidizer causes a severe increase in the burning rate and can cause spontaneous ignition of combustibles.

Class 3: An oxidizer that causes a severe increase in the burning rate of combustible materials with which it comes into contact.

Class 2: An oxidizer that causes a moderate increase in the burning rate of combustible materials with which it comes into contact.

Class 1: An oxidizer that does not moderately increase the burning rate of combustible materials.Oxidizing gas A gas that can support and accelerate combustion of other materials more than air does.Physical hazard

A chemical for which there is evidence that it is one of the following:

• Combustible liquid• Cryogenic fluid• Explosive or flammable solid, liquid, or gas• Solid or liquid organic peroxide• Solid or liquid oxidizer• Oxidizing gas• Pyrophoric solid, liquid, or gas• Unstable (reactive) solid, liquid, or gas material• Water-reactive solid or liquid material

Toxic A chemical falling within any of these categories:

• Has a median lethal dose (LD50) of more than 50 milligrams per kilogram but not more than 500 milligrams per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each.

• A chemical that has a median lethal dose (LD50) of more than 200 milligrams per kilogram but not more than 1000 milligrams per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each.

• A chemical that has a median lethal concentration (LC50) in air of more than 200 parts per mil-lion but not more than 2000 part per million by volume or less of gas or vapor, or more than 2 milligrams per liter but not more than 20 milligrams per liter of mist, fume, or dust, when ad-ministered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each.


NCEES 299


Unstable (reactive) material

A material, other than an explosive, that in the pure state or as commercially produced will vigor-ously polymerize, decompose, condense, or become self-reactive and undergo other violent chemical changes, including explosion, when it is either:

• Exposed to heat, friction, or shock• In the absence of an inhibitor• In the presence of contaminants• In contact with incompatible materials

Unstable (reactive) materials are subdivided into:

Class 4: Materials that in themselves are readily capable of detonation or explosive decomposi-tion or explosive reaction at normal temperatures and pressures. Includes materials that are sensitive to mechanical or localized thermal shock at normal temperatures and pressures

Class 3: Materials that in themselves are capable of detonation or of explosive decomposition or explosive reaction but which require a strong initiating source or which must be heated under confinement before initiation. Includes materials that are sensitive to thermal or mechanical shock at elevated temperatures and pressures

Class 2: Materials that in themselves are normally unstable and readily undergo violent chemi-cal change but do not detonate; includes materials that can undergo chemical change with rapid release of energy at normal temperatures and pressures and that can undergo violent chemical change at elevated temperatures and pressures

Class 1: Materials that in themselves are normally stable but that can become unstable at elevated temperatures and pressures

Water-reactive material

A material that explodes; violently reacts; produces flammable, toxic, or other hazardous gases; or evolves enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture. Water-reactive materials are subdivided into:

Class 3: Materials that react explosively with water without requiring heat or confinement

Class 2: Materials that react violently with water or have the ability to boil water. Materials that produce flammable, toxic, or other hazardous gases, or evolve enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture

Class 1: Materials that react with water with some release of energy, but not violently

Source: International Code Council, International Building Code, 2015.


300 NCEES

6.2 Economic Considerations

NomenclatureAbbreviation Definition

A Uniform amount per interest periodBV Book valueC Cost, present worthDj Depreciation in year j

F Future worth, value, or amountG Uniform gradient amount per interest periodi Interest rate per interest periodm Number of compounding periods per interest periodn Number of interest periods, or the expected life of an assetP Present worth, value, or amountr Nominal annual interest rateSn Expected salvage value in year n

Subscriptse Effective

j At time j

n At time n

6.2.1 Cost Estimation and Project Evaluation

Basic EquationsFactor Name Converts Symbol Formula

Single payment Compound amount to F given P (F/P, i%, n) F = P (1 + i)n

Single payment Present worth to P given F (P/F, i%, n) P = F (1 + i)-n

Uniform series Sinking fund to A given F (A/F, i%, n) ( )A F i

i1 1n= + −d n

Capital recovery to A given P (A/P, i%, n)( )( )A P ii i1 11

n

n=

+ −+f p

Uniform series Compound amount to F given A (F/A, i%, n) ( )F A i

i1 1n= + −d n

Uniform series Present worth to P given A (P/A, i%, n)

( )( )P A i i

i1

1 1n

n=

++ −f p

Uniform gradient Present worth to P given G (P/G, i%, n)

( )( )

( )P Gi ii

i in

11 1

1n

n

n2=+

+ −− +f p

Uniform gradient* Future worth to F given G (F/G, i%, n) ( )F G

ii

in1 1n

2=+ −

−f p

Uniform gradient Uniform series to A given G (A/G, i%, n)

( )A G i in1

1 1n= − + −d n


NCEES 301

Basic Equations (cont'd)Factor Name Converts Symbol Formula

Interest rate to ic given r,m i mr1 1e

m= + −c m

Book value initial costBV D jR= −

* GF

iAF n

AF

GA#=

−=

Depreciation Methods

Method Description Formula Stipulations

Straight line

Annual depreciation cost d n

V Vs=−

where d = annual depreciation, in $ per year V = original value of the property at start the service-life period, completely installed and ready for use, in $ Vs = salvage value of property at end of service life, in $ n = service life, in years Va = asset or book value a = number of years in actual use i = annual interest rate expressed as a fraction R = uniform annual payments made at end of each year (annual depreciation cost), in $ V - Vs = total amount of the annuity accumulated in an estimated service life of n years (original value of property minus salvage value at end of service life), in $

Book value V V ada = −

Declining balance (or fixed percentage)

Fixed percentage factor f V

V1 sn1

= − d n

Book value V V f1aa= −` j

Sinking fund

Depreciation for year a d

n nn a V V

12 1

a s=+

− +−

__ `i

i j

Book value V V V Vii

1 11 1

a s n

a

= − −+ −+ −` __j

ii

Source: Peters, Max S., and Klaus D. Timmerhaus, Plant Design and Economics for Chemical Engineers, 4th ed., New York: McGraw-Hill, Inc., 1991, pp. 278 and 280.


302 NCEES

6.2.1.1 Cost IndiciesCost indices are used to update historical cost data to the present. If a purchase cost is available for an item of equipment in year M, the equivalent current cost can be found using:

$ ( )Current Cost in year Index in yearCurrent IndexM M= d n

Cost IndexYear Equipment Index Labor Index Material Index

0 341 100 1001 344 107 1062 352 116 1123 360 128 1134 368 139 1205 383 147 1276 401 155 1397 421 164 1618 432 176 1749 444 187 18810 503 197 20511 552 210 22812 579 218 24113 514 223 24814 554 231 25115 569 236 255

6.2.1.2 Scaling Equipment CostsThe cost of Unit A at one capacity related to the cost of a similar Unit B with X times the capacity of Unit A is approximately X n times the cost of Unit B, or:

Cost of Unit A Cost of Unit B Capacity of Unit BCapacity of Unit A n

= e o

Typical Scaling Factors (n) for Equipment Cost vs. CapacityEquipment Size Range Exponent

Agitator, propeller 0.50Agitator, turbine 0.30Boiler, industrial, all sizes 0.50Boiler, package 0.72Centrifuge, horizontal basket 1.72Centrifuge, solid bowl 1.00Conveyor, belt 0.65Conveyor, bucket 0.77Conveyor, screw 0.76Conveyor, vibrating 0.87

Compressor, reciprocating, air-cooled, two-stage, 150 psig discharge 10 to 400 minft3 0.69


NCEES 303

Typical Scaling Factors (n) for Equipment Cost vs. Capacity (cont'd)Equipment Size Range Exponent

Compressor, rotary, single-stage, sliding vane, 150 psig discharge 100 to 1000 minft3 0.79

Crystallizer, growth 0.65Crystallizer, forced circulation 0.55Crystallizer, batch 0.70Dryer, drum, single vacuum 10 to 102 ft2 0.76Dryer, drum, single atmospheric 10 to 102 ft2 0.40Dust collector, cyclone 0.80Dust collector, cloth filter 0.68

Dust collector, precipitator 0.75

Evaporator, forced circulation 0.70

Evaporator, vertical and horizontal tube 0.53

Fan, centrifugal 103 to 104 minft3 0.44

Fan, centrifugal 2 x 104 to 7 x 104minft3 1.17

Filter, plate and press 0.58Filter, pressure leaf 0.55Heat exchanger, shell and tube, floating head, carbon steel 100 to 400 ft2 0.60Heat exchanger, shell and tube, fixed sheet, carbon steel 100 to 400 ft2 0.44Mill, ball and roller 0.65Mill, hammer 0.85Motor, squirrel cage, induction, 440 volts, explosion proof 5 to 10 hp 0.69Motor, squirrel cage, induction, 440 volts, explosion proof 20 to 200 hp 0.99Pump, centrifugal, carbon steel 0.67Pump, centrifugal, stainless steel 0.70Pump, reciprocating, cast iron, horizontal, including motor 2 to 100 gpm 0.34Reactor, stainless steel, 300 psi 100 to 1000 gal 0.56Tanks and vessels, pressure, carbon steel 0.60Tanks and vessels, horizontal, carbon steel 0.50Tanks and vessels, stainless steel 0.68Tray, bubble cap, carbon steel 3- to 10-ft diameter 1.20Tray, sieve, carbon steel 3- to 10-ft diameter 0.86

Source: Guthrie, K.M., "Data and Techniques for Preliminary Capital Cost Estimating," Chemical Engineering, New York: Chemical Engeering, 1969.


304 NCEES

6.3 Design

6.3.1 Process DesignNote: The symbology used in this reference is intended to be used for the Chemical PE exam. It does not necessarily correspond to a particular standard.

6.3.1.1 Piping and Instrumentation Diagram (P&ID) Equipment Tag Nomenclature

Mechanical Function CodesCode Equipment or FunctionAG AgitatorAX Packaged unitBL BlowerBX BoilerCL ColumnCM CompressorCR Crane and winchCV ConveyorDR DryerEX ExpanderFA FanFI FilterFL FlareFX Fired furnace, heaterGN GeneratorHV HVACHX Unfired heat transfer equipment, e.g., heat

exchanger, condenser, cooler, reboilerMI Mixer, stirrer, mixing nozzle, inductor, ejectorPM PumpRX ReactorTB TurbineTK TankTX Thermal oxidizer, incineratorVS Vessel, pig receiver/launcherXX Material handling equipment, lift


NCEES 305

6.3.1.2 P&ID Equipment Symbols

CARTRIDGETYPE FILTER

FILTER

LIQUID EXPANDER HYDRAULIC TURBINE

GAS EXPANDER/STEAM TURBINE

GAS TURBINE

GEAR BOX

DIESEL ENGINE

MOTOR

GENERATOR

DRIVERS

G

D

M

G

FURNACE

FIRED HEATER

OTHERS

EJECTOR/EDUCTOR

MIXER/AGITATOR

VESSELS

VERTICAL1 AND 2 DIAMETERS

VESSEL WITHBODY FLANGE

VESSEL WITH HEATINGOR COOLING JACKET

FLAT-TOPVESSEL

HORIZONTALWITH BOOT

HORIZONTAL

NON-PRESSUREVESSEL


306 NCEES

AIR-COOLEDHEAT EXCHANGER

HEABRAZED PLATE-FIN

T EXCHANGER

PLATE-FRAME-TYPEHEAT EXCHANGER

HEAT EXCHANGERS

KETTLE-TYPEU-TUBE

KETTLE-TYPEFLOATING HEAD

KETTLE-TYPEFIXED TUBESHEET

FLOATING HEADAND COVER PLATE

FIXED TUBESHEET

U-TUBE

FLOATING HEAD

VERTICAL HEAT EXCHANGERFIXED TUBESHEET

VERTICAL HEAT EXCHANGERFLOATING HEAD

OUTER COILFOR EQUIPMENT

HEAT RECOVERY COILSVERTICAL TUBES

HEAT RECOVERY COILSHORIZONTAL TUBES

HEAT EXCHANGERS


NCEES 307

PUMP AND COMPRESSORS

CENTRIFUGAL COMPRESSOR

AXIAL COMPRESSOR

RECIPROCATING COMPRESSOR

SCREW COMPRESSOR

BLOWER/FAN

ROTARY (GEAR SCREW) PUMP

PROPORTIONING(METERING) PUMP

DIAPHRAGM PUMP

VACUUM PUMP

SUMP PUMP

VERTICAL PUMP

CENTRIFUGAL PUMP

M

M

TANKS

DOME ROOF TANK

FLOATING ROOF TANK

CONE ROOF TANK

SPHERICAL TANK

CONICAL BOTTOM TANK

LINE SYMBOLS

PRIMARY LINE

SECONDARY LINE

UNDERGROUND LINE

TRACED LINE

JACKETED LINE

FLEXIBLE HOSE (FLANGED)

FLEXIBLE HOSE (COUPLING)


308 NCEES

VALVE AND CONTROL SYMBOLS

GATE VALVE

GLOBE VALVE

BALL VALVE

PLUG VALVE

BUTTERFLY VALVE

NEEDLE VALVE

DIAPHRAGM VALVE

CHECK VALVE

3-WAY VALVE

4-WAY VALVE

DAMPER

PINCH VALVE

PRESSURE SAFETY RELIEF VALVE

VACUUM SAFETY RELIEF VALVE

P

VALVE AND CONTROL SYMBOLS

PILOT-ACTUATED RELIEF OR SAFETY VALVE ACTUATOR

SPRING- OR WEIGHT-ACTUATED RELIEF OR SAFETY VALVE ACTUATOR

RUPTURE DISK,PRESSURE RELIEF

RUPTURE DISK,VACUUM RELIEF


NCEES 309

SIGHT GLASS

DRAIN TRAPDT

SPARK ARRESTOR

REDUCER

VENT (WITH HOOD)

GENERAL PIPING SYMBOLS

OPEN VENT WITH GOOSENECK

SIPHON DRAIN

Y TYPE STRAINER

RESTRICTIONORIFICE

RUPTURE DISK

RO

BASKET-TYPE STRAINER

IN-LINE STATIC MIXER

FLAME ARRESTOR

CONSERVATION VENT

FLANGE

GENERAL PIPING SYMBOLS

BLIND FLANGE

QUICK COUPLING

SPECTACLE BLIND (CLOSED)

SPECTACLE BLIND (OPEN)

SCREWED CAP

WELDED END CAP

HOSE CONNECTION

COOLING TOWERS

NATURAL-DRAFTCOOLING TOWER

FORCED-DRAFTCOOLING TOWER

INDUCED-DRAFTCOOLING TOWER

HYPERBOLICCOOLING TOWER


310 NCEES

6.3.1.3 Instrumentation Tag Identifiers and SymbolsThe following identifiers are used in P&ID instrument tags.

Identification LettersFirst 4 Letters Succeeding 3 Letters

Measured or Initiating Variable Modifier Readout or

Passive Function Output Function Modifier

A Analysis AlarmB Burner, combustionC ControlD Differential

E Voltage Sensor (primary element)

F Flow rate Ratio (fraction) G Glass, viewing deviceH Hand HighI Current (electrical) IndicateJ Power Scan

K Time, time schedule Time rate of change Control station

L Level Light LowM Momentary Middle, intermediateO Orifice, restrictionP Pressure, vacuum Point (test) connectionQ Quantity Integrate, totalizeR Radiation RecordS Speed, frequency Safety SwitchT Temperature TransmitU Multivariable Multifunction Multifunction Multifunction

V Vibration, mechanical analysis

Valve, damper, louver

W Weight, force WellX Unclassified X axis Unclassified Unclassified Unclassified

Y Event, state, or presence Y axis Relay, compute,

convert

Z Position, dimension Z axisDriver, actuator, unclassified final control element

Source: Instrumentation Symbols and Identification (ANSI/ISA-5.1-2009), Research Triangle Park, NC: American National Standard, 2009.


NCEES 311

General Instrument or Function Symbols

COMPUTERFUNCTION

PROGRAMMABLELOGIC CONTROL

SHARED DISPLAY,SHARED CONTROL

DISCRETEINSTRUMENTS

PRIMARYLOCATION

ACCESSIBLE TOOPERATOR

FIELDMOUNTED

AUXILIARYLOCATION

**NORMALLY**NORMALLYACCESSIBLE TO

OPERATOR

*IP1

* Abbreviations of the user's choice—such as IP1 (Instrument Panel #1), IC2 (Instrument Console #2), CC3 (Computer Console #3), etc.—may be used when it is necessary to specify instrument or function location.

** Normally inaccessible or behind-the-panel devices or functions may be depicted by using the same symbol but with dashed horizontal lines, as in:

Additional General Instrument or Function Symbols

PILOT LIGHT DIAPHRAGM SEAL INTERLOCK LOGIC

*

* This diamond is approximately half the size of the larger symbols.


312 NCEES

Actuator Symbols

WITH OR WITHOUT POSITIONER OR OTHER

PILOT

DIAPHRAGMSPRING –OPPOSED OR

UNSPECIFIED ACTUATOR

DIAPHRAGMPRESSURE–BALANCED

ROTARY MOTOR (SHOWN TYPICALLY WITH ELECTRIC

SIGNAL, MAY BE HYDRAULIC OR PNEUMATIC)

PREFERRED FOR DIAGRAM ASSEMBLED

WITH PILOT*, ASSEMBLY IS ACTUATED BY ONE

INPUT (SHOWN TYPICALLY WITH ELECTRIC INPUT)

CYLINDER WITHOUT POSITION OR OR OTHER PILOT

SPRING-OPPOSEDSINGLE-ACTING

PREFERRED FOR ANY CYLINDER THAT IS ASSEMBLED WITH A PILOT* SO THAT ASSEMBLY IS ACTUATED

BY ONE CONTROLLED INPUT

M

SOLENOID

SI

I

PREFERRED ALTERNATIVE. A BUBBLE WITH INSTRUMENT TAGGING, E.G. TY-I MAY BE USED INSTEAD OF THE INTERLOCK SYMBOL

CYLINDER WITH POSITIONER AND OVERRIDING PILOT VALVE

S

SINGLE-ACTING CYLINDER(IMPLIED I/P)

FOR PRESSURE RELIEFOR SAFETY VALVES ONLY.

SPRING WEIGHT DENOTES A SPRING WEIGHT OR INTEGRAL PILOT

HAND ACTUATOROR HANDWHEEL

DOUBLE-ACTING

* Pilot may be positioned solenoid valve signal converter, etc.


NCEES 313

Symbols for Self-Actuated Regulators, Valves, and Other Devices

LEVEL REGULATOR WITH MECHANICAL LINKAGE

BACKPRESSUREREGULATOR

SELF-CONTAINED

VACUUM RELIEF VALVE,GENERAL SYMBOL

PSVXX

PRESSURE RELIEF ORSAFETY VALVE,

GENERAL SYMBOL

PSVXX

AUTOMATIC REGULATOR WITH INTEGRAL FLOW

INDICATION

FICVXX

AUTOMATIC REGULATOR WITHOUT INDICATION

FCVXX

FLOW SIGHT GLASS, PLAIN OR WITH PADDLE WHEEL FLAPPER, ETC.

RESTRICTION ORIFICE (ORIFICE PLATE, CAPILLARY TUBE OR MULTI-STAGE

TYPE. ETC.) IN PROCESS LINE

ROXX

HAND CONTROL VALVE IN PROCESS LINE

HVXX

LCVXX

TANK

PRESSURE-REDUCING REGULATOR, SELF- CONTAINED, WITH

HANDWHEEL ADJUST-ABLE SETPOINT

PCVXX PCV

XX

FLOW

HAND

LEVE

LPR

ESSU

RE

FGXX


314 NCEES

RUPTURE DISK OR SAFETY HEAD FOR PRESSURE RELIEF

RUPTURE DISK OR SAFETY HEAD FOR

VACUUM RELIEF

PSEXX

PSEXX

PILOT-OPERATEDRELIEF VALVE

P

PRES

SURE

(CON

TD.)

6.3.2 Process Equipment Design

Comparison of the Common Tray Types

Property Sieve Tray Fixed Valve Tray Moving Valve TrayCapacity High High High to very highEfficiency High High High

TurndownAbout 2:1 Not generally suitable for operation under variable loads

About 2.5:1 Not generally suitable for operation under variable loads

About 4:1 to 5:1 Some special designs achieve 8:1 or more

Entrainment Moderate Moderate ModeratePressure drop Moderate Moderate Slightly higherCost Low Low About 20% higherMaintenance Low Low ModerateFouling tendency Low to very low Low to very low ModerateEffects of corrosion Low Very low Moderate

Main applications

(1) Most columns when turndown is not critical (2) High fouling and corro-sion potential

(1) Most columns when turndown is not critical (2) High fouling and corro-sion potential

(1) Most columns (2) Services where turn-down is important

Source: Green, Don W., and Robert H. Perry, Chemical Engineer's Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-29.


NCEES 315

6.3.2.1 Equipment Relief Installation Practices

Installation Practices for Equipment ReliefSystem Recommendations

VESSEL

For rupture disc in corrosive service, or for highly toxic materials where spring-loaded reliefs may weep.

P For two rupture discs in extremely corrosive service. The first may need to be replaced periodically.

For rupture disc and spring-loaded relief. Normal relief may go through spring-loaded device and rupture disc is backup for larger reliefs.

P For two reliefs in series. The rupture disc protects against toxicity or corrosion. The spring-loaded relief closes and minimizes losses.

For two rupture discs with special valve that keeps one valve always directly connected to vessel. This design is good for polymerization reactors that require periodic cleaning.

VESSEL

A

B

CA. Pressure drop not more than 3% of set pressure.

B. Long radius elbow.

C. If distance is greater than 10 feet, support weight and reaction forces below the long radius elbow.

PIPE

For orifice area of a single safety relief in vapor service; should not exceed 2% of the cross-sectional area of the protected line. May require multiple valves with staggered settings.

A

A. Process lines; should not be connected to safety-valve inlet piping.


316 NCEES

Installation Practices for Equipment Relief (cont'd)System Recommendations

A

B

A. Turbulence-causing device.

B. Dimension shown below:

Device Causing the Turbulence Minimum Number of Straight-Pipe Diameters

Regulator or valve 252 ells or bends not in same plane 202 ells or bends in same plane 151 ell or bend 10Pulsation damper 10

Source: Crowl, D.A., and J.F. Louvar, Chemical Process Safety: Fundamentals With Applications, 2nd ed., New York: Prentice Hall, 2002, pp. 369–370, Figure 8-11.

6.3.3 Siting Considerations

6.3.3.1 Fixed FacilitiesBuilding Siting Evaluation: The procedures used to evaluate the hazards and establish the design criteria for new buildings and the suitability of existing buildings at their specific locations.

Facility: The physical location where the management system activity is performed. In early life-cycle stages, a facility may be the company's central research laboratory or the engineering offices of a technology vendor. In later stages, the facility may be a typical chemical plant, storage terminal, distribution center, or corporate office. Site is used synonymously with facility when describing to Risk Management Plan (RMP) audit criteria.

Fixed Facility: A portion of or a complete plant, unit, site, complex, or any combination thereof that is generally not moveable. In contrast, mobile facilities, such as ships (e.g., transport vessels, floating platform storage and offloading vessels, drilling platforms), trucks, and trains, are designed to be moveable.

Siting: The process of locating a complex, site, plant, or unit.


NCEES 317

Guiding Principles for Location of Fixed Facility

API Recommended Practice 752 is based on the following guiding principles:

a. Locate personnel away from process areas consistent with safe and effective operations.b. Minimize the use of buildings intended for occupancy in close proximity to process areas.c. Manage the occupancy of buildings in close proximity to process areas.d. Design, construct, install, modify, and maintain buildings intended for occupancy to protect occupants against explosion, fire, and toxic material releases.e. Manage the use of buildings intended for occupancy as an integral part of the design, construction, maintenance, and operation of a facility.

Source: "Management of Hazards Associated with Location of Process Plant Permanent Buildings," Section of API Recommended Practice 752, 3rd ed., December 2009.

Overall Building Siting Evaluation Flow Chart

NO NO

NO

NO

YES

START

STOP

IS BUILDINGWITHIN THE SCOPE OF

API752?

IS BUILDING INCLUDED IN THE SITING VALUATION?

IS BUILDINGIMPACTED BY

EXPLOSION, FIRE OR TOXICS?

DESIGN BUILDING (INCLUDING

EXTENSIONS AND MODIFICATIONS TO

EXISTING BUILDINGS) TO MEET BUILDING SITING EVALUATION

CHOOSE BUILDING SITING EVALUATION APPROACH(ES) AND

CRITERIA

ARE BUILDING SITING

EVALUATION CRITERIA MET?

CARRY OUT BUILDING SITING EVALUATION

INCLUDE BUILDING IN MITIGATION PLAN.

DEVELOP AND IMPLEMENT

MITIGATION PLAN.

IMPLEMENT MANAGEMENT OF

BUILDING OCCUPANCYAND/OR MANAGEMENT

OF CHANGE

NO

YES YES

YES

YESIS IT A NEW

BUILDING ORMODIFICATION TO

EXISTINGBUILDING?


318 NCEES

Building Siting Evaluation for ExplosionsSTART

STOP

YES

NO NO

NO

NO

YES

YESYESCOULD BUILDINGBE IMPACTED

BY EXPLOSION?

IS IT A NEWBUILDING OR

MODIFICATION TOEXISTING

BUILDING?

DETERMINEBLAST LOADSON BUILDING

DETERMINEBLAST LOADSON BUILDING

DESIGN BUILDING (INCLUDING EXTENSIONS AND MODIFICATIONS TO EXISTING BUILDINGS) TO MEET BUILDING SITING

EVALUATION FOR EXPLOSION

COMPLETE A BUILDING DAMAGE LEVEL

ASSESSMENT ORA DETAILED STRUCTURAL

ANALYSIS

CARRY OUT MORE DETAILED ANALYSIS?

DOES BUILDINGMEET BUILDING SITING

CRITERIA FOR EXPLOSION?

INCLUDE BUILDING AND MITIGATION PLAN

BUILDING SITING EVALUATION FOR EXPLOSION NOT

REQUIRED.

IMPLEMENT MANAGE-MENT OF THE BUILDING

OCCUPANCY AND/OR MANAGEMENT OF

CHANGE


NCEES 319

Building Siting Evaluation for Fire

START

STOP

NO NO

NO

NO

YES YES YES

YES

YES

NO

COULD BUILDING BE IMPACTED BY

FIRE?ARE SEPARATION DISTANCES MET?

BUILDING SITING EVALUATION FOR FIRE

NOT REQUIRED.

INCLUDE BUILDING IN MITIGATION PLANAND IMPLEMENT MITIGATION PLAN

CARRY OUT MORE DETAILED ANALYSIS.IF NEEDED, INCLUDE

BUILDING IN MITIGATION PLAN AND IMPLEMENT

MITIGATION PLAN

INCLUDE BUILDING AND MITIGATION PLAN AN AND IMPLEMENT MITIGATION

PLAN

CARRY OUT MORE DETAILED ANALYSISIF NEEDED, INCLUDE

BUILDING IN MITIGATION PLAN AND IMPLEMENT

MITIGATION PLAN


BUILDING OCCUPANCY AND/OR MANAGEMENT

OF CHANGE

DOES BUILDINGMEET BUILDING

SITING EVALUATION CRITERIA?

DESIGN BUILDINGTO MEET BUILDINGSITING EVALUATION

CRITERIA.

IS IT A NEW BUILDING OR

MODIFICATIONS TO EXISTING

BUILDING?

DETERMINE FIRE EFFECTS AT BUILDING AND SELECT THE FIRE

PROTECTION CONCEPT

IS A SPACING TABLE APPROACH

USED?


320 NCEES

Building Siting Evaluation for Toxic Material Release

START

STOP

NONO

NO

NO

YES YES

YES

YES

BUILDING SITING EVALUATION FOR TOXIC

NOT REQUIRED

IS THERE POTENTIAL FOR A TOXIC

RELEASE?

IS IT ASSUMED THAT BUILDING IS IMPACTED?

PERFORM TOXIC GAS DISPERSING MODELING.

SELECT PROTECTION CONCEPT FOR TOXIC

MATERIAL.

DESIGN AND BUILDING TO MEET BUILDING

SITING THE EVALUATION CRITERIA.


BUILDING OCCUPANCY AND MANAGEMENT OF

CHANGE.

INCLUDE BUILDING A MITIGATION PLAN AND

IMPLEMENT MITIGATION PLAN

CARRY OUT MORE DETAILED ANALYSIS . IF

NEEDED, INCLUDE BUILDING IN MITIGATION PLAN AND IMPLEMENT

MITIGATION PLAN.

ARE BUILDING SITING EVALUATION CRITERIA

EXCEEDED?

IS IT A NEW BUILDING OR MODIFICATION TO EXISTING

BUILDING?


NCEES 321

6.3.3.2 Portable BuildingsPortable Building: Any rigid structure that can be moved easily to another location within the facility, regardless of the length of time it is kept at the site. Examples of portable buildings include wood framed trailers (single- and double-wide), container boxes, semi-trailers, and portable structures designed to be blast resistant. Lightweight fabric enclosures, such as tents, are excluded.

Guiding Principles for Siting Portable Buildings

API Recommended Practice 753 is based on the following guiding principles:

a. Locate personnel away from covered process areas consistent with safe and effective operations.b. Minimize the use of occupied portable buildings in close proximity to covered process areas.c. Manage the occupancy of portable buildings, especially during periods of increased risk including start-up or planned shut-down operations.d. Design, construct, install, and maintain occupied portable buildings to protect occupants against potential hazards.e. Manage the use of portable buildings as an integral part of the design, construction, maintenance, and operation of a facility.

Source: "Management of Hazards Associated with Location of Process Plant Portable Buildings," Section of API Recommended Practice 753, 1st ed., June 2007.

6.3.3.3 Typical Clearances to Railroads

Typical Clearances to RailroadsNO CONSTRUCTION ACTIVITIES OR OTHER OBSTRUCTION SHALL BE PLACED IN WITHIN THESE LIMITS

12'-0"15'-0"

21'-6

"

UPRR*BNSF**

C L TRACK

TOPOF RAIL

*Union Pacific Railroad**Burlington Northern Santa Fe Railway

(NORMAL TO RAILROAD)MINIMUM CONSTRUCTION CLEARANCE ENVELOPE

Source: State of California Department of Transportation, Standard Drawing XS11-010, July 2014.

PE C

hemical R

eference Handbook

322

NC

EES

6.3.3.4 Building Occupancy

Maximum Allowable Quantity per Control Area of Hazardous Materials Posing a Physical Hazarda,j,m,n,p

Material Class

Group When the Maximum

Allowable Quantity Is Exceeded

Storageb Used in Closed Systemsb Used in Open Systemsb

Solid Pounds (Cubic Feet)

Liquid Gallons

(Pounds)

Gas (Cubic Feet at NTP)


Liquid Gallons

(Pounds)



Liquid Gallons

(Pounds)

Combustible dust N/A H-2 q N/A N/A q N/A N/A q N/A

Combustible liquidc,i

II IIIA IIIB

H-2 or H-3 H-2 or H-3

N/AN/A

120d,e 330d,e

13,200e,fN/A N/A

120d 330d

13,200fN/A N/A

30d 80d

3300f

Combustible fiber Loose Baledo H-3 (100)

(1000) N/A N/A (100) (1000) N/A N/A (20)

(200) N/A

Consumer fireworks 1.4G H-3 125d,e,l N/A N/A N/A N/A N/A N/A N/A

Cryogenics, flammable N/A H-2 N/A 45d N/A N/A 45d N/A N/A 10d

Cryogenics, inert N/A N/A N/A N/A NL N/A N/A NL N/A N/ACryogenics, oxidizing N/A H-3 N/A 45d N/A N/A 45d N/A N/A 10d

Explosives

Division 1.1 Division 1.2 Division 1.3 Division 1.4

Division 1.4G Division 1.5 Division 1.6

H-1 H-1

H-1 or H-2 H-3 H-3 H-1 H-1

1e,g 1e,g 5e,g 50e,g

125d,e,l 1e,g

1d,e,g

(1)e,g (1)e,g (5)e,g (50)e,g N/A (1)e,g N/A

N/A N/A N/A N/A N/A N/A N/A

0.25g 0.25g

1g 50g N/A 0.25g N/A

(0.25)g (0.25)g

(1)g (50)g N/A

(0.25)g N/A

N/A N/A N/A N/A N/A N/A N/A

0.25g 0.25g

1g N/A N/A 0.25g N/A

(0.25)g (0.25)g

(1)g N/A N/A

(0.25)g N/A

Flammable gas Gaseous Liquefied H-2 N/A N/A

(150)d,e1000d,e

N/A N/A N/A (150)d,e

1000d,e N/A N/A N/A

Flammable liquidc 1A 1B and 1C H-2 or H-3 N/A 30d,e

120d,e N/A N/A 30d,e 120d,e N/A N/A 10d

30d

Flammable liquid, combination (1A, 1B, 1C)

N/A H-2 or H-3 N/A 120d,e,h N/A N/A 120d,h N/A N/A 30d,h

Flammable solid N/A H-3 125d,e N/A N/A 125d N/A N/A 25d N/A

Inert gas Gaseous Liquefied

N/A N/A

N/A N/A

N/A N/A

NL NL

N/A N/A

N/A N/A

NL NL

N/A N/A

N/A N/A

C

hapter 6: Plant Design and O

peration

NC

EES

323

Maximum Allowable Quantity per Control Area of Hazardous Materials Posing a Physical Hazarda,j,m,n,p (cont'd)

Material Class

Group When the Maximum

Allowable Quantity Is Exceeded

Storageb Used in Closed Systemsb Used in Open Systemsb


Liquid Gallons

(Pounds)



Liquid Gallons

(Pounds)



Liquid Gallons

(Pounds)

Organic peroxide

UD I II III IV V

H-1 H-2 H-3 H-3 N/A N/A

1e,g 5d,e 50d,e 125d,e

NL NL

(1)e,g (5)d,e (50)d,e (125)d,e

NL NL

N/A N/A N/A N/A N/A N/A

0.25g 1d 50d 125d NL NL

(0.25)g (1)d (50)d (125)d

NL NL

N/A N/A N/A N/A N/A N/A

0.25g 1d 10d 25d NL NL

(0.25)g (1)d (10)d (25)d NL NL

Oxidizer

4 3k

2 1

H-1 H-2 or H-3

H-3 N/A

1e,g 10d,e 250d,e 4000e.f

(1)e,g (10)d,e (250)d,e (4000)e.f

N/A N/A N/A N/A

0.25g 2d

250d 4000f

(0.25)g (2)d

(250)d (4000)f

N/A N/A N/A N/A

0.25g 2d 50d

1000f

(0.25)g (2)d (50)d

(1000)f

Oxidizing gas Gaseous Liquefied H-3 N/A

N/AN/A

(150)d,e1500d,e

N/AN/A N/A

N/A (150)d,e

1500d,e N/A

N/A N/A

N/A N/A

Pyrophoric material N/A H-2 4e,g (4)e,g 50e,g 1g (1)g 10g 0 0

Unstable (reactive) material

4 3 2 1

H-1 H-1 or H-2

H-3 N/A

1e,g 5d,e 50d,e NL

(1)e,g (5)d,e (50)d,e

NL

10g 50d,e

250d,e NL

0.25g 1d 50d NL

(0.25)g (1)d (50)d NL

2e,g 10d,e 250d,e

NL

0.25g 1d 10d NL

(0.25)g (1)d (10)d NL

Water-reactive material

3 2 1

H-2 H-3 N/A

5d.e 50d.e

NL

(5)d.e (50)d.e

NL

N/A N/A N/A

5d 50d

NL

(5)d (50)d

NL

N/A N/A N/A

1d 10d

NL

(1)d (10)d

NL

For SI: 1 cubic foot = 0.028 m3, 1 pound = 0.454 kg, 1 gallon = 3.7785 L NL = not limited; N/A = not applicable; UD = unclassified detonable

Source: International Code Council, International Building Code, 2012 ed. All footnote references are to the IBC.


324 NCEES

a. For use of control areas, see Section 414.2.b. The aggregate quantity in use and storage shall not exceed the quantity listed for storage.c. The quantities of alcoholic beverages in retail and wholesale sales occupancies shall not be limited provided the liquids are packaged in individual containers not exceeding 1.3 gallons. In retail and wholesale sales occupancies, the quantities of medicines, foodstuffs, consumer or industrial products, and cosmetics containing not more than 50 percent by volume of water-miscible liquids, with the remainder of the solutions not being flammable, shall not be limited, provided that such materials are packaged in individual containers not exceeding 1.3 gallons. d. Maximum allowable quantities shall be increased 100% in buildings equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1. Where Note e also applies, the increase for both notes shall be applied accumulatively.e. Maximum allowable quantities shall be increased 100% when stored in approved storage cabinets, day boxes, gas cabinets, or exhausted enclosures or in listed safety cans in accordance with Section 5003.9.10 of the Inter- national Fire Code. Where Note d also applies, the increase for both notes shall be applied accumulatively.f. The permitted quantities shall not be limited in a building equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1.g. Permitted only in buildings equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1.h. Containing not more than the maximum allowable quantity per control area of Class IA, IB, or IC flammable liquids.i. The maximum allowable quantity shall not apply to fuel oil storage complying with Section 603.3.2 of the International Fire Code.j. Quantities in parentheses indicate quantity units in parentheses at the head of each column.k. A maximum quantity of 200 pounds of solid or 20 gallons of liquid Class 3 oxidizers is allowed when such materials are necessary for maintenance purposes, operation, or sanitation of equipment. Storage containers and the manner of storage shall be approved.l. Net weight of the pyrotechnic composition of the fireworks. Where the net weight of the pyrotechnic composition of the fireworks is not known, 25% of the gross weight of the fireworks, including packaging, shall be used.m. For gallons of liquids, divide the amount in pounds by 10 in accordance with Section 5003.1.2 of the Interna- tional Fire Code.n. For storage and display quantities in Group M and storage quantities in Group S occupancies complying with Section 414.2.5, see Tables 414.2.5(1) and 414.2.5(2). o. Densely packed baled cotton that complies with the packing requirements of ISO 8115 shall not be included in this material class.p. The following shall not be included in determining the maximum allowable quantities: 1. Liquid or gaseous fuel in fuel tanks on vehicles 2. Liquid or gaseous fuel in fuel tanks on motorized equipment operated in accordance with this code 3. Gaseous fuels in piping systems and fixed appliances regulated by the International Fuel Gas Code 4. Liquid fuels in piping systems and fixed appliances regulated by the International Mechanical Codeq. Where manufactured, generated, or used in such a manner that the concentration and conditions create a fire or explosion hazard based on information prepared in accordance with Section 414.1.3.

C


peration

NC

EES

325

Maximum Allowable Quantity Per Control Area of Hazardous Material Posing a Health Hazarda,b,c,i

MaterialLiquefied (150)h Storaged Used in Closed Systemsd Used in Open Systemsd


Liquid Gallons (Pounds)e,f

Gas (Cubic Feet at NTP)e

Solid Poundse

Liquid Gallons (Pounds)e

Gas (Cubic Feet at NTP)e

Solid Poundse

Liquid Gallons (Pounds)e

Corrosive 5000 500 Gaseous 810f Liquefied (150)h 5000 500 Gaseous 810f

Liquefied (150)h 1000 100

Highly toxic 10 (10)h Gaseous 20g Liquified (4)g,h 10 (10)i Gaseous 20g

Liquified (4)g,h 3 (3)i

Toxic 500 (500)h Gaseous 810f Liquefied (150)f,h 500 (500)i Gaseous 810f

Liquefied (150)f,h 125 (125)

For SI: 1 cubic foot = 0.028 m3, 1 pound = 0.454 kg, 1 gallon = 3.785 L

a. For use of control areas, see Section 414.2.b. In retail and wholesale occupancies, the quantities of medicines, foodstuffs, consumer or industrial products, and cosmetics containing not more than

50% by volume of water-miscible liquids—with the remainder of the solutions not being flammable—shall not be limited, provided that such materials are packaged in individual containers not exceeding 1.3 gallons.

c. For storage and display quantities in Group M and storage quantities in Group S, occupancies complying with Section 414.2.5, see Tables 414.2.5(1) and 414.2.5(2).

d. The aggregate quantity in use and storage shall not exceed the quantity listed for storage.e. Maximum allowable quantities shall be increased 100% in buildings equipped throughout with an approved automatic sprinkler system in accordance

with Section 903.3.1.1. Where Note f below also applies, the increase for both notes shall be applied accumulatively.f. Maximum allowable quantities shall be increased 100% when stored in approved storage cabinets, gas cabinets, or exhausted enclosures as specified

in the International Fire Code. Where Note e above also applies, the increase for both notes shall be applied accumulatively.g. Allowed only when stored in approved exhausted gas cabinets or exhausted enclosures as specified in the International Fire Code.h. Quantities in parentheses indicate quantity units in parentheses at the head of each column.i. For gallons of liquids, divide the amount in pounds by 10 in accordance with Section 5003.1.2 of the International Fire Code.

Source: International Building Code, 2012 edition. All footnote references are to the IBC.


326 NCEES

International Building Code Area Classification DescriptionsOccupancy

Class Description

A Assembly Group A occupancy includes, among others, the use of a building or structure, or a portion thereof, for the gathering of persons for purposes such as civic, social or religious functions; recreation, food or drink consumption or awaiting transportation.

B Business Group B occupancy includes, among others, the use of a building or structure, or a portion thereof, for office, professional or service-type transactions, including storage of records and accounts. Business occupancies shall include, but not be limited to, the following:

Airport traffic control towers Ambulatory care facilities Animal hospitals, kennels, and pounds Banks Barber and beauty shops Car wash Civic administration Clinic, outpatient Dry cleaning and laundries: pick-up and delivery stations and self-service Educational occupancies for students above the 12th grade Electronic data processing Laboratories: testing and research Motor vehicle showrooms Post offices Print shops Professional services (architects, attorneys, dentists, physicians, engineers, etc.) Radio and television stations telephone exchanges Training and skill development not within a school or academic program

F Factory Industrial Group F occupancy includes, among others, the use of a building or structure, or a portion thereof, for assembling, disassembling, fabricating, finishing, manufacturing, packaging, repair, or processing operations that are not classified as a Group H hazardous or Group S storage occupancy.


NCEES 327

International Building Code Area Classification Descriptions (cont'd)Occupancy

Class Description

F-1 Factory Industrial uses which are not classified as Factory Industrial F-2 Low Hazard. Examples include:

Aircraft (manufacturing, not to include repair) Appliances Athletic equipment Automobiles and other motor vehicles Bakeries Beverages over 16-percent alcohol content Bicycles Boats Brooms or brushes Business machines Cameras and photo equipment Canvas or similar fabric Carpets and rugs (including cleaning) Clothing Construction and agricultural machinery Disinfectants Dry cleaning and dyeing Electric generation plants Electronics Engines (including rebuilding) Food processing and commercial kitchens not associated with restaurants, cafeterias and similar dining facilities Furniture Hemp products Jute products Laundries Leather products Machinery Metals Millwork (sash and door) Motion pictures and television filming (without spectators) Musical instruments Optical goods Paper mills or products Photographic film Plastic products Printing or publishing Recreational vehicles Refuse incineration Shoes Soaps and detergents Textiles Tobacco Trailers Wood: distillation Woodworking (cabinet) Upholstering


328 NCEES


Class Description

F-2 Factory industrial uses that involve the fabrication or manufacturing of noncombustible materials which during finishing, packing or processing do not involve a significant fire hazard. Examples include:

Beverages up to and including 16-percent alcohol content Brick and masonry Ceramic products Foundries Glass products Gypsum Ice Metal products (fabrication and assembly)

H High-Hazard Group H occupancy includes, among others, the use of a building or structure, or a portion thereof, that involves the manufacturing, processing, generation or storage of materials that constitute a physical or health hazard in quantities in excess of those allowed in control areas comply-ing with Section 414, based on the maximum allowable quantity limits for control areas set forth in Tables 307.1(1) and 307.1(2). Hazardous occupancies are classified in Groups H-1, H-2, H-3, H-4 and H-5 and shall be in accordance with this section, with the requirements of Section 415 and the Interna-tional Fire Code. Hazardous materials stored, or used on top of roofs or canopies shall be classified as outdoor storage or use and shall comply with the International Fire Code.

H-1 Buildings and structures containing materials that pose a detonation hazard. Examples include: Deton-able pyrophoric materials, explosives, organic peroxides (unclassified detonable), Class 4 oxidizers, Class 3 detonable and Class 4 unstable (reactive) materials.

H-2 Buildings and structures containing materials that pose a deflagration hazard or a hazard from acceler-ated burning. Examples include:

Class I, II, or IIIA flammable or combustible liquids which are used or stored in normally open containers or systems, or in closed containers or systems pressurized at more than 15 psi (103.4 kPa) gage Combustible dusts where manufactured, generated or used in such a manner that the concentration and conditions create a fire or explosion hazard based on information prepared in accordance with Section 414.1.3 Cryogenic fluids, flammable Flammable gases Organic peroxides, Class I Oxidizers, Class 3, that are used or stored in normally open containers or systems or in closed containers or systems pressurized at more than 15 psi (103.4 kPa) gage Pyrophoric liquids, solids, and gases, nondetonable Unstable (reactive) materials, Class 3, nondetonable Water-reactive materials, Class 3


NCEES 329


Class Description

H-3 Buildings and structures containing materials that readily support combustion or that pose a physical hazard. Examples include:

Class I, II, or IIIA flammable or combustible liquids that are used or stored in normally closed containers or systems pressurized at 15 pounds psi (103.4 kPa) gauge or less Combustible fibers, other than densely packed baled cotton Consumer fireworks, 1.4G (Class C, Common) Cryogenic fluids, oxidizing Flammable solids Organic peroxides, Class II and III Oxidizers, Class 2 Oxidizers, Class 3, that are used or stored in normally closed containers or systems pressurized at 15 pounds psi (103.4 kPa) gage or less Oxidizing gases Unstable (reactive) materials, Class 2 Water-reactive materials, Class 2

H-4 Buildings and structures that contain materials that are health hazards. Examples include:

Corrosives Highly toxic materials Toxic materials

H-5 Semiconductor fabrication facilities and comparable research and development areas in which hazard-ous production materials (HPM) are used and the aggregate quantity of materials is in excess of those listed in Tables 307.1(1) and 307.1(2).

I Institutional Group I occupancy includes, among others, the use of a building or structure, or a portion thereof, in which care or supervision is provided to persons who are or are not capable of self-preserva-tion without physical assistance or in which persons are detained for penal or correctional purposes or in which the liberty of the occupants is restricted.

M Mercantile Group M occupancy includes, among others, the use of a building or structure, or a portion thereof, for the display and sale of merchandise and involves stocks of goods, wares, or merchandise incidental to such purposes and accessible to the public. Mercantile occupancy shall include, but not be limited to, the following:

Department stores Drug stores Markets Motor fuel-dispensing facilities Retail or wholesale stores Sales rooms

R Residential Group R includes among others, the use of a building or structure, or a portion thereof, for sleeping purposes when not classified as an Institution Group I or when not regulated by the Interna-tional Residential Code.

S Storage Group S occupancy includes among others, the use of a building or structure, or a portion thereof, for storage that is not classified as a hazardous occupancy.


330 NCEES


Class Description

S-1 Moderate hazard Storage Group S-1. Buildings occupied for storage uses that are not classifies as Group S-2, including, but not limited to, storage of the following:

Aerosols, levels 2 and 3 Aircraft hangars (storage and repair) Bags: cloth, burlap and paper Bamboos and rattan Baskets Belting: canvas and leather Books and paper in rolls or packs Boots and shoes Buttons, including cloth covered, pearl or bone Cardboard and cardboard boxes Clothing, woolen wearing apparel Cordage Dry boats (indoor) Furniture Furs Glues, mucilage, pastes and size Grains Horns and combs, other than celluloid Leather Linoleum Lumber Motor vehicle repair garages complying with the maximum allowable quantities of hazardous materials listed in Table 307.1(1) (see Section 406.8) Photo engravings Resilient flooring Silks Soaps Sugar Tires, bulk storage of Tobacco, cigars, cigarettes and snuff Upholstery and mattresses Wax candles


NCEES 331


Class Description

S-2 Low-hazard storage, Group S-2. Includes among others, buildings used for the storage of noncombus-tible materials such as products on wood pallets or in paper cartons with or without single thickness divisions; or in paper wrappings. Such products are permitted to have a negligible amount of plastic trim such as knobs, handles or film wrapping. Group S-2 storage shall include, but not be limited to, storage of the following:

Asbestos Beverages up to and including 16-percent alcohol in metal, glass or ceramic containers Cement in bags Chalk and crayons Dairy products in nonwaxed coated paper containers Dry cell batteries Electrical coils Electrical motors Empty cans Food products Foods in noncombustible containers Fresh fruits and vegetables in nonplastic trays or containers Frozen foods Glass Glass bottles, empty or filled with noncombustible liquids Gypsum board Inert pigments Ivory Meats Metal cabinets Metal desks with plastic tops and trim Metal parts Metals Mirrors Oil-filled and other types of distribution transformers Parking garages, open or enclosed Porcelain and pottery Stoves Talc and soapstones Washers and dryers


332 NCEES


Class Description

U General. Buildings and structures of an accessory character and miscellaneous structures not classified in any specific occupancy shall be constructed, equipped and maintained to conform to the require-ments of this code commensurate with the fire and life hazard incidental to their occupancy. Group U shall include, but not be limited to, the following:

Agricultural buildings Aircraft hangars, accessory to a one- or two-family residence (see Section 412.5) Barns Carports Fences more than 6 feet (1829 mm) in height Grain silos, accessory to a residential occupancy Greenhouses Livestock shelters Private garages Retaining wall Sheds Stables Tanks Towers

6.3.3.5 Area Separation Requirements

Required Separation of Occupancies (Hours)

OccupancyA, E I-1, I-3,

I-4 I-2 Ra F-2, S-2b, U

B, F-1, M, S-1 H-1 H-2 H-3, H-4 H-5

S NS S NS S NS S NS S NS S NS S NS S NS S NS S NSA, E N N 1 2 2 NP 1 2 N 1 1 2 NP NP 3 4 2 3 2 NP

I-1, I-3, I-4 — — N N 2 NP 1 NP 1 2 1 2 NP NP 3 NP 2 NP 2 NPI-2 — — — — N N 2 NP 2 NP 2 NP NP NP 3 NP 2 NP 2 NPRa — — — — — — N N 1c 2c 1 2 NP NP 3 NP 2 NP 2 NP

F-2, S-2b, U — — — — — — — — N N 1 2 NP NP 3 4 2 3 2 NPB, F-1, M,

S-1 — — — — — — — — — — N N NP NP 2 3 1 2 1 NP

H-1 — — — — — — — — — — — — N NP NP NP NP NP NP NPH-2 — — — — — — — — — — — — — — N NP 1 NP 1 NP

H-3, H-4 — — — — — — — — — — — — — — — — 1d NP 1 NPH-5 — — — — — — — — — — — — — — — — — — N NP

S = Buildings equipped throughout with an automatic sprinkler system installed in accordance with Section 903.3.1.1 NS = Buildings not equipped throughout with an automatic sprinkler system installed in accordance with Section 903.3.1.1 N = No separation requirement NP = Not permitteda. See Section 420.b. The required separation from areas used only for private or pleasure vehicles shall be reduced by 1 hour but to

not less than 1 hour.c. See Section 406.3.4.d. Separation is not required between occupancies of the same classification.


NCEES 333

6.3.3.6 Wind DirectionPrevailing winds should be considered in both plant siting and layout:

a. For siting, it is undesirable to locate a plant where prevailing winds would carry any fugitive emissions into nearby residential areas.

b. In laying out a plant, safety considerations dictate that process units be located such that:1. Prevailing winds would not carry potentially flammable releases to an area of the plant where there

could be a source of ignition.2. Prevailing winds would not carry potentially hazardous or toxic releases to an area of the plant where

workers are in enclosed areas, e.g., offices, control rooms, or enclosed process buildings.

6.3.4 Instrumentation and Process Control

6.3.4.1 First-Order Control System ModelsThe transfer function model for a first-order system is

( )( )R sY s

sK1x

= +

where

K = steady-state gain

t = time constant

The step response of a first-order system to a step input of magnitude M is

( ) ( )y t y e KM e1/ /t t0= + −x x− −

In the chemical process industry, y0 is typically taken to be zero, and y(t) is referred to as a deviation variable.

For systems with time delay (dead time or transport lag) q, the transfer function is

( )( )R sY s

sKe

1s

x= +

i−

The step response for t ≥ q to a step of magnitude M is

( ) ( ) ( )y t y e KM e u t1( )/ ( )/t t0 i= + − −i x i x− − − −8 B

where

u(t) = unit step function

6.3.4.2 Second-Order Control System ModelsOne standard second-order control system model is

( )( )R sY s

s sK2 n n

n2 2

2

g~ ~

~=+ +


334 NCEES

where


z = the damping ratio

wn = the undamped natural (z = 0) frequency

1d n2~ ~ g= − , the damped natural frequency

1 2r n2~ ~ g= − , the damped resonant frequency

If the damping ratio z is less than unity, the system is said to be underdamped; if z is equal to unity, it is said to be critically damped; and if z is greater than unity, the system is said to be overdamped.

For a unit step input to a normalized, underdamped, second-order control system, the time required to reach a peak value tp and the value of that peak Mp are determined by

t1

pn

2~ g

r=−

M e1 /p

1 2= + rg g− −

The percent overshoot (%OS) of the response is determined by

%OS e100 / 1 2= rg g− −

For an underdamped, second-order system, the logarithmic decrement is

nm xx1 1

12

k mk

2dg

rg= =−+

d nwhere xk and xk+m are the amplitudes of oscillation at cycles k and k + m, respectively.

The period of oscillation t is related to wd by

wdt = 2p

The time required for the output of a second-order system to settle to within 2% of its final value (2% settling time) is defined to be

T 4s

ng~=

An alternative form commonly employed in the chemical process industry is

( )( )R sY s

s sK2 12 2x gx

=+ +

where


z = the damping ratio

t = the inverse natural frequency


NCEES 335

Feedback Control

CONTROLLER

COLDPROCESSFLUID

STEAMHOTPROCESSFLUID

TEMPERATURETRANSMITTERTT

TIC

Feed Forward Plus Feedback Control

COLDPROCESSFLUID

STEAM

HOTPROCESSFLUID

CONTROLLER

FLOWTRANSMITTER

FT

FIC


336 NCEES

Feed Forward Plus Feedback Control

TT

FTCOLDPROCESSFLUID

STEAM

HOTPROCESSFLUID

FEEDBACKCONTROL

SUMMINGCONTROLLER

FEED FORWARDCONTROLLER

TEMPERATURETRANSMITTER

FLOWTRANSMITTER

FIC QIC TIC

Feedback Control

COLDPROCESSFLUID

STEAMFLOW

TRANSMITTERHOTPROCESSFLUID

TEMPERATURETRANSMITTER

PRIMARYCONTROLLER

SECONDARYCONTROLLER

TT

FT

TIC

FIC

C


peration

NC

EES

337

6.3.5 Materials of Construction

6.3.5.1 Thermoplastics

Typical Thermoplastic Properties

Property UnitPP PVC CPVC PVDF ECTFE ETFE FEP TFE PFA

Homo- polymer Copolymer Homo-

polymer Copolymer

Density cmg3 0.91 0.88–0.91 1.38 1.5 1.75–1.79 1.76–1.79 1.68 1.70 2.12–2.17 2.2–2.3 2.12–2.17

Melting point (crystalline)

°C 160–175 150–175 — — 160–170 141–160 220–245 270 275 327 310°F 320–347 302–347 — — 320–340 285–320 460 518 527 621 590

Physical PropertiesBreak strength; ASTM D 638 kpsi 4.5–6.0 4.0–5.3 6.0–7.5 — 4.5–7.0 3.5–6.0 6.6–7.8 6.5 2.7–3.1 2.0–2.7 4.0–4.5

Modulus flex @ 73oF; ASTM D 790

MPa 1135–1550 345–1035 — — — — — — — — —

kpsi 165–225 50–150 — — 165–325 90–180 180–260 200 80–95 190–235 120

Yield strength; ASTM D 638 kpsi 4.5–5.4 1.6–4.0 — — 5.0–8.0 2.9–5.5 — 7.1 — — —

Thermal PropertiesHTD at 0.46 MPa (66 psi); ASTM D 648

°C 107–121 75–89 57 — 132–150 93–110 90 104 70 221 75

°F 225–250 167–192 135 — 270–300 200–230 194 220 158 250 166

Linear coefficient of expansion; ASTM D 696

in. Cin. 10-

5#c

-10 7–9.5 4.4 3.9 7.2–14.4 14.0 8 6 8–11 10 12

Conductivity; ASTM C 177

-m KW 0.1 0.16 — — 0.17–0.19 0.16 — — — — —

ft hr in.F

Btu- -2 c 0.7 1.1 — — 1.18–1.32 1.11 — — — — —

Source: Perry, R.H., Properties of Materials, 8th ed., New York: McGraw-Hill, 2008.


338 NCEES

6.3.5.2 Gasket Materials

Important Properties of Gasket Materials*

Material Max Service Temp °F Important Properties

Rubber (straight):

Natural 225Good mechanical properties. Impervious to water. Fair to good resistance to acids, alkalies. Poor resistance to oils, gasoline. Poor weathering, aging properties.

Styrene-butadiene (SBR) 250 Better water resistance than natural rubber. Fair to good resistance to acids, alkalies. Unsuitable with gasoline, oils, and solvents.

Butyl 300 Very good resistance to water, alkalies, many acids. Poor resistance to oils, gasoline, most solvents (except oxygenated).

Nitrile 300 Very good resistance to water. Excellent resistance to oils, gasoline. Fair to good resistance to acids, alkalies.

Polysulfide 150Excellent resistance to oils, gasoline, aliphatic, and aromatic hydro-carbon solvents. Very good resistance to water. Good resistance to alkalies. Fair acid resistance. Poor mechanical properties.

Neoprene 250Excellent mechanical properties. Good resistance to nonaromatic petroleum, fatty oils, solvents (except aromatic, chlorinated, or ketone types). Good water and alkali resistance. Fair acid resistance.

Silicone 600Excellent heat resistance. Fair water resistance. Poor resistance to steam at high pressures. Fair to good acid, alkali resistance. Poor (except fluorosilicone rubber) resistance to oils, solvents.

Acrylic 450Good heat resistance but poor cold resistance. Good resistance to oils, aliphatic and aromatic hydrocarbons. Poor resistance to water, alkalies, some acids.

Chlorosulfonated polyethylene (Hypalon) 250

Excellent resistance to oxidizing chemicals, ozone, weathering. Relatively good resistance to oils, grease. Poor resistance to aromat-ic or chlorinated hydrocarbons. Good mechanical properties.

Floroelastomer (Viton, Fluorel 2141, Kel-F) 450

Can be used at high temperatures with many fuels, lubricants, hy-draulic fluids, solvents. Highly resistant to ozone, weathering. Good mechanical properties.

Asbestos:Compressed asbestos-rubber sheet To 700 Large number of combinations available; properties vary widely

depending on materials used.Asbestos-rubber woven sheet To 250 Same as above.

Asbestos-rubber (beater addition process) 400 Same as above.

Asbestos composites To 1000 Same as above.

Asbestos-TFE To 500 Combines heat resistance and sealing properties of asbestos with chemical resistance of TFE.

Cork compositions 250

Low cost. Truly compressible materials that permit substantial deflections with negligible side flow. Conform well to irregular surfaces. High resistance to oils. Good resistance to water, many chemicals. Should not be used with inorganic acids, alkalies, oxidiz-ing solutions, live steam.


NCEES 339

Important Properties of Gasket Materials* (cont'd)


Cork rubber 300 Controlled compressibility properties. Good conformability, fatigue resistance. Chemical resistance depends on kind of rubber used.

Plastics:

TFE (solid) (tetrafluoroethylene, Teflon) 500

Excellent resistance to almost all chemicals and solvents. Good heat resistance; exceptionally good low-temperature properties. Rela-tively low compressibility and resilience.

TFE (filled) To 500 Selectively improved mechanical and physical properties. However, fillers may lower resistance to specific chemicals.

TFE composite To 500 Chemical and heat resistance comparable with solid TFE. Inner gasket material provides better resiliency and deformability.

CFE (chlorotrifluoro- ethylene, Kel-F) 350 Higher cost than TFE. Better chemical resistance than most other

gasket materials, although not quite as good as TFE.

Vinyl 212 Good compressibility, resiliency. Resistant to water, oils, gasoline, and many acids and alkalies. Relatively narrow temperature range.

Polyethylene 150 Resists most solvents. Poor heat resistance.Plant fiber:

Neoprene-impregnated wood fiber 175 Nonporous; recommended for glycol, oil, and gasoline to 175°F.

SBR-bonded cotton 230 Good water resistance.Nitrile rubber-cellulose fiber Resists oil at high temperatures.

Vegetable fiber, glue binder 212 Resists oil and water to 212°F.

Vulcanized fiber Low cost. Good mechanical properties. Resists gasoline, oils, greases, waxes, many solvents.

Inorganic fibers To 2200 Excellent heat resistance. Poor mechanical properties.Felt:

Pure felt

Resilient, compressible, and strong, but not impermeable. Resists medium-strength mineral acids and dilute mineral solutions if not intermittently dried. Resists oils, greases, waxes, most solvents. Damaged by alkalies.

TFE-impregnated 300 Good chemical and heat resistance.Petrolatum- or paraffin-impregnated High water repellency.

Rubber-impregnated Many combinations available; properties vary widely depending on materials used.


340 NCEES



Metal:Lead 500 Good chemical resistance. Best conformability of metal gaskets.Tin Good resistance to neutral solutions. Attacked by acids and alkalies.

Aluminum 800 High corrosion resistance. Slightly attacked by strong acids and alkalies.

Copper, brass Good corrosion resistance at moderate temperatures.Nickel 1400 High corrosion resistance.

Monel 1500 High corrosion resistance. Good against most acids and alkalies, but attacked by strong hydrochloric and strong oxidizing acids.

Inconel 2000 Excellent heat, oxidation resistance.Stainless steel High corrosion resistance. Properties depend on type used.

Metal composites Many combinations available; properties vary widely depending on materials used.

Leather 220 Low cost. Limited chemical and heat resistance. Not recommended against pressurized steam, acid, or alkali solutions.

Glass fabric High strength and heat resistance. Can be impregnated with TFE for high chemical resistance.

Packing and Sealing Materials

Rubber (straight) 600 See Gasket Materials for properties. Mainly used for ring-type seals, although some types are available as spiral packings.

Rubber composites:

Cotton-reinforced 350High strength. Chemical resistance depends on type of rubber used; however, most types are noted for high resistance to water, aqueous solutions.

Asbestos-reinforced 450 High strength combined with good heat resistance.Asbestos:

Plain, braided asbestos 500 Heat resistance combined with resistance to water, brine, oil, many chemicals. Can be reinforced with wire.

Impregnated asbestos To 750

Environmental properties vary widely depending on type of asbestos and impregnant used. Neoprene-cemented type resists hot oils, gaso-line, and solvents. Oil-and-wax-impregnated type resists caustics. Wax-impregnated blue asbestos type has high acid resistance. TFE-impregnated has good all-around chemical resistance.

Asbestos composites To 1200 End properties vary widely depending on secondary material used.Metals:

Copper To 1500

Properties depend on other construction materials and form of cop-per used. Packing made of copper foil over asbestos core resists steam and alkalies to 1000°F. Packing of braided copper tinsel resists water, steam, and gases to 1500°F.

Aluminum To 1000 Resists hot petroleum derivatives, gases, foodstuffs, many organic acids.

Lead 550 Many types are available.


NCEES 341



Organic fiber:Flax 300 Good water resistance. Jute 300 Good water resistance. Ramie 300 Good resistance to water, brine, cold oil.Cotton 300 Good resistance to water, alcohol, dilute aqueous solutions. Rayon 300 Good resistance to water, dilute aqueous solutions. Felt 300 See Gasket Materials.

Leather To 210 Good mechanical properties for sealing. Resistant to alcohol, gaso-line, many oils and solvents, synthetic hydraulic fluids, water.

TFE To 500 Available in many forms, all of which have high chemical resis-tance.

Carbon graphite 700 Good bearing and self-lubricating properties. Good resistance to chemicals, heat.

* From Materials in Engineering Design, New York: Reinhold, 1959, p. 11-126.

Source: Perry, R.H., and D. Green, Chemical Engineer's Handbook, 6th ed., New York: McGraw-Hill, 1984.

6.3.5.3 CorrosionCorrosion is a natural process that converts a refined metal to a more stable form such as its oxide, hydroxide, or sulfide. It is the gradual destruction of a material by chemical reaction with its environment. Corrosion effects must be taken into account during the design of any system, unit, facility, or plant.

Use the following corrosion data charts to assist in narrowing the field of choice of materials. Once the choice has been narrowed, the effects of contaminants, aeration, galvanic coupling, erosion, and so on must be taken into account. Field testing is best for final suitability decisions.


342 NCEES

Source: All corrosion data from Perry, John H., Perry's Chemical Engineers' Handbook, 6th ed., New York: McGraw-Hill, 1963, pp. 23-13 to 23-30.

Detailed Corrosion Data on Construction Materials

ASPHALTIC RESINSSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY

===

COPPER, AL BRONZE, TIN BRONZE< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====

EPOXY RESINSSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY

===

FURANE RESINSSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY

===

GLASS< 0.005 IN. PER YR. 0.005 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====

HASTELLOY B< 0.002 IN. PER YR.< 0.02 IN. PER YR.. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====

HASTELLOY C< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====

HASTELLOY D< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====

ACID

,AC

ETIC

ACID

,BO

RIC

ACID

,CH

ROMI

C

ACID

,CI

TRIC

ACID

,FO

RMIC

ACID

,HY

DROC

HLOR

IC

ACID

,HY

DROF

LUOR

IC

KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

ALUMINUM< 0.005 IN. PER YR. 0.005 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====

AIR FREE AIR FREE AIR FREE

CARBON-FILLEDCEMENT

AERATED500 F

400 F 450 F

AERATED ORNON-AERATED

AERATED ORAIR-FREE

1,500 F

NOTE SYMBOLS ON VERTICAL HEAVY LINES REPRESENT 100% CONCENTRATION. SYMBOLS ON

HORIZONTAL HEAVY LINES REPRESENT 300 F. TEMPERATURE.

AIR FREE AIR FREE AIR FREE

CARBON-FILLEDCEMENT

AERATED500 F

400 F 450 F

AERATED ORNON-AERATED

AERATED ORAIR-FREE

1500 F

12½ 25 37½

12½ 25 37½


NCEES 343

Detailed Corrosion Data on Construction Materials (cont'd)

IRON, CAST

MONEL

NEOPRENE

NICKEL

PHENOLIC RESINS

POLYETHYLENE

RUBBER (NATURAL, GR-S)

RUBBER, BUTYL

SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY

===

SATISFACTORYFOR LIMITED USE ONLYUNSATISFACTORY

===

SATISFACTORYSATISFACTORY FOR LIMITED USEGENERALLY UNSATISFACTORY

===

SATISFACTORYSATISFACTORY FOR LIMITED USEGENERALLY UNSATISFACTORY

===

COMPLETE RESISTANCE SOME ATTACK ATTACK OR DECOMPOSITION

===

< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====


====


====

ACID

,AC

ETIC

ACID

,BO

RIC

ACID

,CH

ROMI

C

ACID

,CI

TRIC

ACID

,FO

RMIC

ACID

,HY

DROC

HLOR

IC

ACID

,HY

DROF

LUOR

IC

AIR FREE

AIR FREE AIR FREE AIR FREE AIR FREE

AIR FREE AIR FREE AIR FREEAERATED

AERATED

HARD RUBBER

HARD RUBBER HARDRUBBER

SOFT GR-SCANNOT BE USED

KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F


344 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

STAINLESS STEEL, 18-8

STAINLESS STEEL, TYPE 316

STAINLESS STEEL, 12% Cr


STEEL

STYRENE COPOLYMERS, HIGH IMPACT

ZIRCONIUM


===


====

< 0.002 IN. PER YR. 0.002 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====

< 0.002 IN. PER YR.< 0.02 IN. PER YR.0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====


====


====


====

ACID

,AC

ETIC

ACID

,BO

RIC

ACID

,CH

ROMI

C

ACID

,CI

TRIC

ACID

,FO

RMIC

ACID

,HY

DROC

HLOR

IC

ACID

,HY

DROF

LUOR

IC

STRESS CORROSION


NCEES 345


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

ALUMINUM

ASPHALTIC RESINS

COPPER, AL BRONZE, TIN BRONZE

EPOXY RESINS

FURANE RESINS

GLASS

HASTELLOY B

HASTELLOY C

HASTELLOY D

= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.

= SATISFACTORY= SATISFACTORY FOR LIMITED SERVICE= UNSATISFACTORY

= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.




= SATISFACTORY= SATISFACTORY FOR LIMITED USE= NOT RECOMMENDED

= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY


ACID

,NI

TRIC

ACID

,OX

ALIC

ACID

,PH

OSPH

ORIC

ACID

,SU

LFUR

IC

ALUM

INUM

CHLO

RIDE

ALUM

INUM

PO

TASS

IUM

SULF

ATE

(ALU

M)

AMMO

NIA,

AQUE

OUS

AIR FREE DRYAIR FREE AERATED,NO VELOCITY

AERATED

600 F

250 PSIHCI AND

TECH

TECHSLUDGE-

400 F

IN ETHANOL

NOTRECOMMENDED

IN ETHANOL

IN ETHANOL

300

200


346 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

ACID

,NI

TRIC

ACID

,OX

ALIC

ACID

,PH

OSPH

ORIC

ACID

,SU

LFUR

IC

ALUM

INUM

CHLO

RIDE

ALUM

INUM

PO

TASS

IUM

SULF

ATE

(ALU

M)

AMMO

NIA,

AQUE

OUS


===

SATISFACTORYFOR LIMITED USEUNSATISFACTORY

===

SATISFACTORYSATISFACTORY FOR LIMITED SERVICE

===

SATISFACTORYSATISFACTORY FOR LIMITED SERVICEGENERALLY UNSATISFACTORY

GENERALLY UNSATISFACTORY

===

COMPLETE RESISTANCE SOME ATTACK ATTACK OR DECOMPOSITION

===


====


====


====

IRON, CAST

MONEL

NEOPRENE

NICKEL

PHENOLIC RESINS

POLYETHYLENE


RUBBER, BUTYL

AIR FREE,NO VELOCITY

AIR FREEAIR FREE

AERATED

AERATED

IN ETHANOL

AERATED,NO VELOCITY

AERATED,NO VELOCITY


NCEES 347


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F





STEEL


ZIRCONIUM


===


====


====


====


====


====


====

ACID

,NI

TRIC

ACID

,OX

ALIC

ACID

,PH

OSPH

ORIC

ACID

,SU

LFUR

IC

ALUM

INUM

CHLO

RIDE

ALUM

INUM

PO

TASS

IUM

SULF

ATE

(ALU

M)

AMMO

NIA,

AQUE

OUS

AIR FREE,NO VELOCITY

STRESSCRACKS

IN ETHANOL


348 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

ALUMINUM

ASPHALTIC RESINS


EPOXY RESINS

FURANE RESINS

GLASS

HASTELLOY B

HASTELLOY C

HASTELLOY D


====


===


====

SATISFACTORYSATISFACTORY FOR LIMITED USENOT RECOMMENDED

===


===


====


====


====


====

AMMO

NIUM

CARB

ONAT

E

AMMO

NIUM

CHLO

RIDE

CALC

IUM

CHLO

RIDE

CALC

IUM

HYPO

CHLO

RITE


NCEES 349


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

AVOID HCI

AND Fe, NI IONS

IRON, CAST

MONEL

NEOPRENE

NICKEL

PHENOLIC RESINS

POLYETHYLENE

RUBBER (NATURAL, GR–S)

RUBBER, BUTYL


====


====


====


===


===


===


===

COMPLETE RESISTANCESOME ATTACKATTACK OR DECOMPOSITION

===

AMMO

NIUM

CARB

ONAT

E

AMMO

NIUM

CHLO

RIDE

CALC

IUM

CHLO

RIDE

CALC

IUM

HYPO

CHLO

RITE


350 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F





STEEL pH > 7pH > 7

ZIRCONIUM< 0.002 IN. PER YR. 0.002 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.

====


====


====


====


====


STYRENE COPOLYMERS, HIGH IMPACTSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY

===

====

AMMO

NIUM

CARB

ONAT

E

AMMO

NIUM

CHLO

RIDE

CALC

IUM

CHLO

RIDE

CALC

IUM

HYPO

CHLO

RITE


NCEES 351


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

AIR FREE

0.09% HCI

COPP

ERSU

LFAT

E

ETHA

NOL

ETHY

LENE

GLYC

OL

FERR

ICCH

LORI

DE

FERR

OUS

CHLO

RIDE

FERR

OUS

SULF

ATE

GLYC

ERIN

E

ALUMINUM

ASPHALTIC RESINS


EPOXY RESINS

FURANE RESINS

GLASS

HASTELLOY B

HASTELLOY C

HASTELLOY D




= SATISFACTORY= SATISFACTORY FOR LIMITED USE= NOT RECOMMENDED







352 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

PITS

COPP

ERSU

LFAT

E

ETHA

NOL

ETHY

LENE

GLYC

OL

FERR

OUS

CHLO

RIDE

FERR

OUS

SULF

ATE

FERR

ICCH

LORI

DE

GLYC

ERIN

E

IRON, CAST

MONEL

NEOPRENE

NICKEL

PHENOLIC RESINS

POLYETHYLENE

RUBBER (NATURAL, GR–S)

RUBBER, BUTYL


====


====


====


===


===


===


===

COMPLETE RESISTANCESOME ATTACKATTACK OR DECOMPOSITION

===


NCEES 353


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

DRYDISCOLORSDISCOLORS

COPP

ERSU

LFAT

E

ETHA

NOL

ETHY

LENE

GLYC

OL

FERR

ICCH

LORI

DE

FERR

OUS

CHLO

RIDE

FERR

OUS

SULF

ATE

GLYC

ERIN

E












STEEL


ZIRCONIUM


354 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

AIR FREEAIR FREE AIR FREE

HYDR

OGEN

PERO

XIDE

MAGN

ESIU

MCH

LORI

DE

MAGN

ESIU

MSU

LFAT

E

METH

ANOL

NICK

ELCH

LORI

DE

NICK

ELSU

LFAT

E

PHEN

OL

POTA

SSIU

MHY

DROX

IDE










ALUMINUM

ASPHALTIC RESINS


EPOXY RESINS

FURANE RESINS

GLASS

HASTELLOY B

HASTELLOY C

HASTELLOY D


NCEES 355


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

DRY

AIRFREE

SULFER FREE

ALKALINEDISCOLORS

AIR FREE

AIR FREE,PITS

DRY

HYDR

OGEN

PERO

XIDE

MAGN

ESIU

M CH

LORI

DE

MAGN

ESIU

MSU

LFAT

E

METH

ANOL

NICK

ELNI

TRAT

E

NICK

ELSU

LFAT

E

PHEN

OL

POTA

SSIU

MHY

DROX

IDE

IRON, CAST

MONEL

NEOPRENE

NICKEL

PHENOLIC RESINS

POLYETHYLENE


RUBBER, BUTYL





= SATISFACTORY= SATISFACTORY FOR LIMITED SERVICE= GENERALLY UNSATISFACTORY


= COMPLETE RESISTANCE= SOME ATTACK= ATTACK OR DECOMPOSITION

= SATISFACTORY= FOR LIMITED USE ONLY= UNSATISFACTORY


356 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

PITS

STRESSCRACKS

ALKALINE

STRESS CRACKS

DISCOLORS,SULFUR FREE

AIR FREE

800 F.

800 F.

pH > 7 pH > 7

HYDR

OGEN

PERO

XIDE

MAGN

ESIU

M CH

LORI

DE

MAGN

ESIU

MSU

LFAT

E

METH

ANOL

NICK

ELNI

TRAT

E

NICK

ELSU

LFAT

E

PHEN

OL

POTA

SSIU

MHY

DROX

IDE












STEEL


ZIRCONIUM


NCEES 357


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

PITS AIR FREE

10 20 30

POTA

SSIU

MSU

LFAT

E

SODI

UMCA

RBON

ATE

SODI

UMCH

LORI

DE

SODI

UMHY

DROX

IDE

SODI

UMNI

TRAT

E

ZINC

CHLO

RIDE

ZINC

SULF

ATE










ALUMINUM

ASPHALTIC RESINS


EPOXY RESINS

FURANE RESINS

GLASS

HASTELLOY B

HASTELLOY C

HASTELLOY D


358 NCEES


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

AIR FREE

AIR FREE

DRY950 F.

1300 F.

1300 F.

DRY

600 F.STRESS CRACKS

400F.

POTA

SSIU

MSU

LFAT

E

SODI

UMCA

RBON

ATE

SODI

UMCH

LORI

DE

SODI

UMHY

DROX

IDE

SODI

UMNI

TRAT

E

ZINC

CHLO

RIDE

ZINC

SULF

ATE


= SATISFACTORY= FOR LIMITED USE ONLY= UNSATISFACTORY

= COMPLETE RESISTANCE= SOME ATTACK= ATTACK OR DECOMPOSITION







NCEES 359


KEY TO CHARTS

CONCENTRATION, %

300

200

100

00 50 100TE

MPER

ATUR

E, °F

STRESS CRACKSAT HIGHER TEMPS.

DRYpH > 7

STRESSCRACKS

POTA

SSIU

MSU

LFAT

E

SODI

UMCA

RBON

ATE

SODI

UMCH

LORI

DE

SODI

UMHY

DROX

IDE

SODI

UMNI

TRAT

E

ZINC

CHLO

RIDE

ZINC

SULF

ATE





STEEL


ZIRCONIUM


===


====


====


====


====


====


====


360 NCEES

6.3.5.4 Galvanic Corrosion

Galvanic Corrosion0.2 0 –0.2 –0.4 –0.6 –0.8 –1.0 –0.2 –1.4 –1.6

ALLOY 20 STAINLESS STEELNICKEL IRON CHROMIUM ALLOY 825TITANIUMGOLD, PLATINUMGRAPHITE

MAGNESIUM ZINC BERYLLIUM ALUMINUM ALLOYS CADMIUM MILD STEEL & CAST IRON LOW ALLOY STEELAUSTIENITIC CAST IRONALUMINUM BRONZENAVAL BRASS, YELLOW BRASS & RED BRASSTINCOPPER50/50 LEAD TIN SOLDERADMIRALTY BRASS, ALUMINUM BRASSMANGANESE BRONZESILICON BRONZESTAINLESS STEEL – GRADES 410, 416NICKEL SILVER90/10 COPPER NICKEL80/20 COPPER NICKELSTAINLESS STEEL – GRADE 430LEAD70/30 COPPER NICKELNICKEL ALUMINUM BRONZENICKEL CHROMIUM ALLOY 600NICKEL 200SILVERSTAINLESS STEEL – GRADES 302, 304, 321 & 347NICKEL COPPER ALLOYS – 400, K500STAINLESS STEEL – GRADES 316 & 317

MAGNESIUM ZINC BERYLLIUM ALUMINUM ALLOYS CADMIUM MILD STEEL & CAST IRON LOW ALLOY STEELAUSTIENITIC CAST IRONALUMINUM BRONZENAVAL BRASS, YELLOW BRASS & RED BRASSTINCOPPER50/50 LEAD TIN SOLDERADMIRALTY BRASS, ALUMINUM BRASSMANGANESE BRONZESILICON BRONZESTAINLESS STEEL – GRADES 410, 416NICKEL SILVER90/10 COPPER NICKEL80/20 COPPER NICKELSTAINLESS STEEL – GRADE 430LEAD70/30 COPPER NICKELNICKEL ALUMINUM BRONZENICKEL CHROMIUM ALLOY 600NICKEL 200SILVERSTAINLESS STEEL – GRADES 302, 304, 321 & 347NICKEL COPPER ALLOYS – 400, K500STAINLESS STEEL – GRADES 316 & 317

ALLOY 20 STAINLESS STEELNICKEL IRON CHROMIUM ALLOY 825TITANIUMGOLD, PLATINUMGRAPHITE

MOST NOBLE – CATHODIC LEAST NOBLE – ANODICMOST NOBLE – CATHODIC LEAST NOBLE – ANODIC

Note: Unshaded symbols show ranges exhibited by stainless steels in acidic water such as may exist in crevices or in stagnant, low-velocity, or poorly aerated water.

Source: Atlas Steels, Atlas Technical Note No. 7: "Galvanic Corrosion," www.atlassteels.com.au, August 2010.

6.3.5.5 Electrochemistry

Electrochemical TermsTerm Definition

Cathode The electrode at which reduction occursAnode The electrode at which oxidation occursOxidation The loss of electronsReduction The gaining of electronsCation Positive ionAnion Negative ion


NCEES 361

6.3.5.6 Standard Oxidation Potentials

Standard Oxidation Potentials for Corrosion Reactions*

Corrosion Reaction Potential (Eo) Volts vs. Normal Hydrogen Electrode

Au Au e33" ++ − -1.498

H O O H e2 4 42 2" + ++ − -1229

Pt Pt e22" ++ − -1.200

Pd Pd e22" ++ − -0.987

Ag Ag e" ++ − -0.799

2Hg Hg e222" ++ − -0.788

Fe Fe e2 3" ++ + − -0.771

OH O H O e4 2 42 2" + +− −^ h -0.401

Cu Cu e22" ++ − -0.337

Sn Sn e22 4" ++ + − -0.150

H H e2 22 " ++ − +0.000

Pb Pb e22" ++ − +0.126

Sn Sn e22" ++ − +0.136

Ni Ni e22" ++ − +0.250

Co Co e22" ++ − +0.277

Cd Cd e22" ++ − +0.403

Fe Fe e22" ++ − +0.440

Cr Cr e33" ++ − +0.744

Zn Zn e22" ++ − +0.763

Al Al e33" ++ − +1.662

Mg Mg e22" ++ − +2.363

Na Na e" ++ − +2.714

K K e" ++ − +2.925

*Measured at 25°C. Reactions are written as anode half-cells. Arrows are reversed for cathode half-cells.

Note: In some chemistry texts, the reactions and the signs of the values (in this table) are reversed; for example, the half-cell potential of zinc is given as –0.763 volt for the reaction Zn e Zn22 "++ − . When the potential Eo is positive, the reaction

proceeds spontaneously as written.

Source: Republished with permission of Houghton Mifflin Harcourt, from Flinn, Richard A., and Paul K. Trojan, Engineering Materials and Their Applications, 3rd ed., 1986. Permission conveyed through Copyright Clearance Center, Inc.


362 NCEES

6.4 Operation

6.4.1 Process and Equipment Reliability

6.4.1.1 Operating ProceduresThe main types of process operating procedures are

1. Standard Operating Procedures (SOP)—Written instructions documenting step-by-step instructions for safely performing a task within operating limits. The SOP covers all modes of operation. The purpose of the standard operating procedure is to ensure operations are always carried out correctly and in the same manner. An SOP should be available at the place where the work is done.

2. Startup/Shutdown Procedures—Written procedures for startup and shut-down phased so that interlinked plant operations can resume or stop in a safe and controlled manner.

3. Emergency or Abnormal Operating Procedures—Written instructions documenting step-by-step instructions for reaching a safe state following a process in an upset condition.The emergency procedures should cover the PPE, the level of intervention which is safe, and when to evacuate. The procedures will also need to tie in with site emergency plans.

4. Temporary Operating Procedures—Written instructions for a finite period of time. At the conclusion of this time, the facility returns to using the Standard Operating Procedures. Temporary operating procedures should include an expiration date.

5. Maintenance Procedures—Written instructions that address material control and maintenance practices needed to ensure system operability and integrity. These procedures specify the required maintenance, testing, and inspection frequencies.

Source: Guidelines for Engineering Design for Process Safety, 2nd ed., 5.3.2 "Testing Instrumentation," Center for Chemical Process Safety/AlChE, 2012, pp. 135–137.

The zones for safe operation of process equipment are defined as

1. Normal Operating Zone: The minimum or maximum values of an operating parameter that define the boundaries of normal operations. Some examples of operating parameters to be defined include• High and low pressure

• High and low temperature

• High and low level

• High and low pH

• High and low flow

2. Troubleshooting Zone: An area that provides time for troubleshooting, so that operations personnel can make adjustments in time to return the operating parameters to the Normal Operating Zone. Human factors and process response time generally indicate zone size. Immediate actions, and in some cases predeter-mined actions, to avoid Safe Operating Limit (SOL) deviation are taken in this zone.

3. Buffer Zone: The upper and lower area of the known safe zone provides a buffer to ensure no operating parameter can reach the Unknown/Unacceptable Operation Zone. Factors that influence Buffer Zone size may include engineering judgment, reliability of instrumentation, operating experience, probability and consequence of human error, and so on. A process will not be operated intentionally in this zone.


NCEES 363

4. Safe Operating Limit (SOL): A value for an operating parameter that defines the equipment or process unit's safe-operating envelope, beyond which a process will not intentionally be operated due to the risk of imminent, catastrophic equipment failure or loss of containment. Operational or mechanical corrective ac-tion ceases and immediate predetermined actions are taken at these operating parameter values in order to bring equipment and process units to a safe state. Each SOL should be documented in the plant's Process Safety Information.

5. Unacceptable or Unknown Operating Zone: An area beyond the Safe Operating Limit. A process will not be intentionally operated in this zone.

Operation Zones for Process Equipment

SAFE OPERATING LIMIT

EQUIPMENT LIMIT

INSTRUMENT RANGEUNACCEPTABLE/UNKNOWN

OPERATING ZONE

UNACCEPTABLE/UNKNOWNOPERATING ZONE

BUFFER ZONE

BUFFER ZONE

TROUBLESHOOTING ZONE

TROUBLESHOOTING ZONE

NORMALOPERATING ZONE

EQUIPMENT LIMIT

INSTRUMENT RANGE

SAFE OPERATING LIMIT

NEVER EXCEED LIMIT

NEVER EXCEED LIMIT

MAXIMUM NORMAL OPERATING LIMIT

MINIMUM NORMAL OPERATING LIMIT

Source: Smith, David J., Reliability, Maintainability and Risk—Practical Methods for Engineers, 5th ed., Appendix A1: "Terms Related to Failure," Amsterdam: Elsevier, 1997.


364 NCEES

6.4.1.2 Maintenance and Reliability

Maintenance and ReliabilityTerm Definition Example or Application

Availability

Availability (%) = Total TimeUp Time

The proportion of time that an item is capable of operating to specification within a large time interval.

The availability of a gas turbine generator was increased to 95% by minimizing the scheduled maintenance duration.

DiversityThe same performance of a function by two or more independent and dissimilar means.

In-line check valves of two different tech-nologies or separate manufacturers are installed to decrease the likelihood of reverse flow from waste-water treatment back to the process.

Failure Modes and Effects Analysis (FMEA)

A qualitative tool for analysis identify-ing all the ways a particular component can fail and the effects of the failure on the system.

An FMEA identifies internal spring failure from excessive wear on a solenoid valve. The local and system consequences are documented. A recommendation is made for regular inspection to prevent this point of failure.

Mean Time Between Failures (MTBF)

The total cumulative functioning time of a population divided by the number of failures, MTBF is used for items that involve repair and excludes downtime.

MTBF Number of FailuresTotal Up Time=

For 10,000 total hours of recorded uptime, the MTBF for 4 power supplies is 2500 hours.

Predictive Maintenance

The aim of predictive maintenance is, first, to predict when equipment failure may occur and, second, to prevent oc-currence of that failure by performing maintenance.

A plant predictive maintenance program could use regular vibration analyses and motor current signature analyses to deter-mine equipment conditions and predict failure.

Preventive MaintenanceActions carried out for the purpose of keeping equipment or instrumentation in a specified condition.

A preventive maintenance program for a centrifugal pump at a plant could include monthly inspection of the gland packing, bearing lubrication, and pump mountings.

Redundancy

The provision of more than one means of achieving a function.

Active/Duty: All items remain operating prior to failure.

Standby: Replicated items do not oper-ate until needed.

An active pump runs continuously for long periods of time without having to go through the start-up process. The standby pump remains dormant and is tested regu-larly to ensure reliability.

Reliability

The probability that the system will not leave the operational state. The avail-ability for a given system is always greater than or equal to the reliability.

Safety-instrumented function; probability of failure on demand.


NCEES 365

6.4.1.3 Decision-Tree Approach to Determine the Optimum Maintenance Period

Decision Tree for Optimum Maintenance

YES YES YES

NO NO NOIS IMPACT AND FREQUENCY OF FAILURE ON AVAILABILITY AND COST ACCEPTABLE?

IS FAILURE PREDICTABLE

IS IMPENDING FAILURE DETECTABLE?

UNSCHEDULED MAINTENANCE

PREVENTIVE MAINTENANCE

PREDICTIVE MAINTENANCE

UNSCHEDULED MAINTENANCE

CALENDAR TIME BASIS

USAGE BASIS

CONTINUOUS MONITORING

PERIODIC MANUAL MONITORING

Source: Koshal, D., Manufacturing Engineer's Reference Book, 18.6.3 "Establishing Preventive-Maintenance Routines," Amsterdam: Elsevier, 1993.

6.4.1.4 Typical Equipment Failure Diagram

Equipment FailureTYPICAL EQUIPMENT FAILURE DIAGRAM

DURING EXTREMEEVENTS

DURING NORMALOPERATION

FAILU

RE R

ATE

(λ)

WEAROUTPERIOD

INFANTMORALITY

TIME

USEFUL LIFEPERIOD


366 NCEES

6.4.2 Process Improvement and TroubleshootingThe variety and complexity of modern processing industries requires that engineers be able to find ways to improve the processes of their facilities for the benefit of their employers or clients. Process improvement allows for the optimization of utilities, raw materials, and other resources to maximize production and minimize the cost per unit produced.

Engineers who are tasked with process improvement and troubleshooting focus their knowledge and training to make a facility or process work more efficiently and economically.

Work in this area will focus on one of the following types of activities:

• Optimum balance of process variables• Increased capacity—Debottleneck and/or add equipment• Improved product quality—Control contamination and deterioration• Improved mechanical performance—Reduce corrosion and fouling• Decreased utility and raw material consumption—Steam, power, water, chemicals, and so on• More efficient maintenance• Improved safety practices

The use of data is paramount to any of the activities listed above. The modern process-industries plant typically has an abundance of data that is part of the control systems. This data is collected from all aspects and areas of the facility.

One of the most common methods of using data to improve a process is the DMAIC method. The five phases in the DMAIC method are

1. Define the problem and system by setting goals and understanding the requirements of the customer and the system.

2. Measure the key aspects of the process and gather the data that is available and relevant to the issue, project, or problem to be solved. This data can be used to determine the "as is" state of the process.

3. Analyze the data to investigate the process and determine the cause-and-effect relationships in the process. Seek out the root cause(s) of the problem being evaluated.

4. Improve or optimize the current process based on data analysis techniques to create a new, future-state process and run pilot trials to establish the process capability.

5. Control the new process to ensure that any deviations are corrected quickly before they result in defects or issues.

Data analysis can be a complex activity and techniques in this area include

5 Whys Analysis of varianceRegression analysis CorrelationCause-and-effect diagraming Control/run chartsDesign of experiments Pareto analysisTaguchi loss function Value stream mappingGeneral linear modeling Axiomatic designCost-benefit analysis Root-cause analysis


NCEES 367

One of the most useful techniques for troubleshooting is root-cause analysis (RCA). RCA is a method of problem-solving used to identify the root cause(s) of faults or problems.

A factor is considered a root cause if removal from the problem-fault sequence prevents the final undesirable event from recurring. A causal factor is one that affects an event's outcome and, if removed, might benefit the process but does not prevent the recurrence of the problem being addressed. RCA is applied to methodically identify and correct the root causes of events, rather than to simply address the symptomatic result. Focusing correction on root causes has the goal of entirely preventing problem recurrence. RCA is typically used as a reactive method for identifying event causes, revealing problems, and solving them. Analysis is most typically done after an event has occurred; however, it can also be used as a predictive tool.

The basic steps in root-cause analysis are:

1. Define the problem or describe the event to prevent in the future.2. Gather data and evidence, classifying it along a time line.3. Data-mine for clusters of similar problems that are close to the problem or event.4. Ask why this happens and identify the causes, giving each sequential step toward the problem or event.5. Classify all causes into either "causal" or "root."6. Identify any other items that affect the problem or event.7. Identify the corrective action(s) that will, with certainty, prevent recurrence of each harmful effect.8. Identify solutions that prevent recurrence and that are within the control of the institution.9. Implement the recommended root-cause corrections.10. Ensure effectiveness by observing the implemented solutions in operation.

Observation is one of the best ways to identify issues that need to be addressed when working and troubleshooting in any type of plant.

6.5 Safety, Health, and Environment

6.5.1 General

6.5.1.1 Definition of SafetySafety is the condition of protecting people from threats or failure that could harm their physical, emotional, occu-pational, psychological, or financial well-being. Safety is also the control of known threats to attain an acceptable level of risk. The United States relies on public codes and standards, engineering designs, and corporate policies to ensure that a structure or place does what it should do to maintain a steady state of safety—that is, long-term stability and reliability. Some safety/regulatory agencies that develop codes and standards commonly used in the United States are shown below.

Insurance, Safety, and Regulatory AgenciesAcronym Name Jurisdiction

ANSI American National Standards Institute Nonprofit standards organizationCGA Compressed Gas Association Nonprofit trade associationCSA Canadian Standards Association Nonprofit standards organizationFAA Federal Aviation Administration U.S. federal regulatory agencyFMG FM Global InsuranceIEC International Electrotechnical Commission Nonprofit standards organization

ITSNA Intertek Testing Services NA (formerly Edison Testing Labs) Nationally recognized testing laboratory


368 NCEES

Insurance, Safety, and Regulatory Agencies (cont'd)Acronym Name Jurisdiction

MSHA Mine Safety and Health Administration Federal regulatory agencyNFPA National Fire Protection Association Nonprofit trade organizationOSHA Occupational Health and Safety Administration Federal regulatory agencyUL Underwriters Laboratories Nationally recognized testing laboratoryUSCG United States Coast Guard Federal regulatory agencyUSDOT United States Department of Transportation Federal regulatory agencyUSEPA United States Environmental Protection Agency Federal regulatory agency

6.5.1.2 Elements of Process Safety Management (PSM)The U.S. Occupational Safety and Health Administration (OSHA) 1910.119 defines all 14 elements of a process safety management plan:

1. Employee Participation—Consult with employees and their representatives on the development and conduct of hazard assessments and the development of chemical accident prevention plans, and provide access to these and other records required under the standard.

2. Process Safety Information—Develop and maintain written safety information identifying workplace chemical and process hazards, equipment used in the processes, and technology used in the processes.

3. Process Hazard Analysis—Perform a workplace hazard assessment including, as appropriate, identifica-tion of potential sources of accidental releases, identification of any previous release within the facility that had a potential for catastrophic consequences in the workplace, estimation of workplace effects of a range of releases, and estimation of the health and safety effects of such a range on employees. Establish a system to respond to the workplace hazard assessment findings, which shall address prevention, mitiga-tion, and emergency responses.

4. Operating Procedures—Develop and implement written operating procedures for the chemical processes, including procedures for each operating phase, operating limitations, and safety and health considerations.

5. Training—Provide written safety and operating information for employees and employee training in oper-ating procedures, by emphasizing hazards and safe practices that must be developed and made available.

6. Contractors—Ensure contractors and contract employees are provided with appropriate information and training.

7. Pre-startup Safety Review—Conduct pre-startup safety reviews of all newly installed or modified equip-ment.

8. Mechanical Integrity—Establish maintenance systems for critical process-related equipment, including written procedures, employee training, appropriate inspections, and testing of such equipment to ensure ongoing mechanical integrity. Establish a quality-assurance program to ensure that initial process-related equipment, maintenance materials, and spare parts are fabricated and installed consistent with design specifications.

9. Hot-Work Permit—A permit must be issued for hot-work operations conducted on or near a covered process. The permit must document that the fire prevention and protection requirements have been imple-mented prior to beginning the hot-work operations; it must indicate the date(s) authorized for hot work and identify the object on which hot work is to be performed. The permit must be kept on file until completion of the hot work.

10. Management of Change—Establish and implement written procedures managing change to process chemicals, technology, equipment, and facilities.

11. Incident Investigation—Investigate every incident that results in or could have resulted in a major accident in the workplace, with any findings to be reviewed by operating personnel and modifications made if appropriate.


NCEES 369

12. Emergency Planning and Response—Develop and implement an emergency action plan for the entire plant in accordance with the provisions of other OSHA rules. Include in the emergency action plan proce-dures for handling small releases of hazardous chemicals.

13. Compliance Audits—Employers must certify that they have evaluated compliance with the provisions of PSM at least every three years. This will verify that the procedures and practices developed under the standards are adequate and are being followed.

14. Trade Secrets—Employers must make available all information necessary to comply with PSM to those persons responsible for compiling the process safety information, those developing the process hazard analysis, those responsible for developing the operating procedures, and those performing incident inves-tigations, emergency planning and response, and compliance audits, without regard to the possible trade-secret status of such information.

6.5.1.3 Safety, Health, and PreventionA traditional preventive approach to both accidents and occupational illness involves recognizing, evaluating, and controlling hazards and work conditions that may cause physical injuries or adverse health effects.

Hazard is the capacity to cause harm. It is an inherent quality of a material or a condition. For example, a rotating saw blade or an uncontrolled high-pressure jet of water has the capability (hazard) to slice through flesh. A toxic chemical or a pathogen has the capability (hazard) to cause illness.

Risk is the chance or the probability that a person will experience harm and is not the same as a hazard. Risk al-ways involves both probability and severity elements. The hazard associated with a rotating saw blade or the water jet continues to exist, but the probability of causing harm, and thus the risk, can be reduced by installing a guard or by controlling the jet's path. Risk is expressed by the equation:

Risk = Hazard # Probability

When people discuss the hazards of disease-causing agents, the term exposure is typically used more than probabil-ity. If a certain type of chemical has a toxicity hazard, the risk of illness rises with the degree to which that chemi-cal contacts your body or enters your lungs. In that case, the equation becomes:

Risk = Hazard # Exposure

Organizations evaluate hazards using multiple techniques and data sources.

6.5.1.4 Job Safety AnalysisJob safety analysis (JSA) is known by many names, including activity hazard analysis (AHA), or job hazard analy-sis (JHA). Hazard analysis helps integrate accepted safety and health principles and a specific task. In a JSA, each basic step of the job is reviewed, potential hazards identified, and recommendations documented as to the safest way to do the job. JSA techniques work well when used on a task that the analysts understand well. JSA analysts look for specific types of potential accidents and ask basic questions about each step, such as these:

Can the employee strike against or otherwise make injurious contact with the object? Can the employee be caught in, on, or between objects? Can the employee strain muscles by pushing, pulling, or lifting? Is exposure to toxic gases, vapors, dust, heat, electrical currents, or radiation possible?


370 NCEES

6.5.2 Protection Systems

6.5.2.1 Major Types of Relief Devices

Relief Devices

BONNET

ADJUSTING SCREW

STEM SPINDLE

VENT (PLUGGED)

CAP

SPRING

SEATING SURFACE

ADJUSTING RINGBODY

NOZZLE

BONNET

ADJUSTING SCREW

STEM SPINDLE

VENT (UNPLUGGED)

CAP

SPRING

DISK

DISK

BELLOWS

SEATING SURFACE

ADJUSTING RINGBODY

NOZZLE

Conventional pressure relief valve (PRV) with a single adjusting ring for blowdown control

Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, Part 1, December 2008, Figure 1.

BONNET

ADJUSTING SCREW

STEM SPINDLE

VENT (PLUGGED)

CAP

SPRING

SEATING SURFACE

ADJUSTING RINGBODY

NOZZLE

BONNET

ADJUSTING SCREW

STEM SPINDLE

VENT (UNPLUGGED)

CAP

SPRING

DISK

DISK

BELLOWS

SEATING SURFACE

ADJUSTING RINGBODY

NOZZLE

Balance-Bellows PRV



NCEES 371

PILOT EXHAUST

PILOT VALVE

SEAT

SEAT

INTERNALPRESSURE PICKUP

MAIN VALVE

OUTLET

INLET

SET PRESSUREADJUSTMENT SCREW

SPINDLE

EXTERNAL BLOWDOWNADJUSTMENT

PILOT SUPPLY LINE

OPTIONALPILOT FILTER

PISTON

Pop-Action Pilot-Operated Valve (Flow-ing Type)


DISC

CARRIERASSEMBLY

Rupture Disk Assembly

Source: Chemical Process Safety: Funda-mentals with Applications, 2nd ed., New York: Prentice Hall, 2002, p. 362, Figure 8-7.


372 NCEES

6.5.2.2 Pressure-Level Relationships for Pressure Relief Valves

Pressure-Level Relationships for PRVs

PRESSURE VESSEL REQUIREMENTSVESSEL

PRESSURE

121120

116

115

110

105

100

95

90

85

TYPICAL CHARACTERISTICS OFPRESSURE RELIEF VALVES

MAXIMUM ALLOWABLE ACCUMULATED PRESSURE (FIRE EXPOSURE ONLY)

MAXIMUM ALLOWABLE ACCUMULATIVE PRESSURE FOR MULTI-VALVE INSTALLATION (OTHER THAN FIRE EXPOSURE)

MAXIMUM ALLOWABLE ACCUMULATED PRESSURE FOR SINGLE–VALVE INSTALLATION(OTHER THAN FIRE EXPOSURE))

MAXIMUM ALLOWABLE WORKING PRESSURE OR DESIGN PRESSURE(SEE NOTE 4)

MAXIMUM EXPECTEDOPERATING PRESSURE(SEE NOTES 5 AND 6)

LEAK TEST PRESSURE (TYPICAL)

CLOSING PRESSURE FORA SINGLE VALVE

BLOWDOWN (TYPICAL)(SEE NOTE 6)

MAXIMUM ALLOWABLE SET PRESSURE FOR SINGLE VALVE

MAXIMUM ALLOWABLE SET PRESSURE FOR ADDITIONAL VALVES (PROCESS)

OVERPRESSURE (MAXIMUM)

THE MAXIMUM ALLOWABLE SET PRESSURE FOR SUPPLEMENTAL VALVES (FIRE EXPOSURE)

SINGLE–VALVE MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING

MULTIPLE VALVES AND MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING

MAXIMUM RELIEVING PRESSUREFOR FIRE SIZING

SIMMER(TYPICAL)

PERC

ENT

OF M

AXIM

UM A

LLOW

ABLE

WOR

KING

PRE

SSUR

E (G

AUGE

)

NOTES:

1. THIS FIGURE CONFORMS WITH THE REQUIREMENTS OF SECTION VIII OF THE ASME BOILER AND PRESSURE VESSEL CODE FOR MAWPS GREATER THAN 30 PSIG.

2. THE PRESSURE CONDITIONS SHOWN ARE FOR PRESSURE RELIEF VALVE INSTALLED A PRESSURE VESSEL.

3. ALLOWABLE SET-PRESSURE TOLERANCES WILL BE IN ACCORDANCE WITH THE APPLICABLE CODES.

4. THE MAXIMUM ALLOWABLE WORKING PRESSURE IS EQUAL TO OR GREATER THAN THE DESIGN PRESSURE FOR COINCIDENT DESIGN TEMPERATURE.

5. THE OPERATING PRESSURE MAYBE HIGHER OR LOWER THAN 90%.

6. SECTION VIII, DIVISION 1, APPENDIX M OF THE ASME CODE SHOULD BE REFERRED TO FOR GUIDANCE ON BLOWDOWN AND PRESSURE DIFFERENTIALS.

Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, Part 1, December 2008.


NCEES 373

6.5.2.3 Designs for Preventing Fires and Explosions

Designs for Fire- and Explosion-PreventionFeature Explanation

Maintenance programsThe best way to prevent fires and explosions is to stop the release of flam mable materials. Preventive maintenance programs are designed to upgrade systems before failures occur.

FireproofingInsulate vessels, pipes, and structures to minimize damage resulting from fires. Add deluge systems and design to withstand some damage from fires and explosions, e.g., use multiple deluge systems with separate shutoffs.

Control rooms Design control rooms to withstand explosions.

Water supplies Provide supply for maximum demand. Consider many deluge systems run ning simul-taneously. Diesel-engine pumps are recommended.

Control valves for deluge Place shutoffs well away from process areas.

Manual fire protection Install hydrants, monitors, and deluge systems. Add good drainage.

Separate units Separate (space) plants on a site, and separate units within plants. Provide access from two sides.

Utilities Design steam, water, electricity, and air supplies to be available during emergencies. Place substations away from process areas.

Personnel areas Locate personnel areas away from hazardous process and storage areas.

Group unitsGroup units in rows. Design for safe operation and maintenance. Create islands of risk by concentrating hazardous process units in one area. Space units so hot work can be performed on one group while another is operating.

Isolation valves Install isolation valves for safe shutdowns. Install in safe and accessible locations at edge of unit or group.

Railroads and flares Process equipment should be separated from flares and railroads. Compressors Place gas compressors downwind and separated from fired heaters.

Dikes Locate flammable storage vessels at edge of unit. Dike vessels to con tain and carry away spills.

Block valves Place automated block valves to stop and/or control flows dur ing emergencies. Con-sider the ability to transfer hazardous materials from one area to another.

Online analyzersAdd appropriate online analyzers to (1) monitor the status of the process, (2) detect problems at their incipient stage, and (3) take appropriate action to minimize effects of problems while still in initial phase of development.

Fail-safe designs Design all controls to fail safely. Add safeguards for automated and safe shutdowns during emergencies.

Safety-instrumented systems (SIS)

Use SIS to automatically bring process to a safe state upon detection of potentially hazardous conditions.

Source: Chemical Process Safety: Fundamentals with Applications, 2nd ed., New York: Prentice Hall, 2002, p. 346, Figure 7-8.


374 NCEES

6.5.3 Industrial HygienePersonal protective equipment (PPE) is designed to protect employees from serious injuries or illnesses resulting from contact with chemical, radiological, physical, electrical, mechanical, or other workplace hazards. Besides face shields, safety glasses, hard hats, and safety shoes, PPE includes a variety of devices and garments, such as goggles, coveralls, gloves, vests, earplugs, and respirators.

6.5.3.1 RespiratorsAssigned protection factors (APFs)—Per 29 CFR 1910.134, employers must use the assigned protection factors (listed in the table that follows) to select a respirator that meets or exceeds the required level of employee protec-tion. When using a combination respirator (e.g., airline respirators with an air-purifying filter), employers must en-sure that the assigned protection factor is appropriate to the mode of operation in which the respirator is being used.

Immediately dangerous to life or health (IDLH)—An atmosphere that poses an immediate threat to life, would cause irreversible adverse health effects, or would impair an individual's ability to escape from a dangerous atmo-sphere.

Powered air-purifying respirator (PAPR)—An air-purifying respirator that uses a blower to force the ambient air through air-purifying elements to the inlet covering.

Supplied-air respirator (SAR) or airline respirator—An atmosphere-supplying respirator for which the source of breathing air is not designed to be carried by the user.

Workplace protection factor (WPF) study—A study, conducted under actual conditions of use in the work-place, that measures the protection provided by a properly selected, fit-tested, and functioning respirator, when the respirator is worn correctly and used as part of a comprehensive respirator program that is in compliance with OSHA's Respiratory Protection Standard at 29 CFR 1910.134. Measurements of Co and Ci are obtained only while the respirator is being worn during performance of normal work tasks (that is, samples are not collected when the respirator is not being worn). As the degree of protection afforded by the respirator increases, the WPF increases.

Simulated workplace protection factor (SWPF) study—A study, conducted in a controlled laboratory setting, in which Co and Ci sampling is performed while the respirator user performs a series of set exercises. The laboratory setting is used to control many of the variables found in workplace studies, while the exercises simulate the work activities of respirator users. This type of study is designed to determine the optimum performance of respirators by reducing the impact of sources of variability through maintenance of tightly controlled study conditions.


NCEES 375

Assigned Protection Factors5

Type of Respirator1,2 Quarter Mask

Half Mask

Full Face Piece

Helmet/Hood

Loose- Fitting

Face Piece1. Air-purifying respirator 5 103 50 — —2. Powered air-purifying respirator (PAPR) — 50 1000 25/10004 253. Supplied-air respirator (SAR) or airline respirator • Demand mode — 10 50 — — • Continuous flow mode — 50 1000 25/10004 25 • Pressure-demand or other positive-pressure mode — 50 1000 — —

4. Self-contained breathing apparatus (SCBA) • Demand mode — 10 50 50 — • Pressure-demand or other positive-pressure mode (e.g., open or closed) — — 10,000 10,000 —

Notes:1. Employers may select respirators assigned for use in higher workplaces concentration of a hazardous

substance for use at lower concentrations of that substance, or when required respirator use is independent of concentration.

2. The assigned protection factors in this table are only effective when the employer implements a continu-ing, effective respirator program as required by this section (29 CFR 1910.134), including training, fit-testing, maintenance, and use requirements.

3. This APF category includes filtering face pieces, and half masks with elastomeric face pieces.4. The employer must have evidence provided by the respirator manufacturer that testing of these respira-

tors demonstrates performance at a level of protection of 1000 or greater to receive an APF of 1000. This level of performance can best be demonstrated by performing a WPF or SWPF study or equivalent testing. Absent such testing, all other PAPRs and SARs with helmets/hoods are to be treated as loose-fitting face piece respirators, and receive an APF of 25.

5. These APFs do not apply to respirators used solely for escape. Tor escape respirators used in associa-tion with specific substances covered by 29 CFR 1910 subpart Z, employers must refer to the appropriate substance-specific standards in that subpart. Escape respirators for other IDLH atmospheres are specified by 29 CFR 1910.134(d)(2)(ii).

Source: OSHA, "Assigned Protective Factors for the Revised Respiratory Protection Standard," OSHA 3352-02, 2009. www.OSHA.gov.


376 NCEES

6.5.3.2 Hazard AssessmentThe fire/hazard diamond below summarizes common hazard data available on the Safety Data Sheet (SDS) and is frequently shown on chemical labels.

BA C

DPosition A – Health Hazard (Blue) 0 = Normal material 1 = Slightly hazardous 2 = Hazardous 3 = Extreme danger 4 = Deadly

Position B – Flammability (Red) 0 = Will not burn 1 = Will ignite if preheated 2 = Will ignite if moderately heated 3 = Will ignite at most ambient temperature 4 = Burns readily at ambient conditions

Position C – Reactivity (Yellow) 0 = Stable and not reactive with water 1 = Unstable if heated 2 = Violent chemical change 3 = Shock short may detonate 4 = May detonate

Position D – (White) ALKALI = Alkali OXY = Oxidizer ACID = Acid Cor = Corrosive W = Use no water = Radiation

6.5.3.3 Globally Harmonized System (GHS)The Globally Harmonized System of Classification and Labeling of Chemicals, or GHS, is a system for standard-izing and harmonizing the classification and labeling of chemicals.

GHS is a comprehensive approach to:

• Defining health, physical, and environmental hazards of chemicals

• Creating classification processes that use available data on chemicals for comparison with the defined hazard criteria

• Communicating hazard information, as well as protective measures, on labels and Safety Data Sheets (SDSs), formerly called Material Safety Data Sheets (MSDSs).


NCEES 377

GHS label elements include:

• Precautionary statements and pictograms: Measures to minimize or prevent adverse effects

• Product identifier (ingredient disclosure): Name or number used for a hazardous product on a label or in the SDS

• Supplier identification: The name, address, and telephone number of the supplier

• Supplemental information: nonharmonized information

Other label elements include symbols, signal words, and hazard statements.

GHS Label ElementsGHS LABEL ELEMENTS

Product Name Or Identifier(Identify Hazardous Ingredients, Where Appropriate)

Signal Word

Physical, Health, Environmental,Hazard Statements

Supplemental Information

Precautionary Measures And Pictograms

First Eight Statements

Name and Address of Company

Telephone Number

Note: Pictograms for hazard statements must have red borders.

Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), United States Department of Labor, Occupational Safety and Health Administration.


378 NCEES

HCS Quick Card

Product Identifier

Signal Word

Supplier Identification

HazardStatements

Hazard Pictograms

Company Name_______________________Street Address________________________City_______________________ State_____Postal Code______________Country_____Emergency Phone Number_____________

Highly flammable liquid and vapor.May cause liver and kidney damage.

Keep container tightly closed. Store in a cool, well-ventilated place that is locked.Keep away from heat/sparks/open flame. No smoking.Only use non-sparking tools.Use explosion-proof electrical equipment.Take precautionary measures against static discharge.Ground and bond container and receiving equipment.Do not breathe vapors.Wear protective gloves.Do not eat, drink or smoke when using this product.Wash hands thoroughly after handling.Dispose of in accordance with local, regional, national, international regulations as specified.

In Case of Fire: use dry chemical (BC) or Carbon Dioxide (CO2) fire extinguisher to extinguish.

First AidIf exposed call Poison Center.If on skin (or hair): Take off immediately any contaminated clothing. Rinse skin with water. Fill weight:____________ Lot Number:___________

Gross weight:__________ Fill Date:______________Expiration Date:________

Danger

}

CODE _______________________________Product Name________________________

Directions for Use______________________________________________________________________________________________________

PrecautionaryStatements} Supplemental Information

}

}

SAMPLE LABEL

EP

AM

PLESS

HiH ghMM

PPrrecae ututStStaatt

SAMnatioonnaal,l,

CC)) oor Cr Caarrbob n Dioxixidede ( (CCOO2)

tely ly aany ny ccoontanta

e}}

OS

HA

349

2-01

R 2

016

Note: Pictograms for hazard statements must have red borders.

Source: United States Department of Labor, Occupational Safety and Health Administration.


NCEES 379

HCS Pictograms and Hazards Card

Note: Pictograms for hazard statements must be printed with red borders.

Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), United States Department of Labor, Occupational Safety and Health Administration.


380 NCEES

Acute Oral Toxicity

DANGERFATAL IF SWALLOWED

DANGERFATAL IF SWALLOWED

DANGERTOXIC IF SWALLOWED

WARNINGHARMFUL IF SWALLOWED

LD50

SIGNAL WORDHAZARD STATEMENT

CATEGORY 1 ≤ 5 mg/kg

CATEGORY 2 > 5 < 50 mg/kg

CATEGORY 3 50 < 300 mg/kg

CATEGORY 4 300 < 2000 mg/kg

CATEGORY 5 2000 > 5000 mg/kg

NO SYMBOL

WARNINGMAY BE HARMFULIF SWALLOWED

PICTOGRAM

6.5.3.4 Safety Data Sheets (SDS)Source: Appendix D to OSHA CFR 1910.1200 - Safety Data Sheets (Mandatory).

A safety data sheet (SDS) must include the information in the table below under the section number and heading indicated for Sections 1–11 and 16. If no relevant information is found for any given subheading within a section, the SDS must clearly indicate that no applicable information is available. Sections 12–15 may be included in the SDS, but are not mandatory.

Minimum Information for a Safety Data SheetHeading Subheading

1. Identification a. Product identifier used on the labelb. Other means of identificationc. Recommended use of the chemical and restrictions on used. Name, address, and telephone number of the chemical manufacturer, importer, or other responsible partye. Emergency phone number

2. Hazard(s) Identification a. Classification on the chemical in accordance with paragraph (d) of §1910.1200b. Signal word, hazard statement(s), symbol(s), and precautionary statement(s) in accordance with paragraph (f) of §1910.1200. (Hazard symbols may be provided as graphical reproductions in black and white or the name of the symbol, e.g., flame, skull and crossbones)c. Describe any hazards not otherwise classified that have been identified during the classification processd. Where an ingredient with unknown acute toxicity is used in a mixture at a concentration = 1% and the mixture is not classified based on testing of the mixture as a whole, a statement that X % of the mixture consists of ingredient(s) of unknown acute toxicity is required


NCEES 381

Minimum Information for a Safety Data Sheet (cont'd)Heading Subheading

3. Composition and Information on Ingredients

Except as provided for in paragraph (i) of §1910.1200 on trade secrets:

For Substances

a. Chemical nameb. Common name and synonymsc. CAS number and other unique identifiersd. Impurities and stabilizing additives that are themselves classified and that contribute to the classification of the substance For Mixtures In addition to the information required for substances:

a. The chemical name and concentration (exact percentage) or concentration ranges of all ingredients that are classified as health hazards in accordance with paragraph (d) of §1910.1200 and either (1) Are present above their cut-off/concentration limits (2) Present a health risk below the cut-off/concentration limitsb. The concentration (exact percentage) shall be specified unless a trade secret claim is made in accordance with paragraph (i) of §1910.1200, when there is batch-to-batch variability in the production of a mixture, or for a group of substantially similar mixtures (See A.0.5.1.2) with similar chemical composition. In these cases, concentration ranges may be used. For All Chemicals for Which a Trade Secret Is Claimed When a trade secret is claimed in accordance with paragraph (i) of §1910.1200, a statement that the specific chemical identity and/or exact percentage (concentration) of composition has been withheld as a trade secret is required.

4. First-aid Measures a. Description of necessary measures, subdivided according to the differ ent routes of exposure, i.e., inhalation, skin and eye contact, and ingestionb. Most important symptoms/ effects, acute and delayedc. Indication of immediate medical attention and special treatment needed, if necessary

5. Fire-fighting Measures a. Suitable (and unsuitable) extinguishing mediab. Specific hazards arising from the chemical (e.g., nature of any hazard ous combustion products)c. Special protective equipment and precautions for fire-fighters

6. Accidental Release Measures a. Personal precautions, protective equipment, and emergency proceduresb. Methods and materials for containment and cleaning up

7. Handling and Storage a. Precautions for safe handlingb. Conditions for safe storage, including any incompatibilities


382 NCEES


8. Exposure Controls and Personal Protection

a. OSHA permissible exposure limit (PEL), American Conference of Governmental Industrial Hygienists' (ACGIH) threshold limit value (TLV), and any other exposure limit used or recommended by the chemical manufacturer, importer, or employer preparing the safety data sheet, where availableb. Appropriate engineering controlsc. Individual protection measures, such as personal protective equipment

9. Physical and Chemical Properties a. Appearance (physical state, color, etc.)b. Odorc. Odor threshholdd. pHe. Melting point/freezing pointf. Initial boiling point and boiling rangeg. Flash pointh. Evaporation ratei. Flammability (solid, gas)j. Upper/lower flammability or explosive limitsk. Vapor pressurel. Vapor densitym. Relative densityn. Solubility(ies)o. Partition coefficient: n-octanol/waterp. Auto-ignition temperatureq. Decomposition temperaturer. Viscosity

10. Stability and Reactivity a. Reactivityb. Chemical stabilityc. Possibility of hazards reactionsd. Conditions to avoid (e.g., static discharge, shock, or vibration)e. Incompatible materialsf. Hazardous decomposition products

11. Toxicological Information Description of the various toxicological (health) effects and the available data used to identify those effects, including:

a. Information on the likely routes of exposure (inhalation, ingestion, skin and eye contactb. Symptoms related to the physical, chemical, and toxicological charac- teristicsc. Delayed and immediate effects and also chronic effects from short- and long-term exposured. Numerical measures of toxicity (such as acute toxicity estimates)e. Whether the hazardous chemical is listed in the National Toxicology Program (NTP) Report on Carcinogens (latest edition) or has been found to be a potential carcinogen in the International Agency for Research on Cancer (IARC) Monographs (latest editions), or by OSHA

12. Ecological Information (Non-mandatory)

a. Ecotoxicity (aquatic and terrestrial, where available)b. Persistence and degradabilityc. Bioaccumulative potentiald. Mobility in soile. Other adverse effects (such as hazardous to the ozone layer)


NCEES 383


13. Disposal Considerations (Non-mandatory)

Description of waste residues and information on their safe handling and method of disposal, including disposal of any contaminated packaging.

14. Transport Information (Non-mandatory)

a. UN numberb. UN proper shipping namec. Transport hazard class(es)d. Packing group, if applicablee. Environmental hazards (e.g., Marine pollutant [Yes/No])f. Transport in bulk (according to Annex II of MARPOL 73/78 and IBC Code)g. Special precautions which a user needs to be aware of, or needs to comply with, in connection with transport or conveyance either within or outside their premises

15. Regulatory Information (Non-mandatory)

Safety, health, and environmental regulations specific for the product in question

16. Other Information, Including Date of Preparation or Last Revision

The date of preparation of the SDS or the last change to it

Source: U.S. Department of Labor, Occupational Safety & Health Administration, www.OSHA.gov.

6.5.3.5 PesticidesThis section establishes four toxicity categories for acute hazards of pesticide products. Category I is the highest category. Most human hazard, precautionary statements, and human personal protective equipment statements are based on the toxicity category of the pesticide product as sold or distributed. In addition, toxicity categories may be used for regulatory purposes other than labeling, such as classification for restricted use and requirements for child-resistant packaging. In certain cases, statements based on the toxicity category of the product as diluted for use are also permitted. A toxicity category is assigned for each of five types of acute exposure, as specified in the table below.

Acute Toxicity Categories for Pesticide ProductsHazard

Indicators I II III IV

Oral LD50Up to and including 50 mg/kg >50 through 500 mg/kg >500 through 5000 mg/kg > 5000 mg/kg

Dermal LD50Up to and including 200 mg/kg >200 through 2000 mg/kg >2000 through 20,000

mg/kg >20,000 mg/kg

Inhalation LC50Up to and including 0.2 mg/liter >0.2 through 2 mg/liter >2 through 20 mg/liter >20 mg/liter

Eye irritationCorrosive: corneal opacity not reversible within 7 days

Corneal opacity reversible within 7 days; irritation persisting for 7 days

No corneal opacity; irrita-tion reversible within 7 days

No irritation

Skin irritation Corrosive Severe irritation at 72 hours

Moderate irritation at 72 hours

Mild or slight irritation at 72 hours

Source: From Regulating Pesticides, U.S. Environmental Protection Agency.


384 NCEES

Pesticide Toxicity CategoriesToxicity Category Signal Word

I PoisonII WarningIII CautionIV Caution

Source: U.S. Environmental Protection Agency 40 CFR 156.

6.5.3.6 Fundamentals of Ventilation

Ventilation Definitions

Aerosol: An assemblage of small particles, solid or liquid, suspended in air. The diameter of the particles may vary from 100 microns down to 0.01 micron or less, e.g., dust, fog, smoke.

Air cleaner: A device designed for the purpose of removing atmospheric airborne impurities such as dusts, gases, mists, vapors, fumes, and smoke. (Air cleaners include air washers, air filters, electrostatic precipitators, and char-coal filters.)

Air filters: An air-cleaning device that removes light particulate loadings from normal atmospheric air before intro-ducing into the building. Usual range: loadings up to 3 grains per thousand cubic feet (0.003 grains per cubic foot). Note: Atmospheric air in heavy industrial areas and in-plant air in many industries have higher loadings than this, and dust collectors are then indicated for proper air cleaning.

Aspect ratio: The ratio of the width (W) to the length (L); AR = LW .

Aspect ratio of an elbow: The width (W) along the axis of the bend divided by the depth (D) in the plane of the

bend; AR = DW .

Blast gate: Sliding damper.

Capture velocity: The air velocity at any point in front of the hood or at the hood opening necessary to overcome opposing air currents and capture the contaminated air at that point by causing it to flow into the hood.

Density factor: The ratio of actual air density to density of standard air. The product of the density factor and the

density of standard air (0.075 ftlb3 ) gives the actual air density in pounds per cubic foot; Density = df # 0.075

ftlb3 .

Dust: Small solid particles created by breakup of larger particles by processes, such as crushing, grinding, drilling, and explosions. Dust particles already in existence in a mixture of materials may escape into the air through such operations as shoveling, conveying, screening, or sweeping.

Dust collector: An air-cleaning device to remove heavy particulate loadings from exhaust systems. Usual range of particulate loading: 0.003 grains per cubic foot or higher.

Entry loss: Loss in pressure caused by air flowing into a duct or hood (inches H2O).

Fumes: Small solid particles formed by the condensation of vapors of solid materials.

Gases: Formless fluids that tend to occupy an entire space uniformly at ordinary temperatures and pressures.

Hood: A shaped inlet designed to capture contaminated air and conduct it into the exhaust duct system.


NCEES 385

Hood flow coefficient: The ratio of flow caused by a given hood static pressure compared to the theoretical flow that would result if the static pressure could be converted to velocity pressure with 100 percent efficiency.

Inch of water: A unit of pressure equal to the pressure exerted by a column of liquid water one inch high at a stan-dard temperature.

Minimum design duct velocity: Minimum air velocity required to move the particles in the air stream (fpm).

Mists: Small droplets of materials that are ordinarily liquid at normal temperature and pressure.

Pressure, static: The potential pressure exerted in all directions by a fluid at rest. For a fluid in motion, it is mea-sured in a direction normal to the direction of flow. Usually expressed in inches of water gauge when dealing with air. (The tendency to either burst or collapse the pipe.)

Pressure, total: The algebraic sum of the velocity pressure and the static pressure (with due regard to sign).

Pressure, velocity: The kinetic pressure in the direction of flow necessary to cause a fluid at rest to flow at a given velocity. Usually expressed in inches of water gauge.

Replacement air: A ventilation term used to indicate the volume of controlled outdoor air supplied to a building to replace air being exhausted.

Slot velocity: Linear flow rate of contaminated air through a slot, fpm.

Smoke: An air suspension (aerosol) of particles, usually but not necessarily solid, often originating in a solid nucleus, formed from combustion or sublimation.

Standard air: Dry air at 70°F and 29.92 (in Hg) barometer. This is substantially equivalent to 0.075 ftlb3 . Specific

heat of dry air = 0.24 Btu/lb/°F.

Turn-down ratio: The degree to which the operating performance of a system can be reduced to satisfy part-load conditions. Usually expressed as a ratio; for example, 30:1 means the minimum operation point is 1/30th of full load.

Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, pp. x–xi.


386 NCEES

Ventilation AbbreviationsAbbreviation Definition Abbreviation Definition

AR Aspect ratio HVAC Heating, ventilation, and air conditioningAs Slot area "wg Inches water gaugeB Barometric pressure L LengthCc Hood flow coefficient mo Mass flow rate

CLR Centerline radius ME Mechanical efficiencydf Overall density factor mm wg Millimeters water gaugedfe Elevation density factor MRT Mean radiant temperaturedfm Moisture density factor Q Flow rate, in cfmdfp Pressure density factor sfpm Surface feet per minutedft Temperature density factor SP Static pressureF dl Loss per unit length (duct) SPgov Higher static pressure at junction of 2 ductsFel Elbow loss coefficient SPh Hood static pressureFen Entry loss coefficient SPs SP, system handling standard airFh Hood entry-loss coefficient TP Total pressureFs Slot loss coefficient V Velocity, in fpmgr Grains Vd Duct velocityH Height VP Velocity pressurehd Loss in straight duct run VPd Duct velocity pressurehe Overall hood entry loss VPr Resultant velocity pressurehel Elbow loss VPs Slot velocity pressurehen Entry loss Vs Slot velocityhh Hood entry loss Vt Duct transport velocity

hs Slot or opening entry loss ~ Moisture content, in lbm dry airlbm H O2

HEPA High-efficiency particulate air filter z Elevation, in feet above sea level

HV Humid volume, in lb dry airft mix3

Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, pp. xii–xiii.


NCEES 387

Ventilation EquationsDescription Equation Units

Velocity pressure (VP) VP 2gV

4005V df

c

2 2t= = c m V in fpm VP in "wg

Total pressure (TP) TP = SP +VP "wg

Hood entry loss (hh) hh = Fh(VPd)

"wg

Values of Fh can be found in the Hood Loss Coefficients table on page 391.

Hood static pressure (SPh) SPh = – (VPd + hh) "wg

Velocity ContoursPlain Circular Opening—% of Opening Velocity Flanged Circular Opening—% of Opening Velocity

100% 60%

30%

15%

7.5%

100% 60%

30%

15%

0 50% OF DIAMETER

100

7.5%

0 50% OF DIAMETER

100

100% 60%

30%

15%

7.5%

100% 60%

30%

15%

7.5%

Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, p. 6-23.


388 NCEES

Summary of Hood Airflow EquationsHood Type Description Aspect Ratio, W/L Airflow

X

L

W

Slot 0.2 or less Q = 3.7 LVXX

X

Flanged Slot 0.2 or less Q = 2.6 LVXX

W L

A = WL

XPlain opening 0.2 or greater

and round Q = VX(10X 2 + A)

X

Flanged opening 0.2 or greater and round Q = 0.75VX(10X 2 + A)

H

W

Booth To suit work Q = VA = VWH

D Canopy To suit work

Q = 1.4 PVD

P = Perimeter D = Height above work

X

LW Plain multiple-slot opening,

2 or more slots0.2 or greater Q = VX(10X 2 + A)

X

LW Flanged multiple-slot opening,

2 or more slots0.2 or greater Q = 0.75VX(10X 2 + A)



NCEES 389

6.5.3.7 Flow-Capture Velocity of Suspended Hoods (Small Side-Draft Hoods)

Freely Suspended Hood

SOURCE

H

L

X Q

Q = VX(10X 2 + A)

Large Hood

SOURCEX

2X

For a large hood with small X, measure X perpendicular to the hood face and not less than 2X from the edge of the opening.

Hood on Bench or Floor

SOURCE X Q

Q = VX(5X 2 + A)

Hood with Wide Flange

SOURCE

FLANGE WIDTH ≥ A

QX

Q = 0.75VX(10X 2 + A)


390 NCEES

whereQ = required exhaust airflow, in acfm or s

m3

X = distance from hood face to farthest point of contamination, in ft or m

A = hood face area, in ft2 or m2

VX = capture velocity at distance X, in fpm or sm , at distance X

Note: Airflow rate must increase as the square of distance of the source from the hood. Baffling by flanging or by placing on bench, floor, etc. has a beneficial effect.

Source: Hood illustrations in this section are from Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, p. 6-19.

6.5.3.8 Flow-Capture Velocity of Canopy Hood

45° MINIMUM

0.4D D

Q = 1.4 PDV

where P = Perimeter of tank, in ft or m

Not recommended if workers must bend over source. V ranges from 50 to 500 fpm or 0.25 to 2.50 sm , depending

on crossdrafts. Side curtains on two or three sides to create a semi-booth or booth are desirable.

Recommended Capture Velocities

Energy of Dispersion ExamplesVX

minft

sm

Little motion Evaporation from tanks, degreasing 75–100 0.38–0.51

Average motion Intermittent container filling, low-speed conveyor transfers, welding, plating, pickling 100–200 0.51–1.02

High Barrel filling, conveyor loading, crushers 200–500 1.02–2.54Very high Grinding, abrasive blasting, tumbling 500–2000 2.54–10.2

Factors affecting choices within ranges:

• Strength of cross-drafts due to makeup air, traffic, etc.• Need for effectiveness in collection:

- Toxicity of contaminants produced by the source - Exposures from other sources, which reduce acceptable exposure from this source - Quantity of air contaminants generated: production rate, volatility, time generated



NCEES 391

Hood Type Efficiency

Hood Loss CoefficientsHood Type Description Hood Entry Loss (Fh) Coefficient

Plain opening 0.93

Flanged opening 0.49

Taper or cone hood 0.15–0.4

Bell mouth inlet 0.04

Orifice 0.55 when duct velocity = slot velocity

Typical grinding hood

Straight takeoff: 0.65

Tapered takeoff: 0.40

Source: ACGIH, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Signature Publications, Cincinnati, Ohio, 2013.


392 NCEES

6.5.3.9 Electrical Safety

Probable Effects of Various Levels of Current on the Human BodyLevel of Current (milliamperes) Probable Effect

1 mA Perception level. Slight tingling sensation. Still dangerous under certain conditions.

5 mA Slight shock felt; not painful but disturbing. Average individual can let go. How-ever, strong involuntary reactions to shocks in this range may lead to injuries.

6 mA-16 mA Painful shock; begin to lose muscular control. Commonly referred to as the freezing current or "let-go" range.

17 mA-99 mA Extreme pain, respiratory arrest, severe muscular contractions. Individual cannot let go. Death is possible.

100 mA-2000 mA Ventricular fibrillation (uneven, uncoordinated pumping of the heart). Muscular contraction and nerve damage begins to occur. Death is likely.

>2000 mA Cardiac arrest, internal organ damage, and severe burns. Death is probable.

Sources: NIOSH, Worker Deaths by Electrocution; A Summary of NIOSH Surveillance and Investigative Findings, Ohio: U.S. Health and Human Services, 1998. And Greenwald, E.K., Electrical Hazards and Accidents—Their Cause and

Prevention, New York: Van Nostrand Reinhold, 1991.

6.5.3.10 Risk Assessment/Toxicology

The Dose-Response Curve

The dose-response curve relates toxic response (i.e., percentage of test population exhibiting a specified symptom

or dying) to the logarithm of the dosage (i.e., kg daymg: ingested). A typical dose-response curve is shown below.

Typical Dose-Response Curve

100

50

10

TOXICANT

TOXI

C RE

SPON

SE %

LOGARITHM OF LD50 DOSELD50LD10

where

LC50 = Median lethal concentration in air that, based on laboratory tests, is expected to kill 50% of a

group of test animals when administered as a single exposure over one or four hours.

LD50 = Median lethal single dose, based on laboratory tests, expected to kill 50% of a group of test

animals, usually by oral or skin exposure.

Similar definitions exist for LC10 and LD10, where the corresponding percentages are 10%.


NCEES 393

The following table lists the LD50 values for several chemicals:

Comparative Acutely Lethal DosesActual

Ranking Number

LD50 kgmge o Toxic Chemical

1 15,000 PCBs2 10,000 Alcohol (ethanol)3 4000 Table salt—sodium chloride4 1500 Ferrous sulfate—an iron supplement5 1375 Malathion—a pesticide6 900 Morphine7 150 Phenobarbital—a sedative8 142 Tylenol (acetaminophen)9 2 Strychnine10 1 Nicotine11 0.5 Curare —an arrow poison12 0.001 2,3,7,8-TCDD (dioxin)13 0.00001 Botulinum toxin (food poison)

Adapted from Loomis, T.A., and A.W. Hayes. Loomis's Essentials of Toxicology, 4th ed., San Diego: Academic Press, 1996.

Selected Chemical Interaction Effects

Effect Relative toxicity (hypothetical) Example

Additive 2 + 3 = 5 Organophosphate pesticidesSynergistic 2 + 3 = 20 Cigarette smoking + asbestos

Antagonistic 6 + 6 = 8 Toluene + benzene or caffeine + alcohol

Adapted from Williams, P.L., R.C. James, and S.M. Roberts. Principles of Toxicology: Environmental and Industrial Applications, 2nd ed., New York: Wiley, 2000.


394 NCEES

Exposure Limits for Selected Compounds(a)

Substance CAS No.(c)

Regulatory Limits Recommended Limits

OSHA PEL(b) NIOSH REL(g)

(as of 4/26/13)ACGIH® 2015

TLV® (h)

ppm (d)

mmg3

(e)

Up to 10-hour TWA, (ST) STEL, (C) Ceiling (f)

8-hour TWA, (ST) STEL, (C) Ceiling

Acetic acid 64-19-7 10 25 10 ppm (ST) 15 ppm

10 ppm (ST) 15 ppm

Acetone 67-64-1 1000 2400 250 ppm 250 ppm (ST) 500 ppm

Benzoyl peroxide 94-36-0 5 mmg

5 3 mmg

5 3

Bromine 7726-95-6 0.1 0.7 0.1 ppm (ST) 0.3 ppm

0.1 ppm (ST) 0.2 ppm

Butyl mercaptan 109-79-5 10 35 (C) 0.5 ppm [15-min] 0.5 ppm

Carbon dioxide 124-38-9 5000 9000 5000 ppm (ST) 30,000 ppm

5000 ppm (ST) 30,000 ppm

Carbon monoxide 630-08-0 50 55 35 ppm (C) 200 ppm 25 ppm

Chlorine 7782-50-5 (C) 1 (C) 3 (C) 0.5 ppm [15-min]

0.5 ppm (ST) 1 ppm

Chloroform (trichloromethane) 67-66-3 (C) 50 (C) 240 (ST) 2 ppm

[60-min] 10 ppm

Cresol, all isomers 1319-77-3 5 22 2.3 ppm ( )mmg

IFV20 3

Cumene 98-82-8 50 245 50 ppm 50 ppmEthyl alcohol (ethanol) 64-17-5 1000 1900 1000 ppm (ST) 1000 ppm

Ethyl ether 60-29-7 400 1200 N/A 400 ppm (ST) 500 ppm

Iodine 7553-56-2 (C) 0.1 (C) 1 (C) 0.1 ppm 0.01 ppm (IFV) (ST) 0.1 ppm (V)

Isopropyl ether 108-20-3 500 2100 500 ppm 250 ppm (ST) 310 ppm

L.P.G. (liquefied petroleum gas) 68476-85-7 1000 1800 1000 ppm N/A

Methyl mercaptan 74-93-1 (C) 10 (C) 20 (C) 0.5 ppm [15-min] 0.5 ppm

Naphthalene 91-20-3 10 50 10 ppm (ST) 15 ppm

10 ppm (ST) 15 ppm

Ozone 10028-15-6 0.1 0.2 (C) 0.1 ppm0.05–0.20 ppm depending on

workload and time


NCEES 395

Exposure Limits for Selected Compounds(a) (cont'd)

Substance CAS No.(c)

Regulatory Limits Recommended Limits

OSHA PEL(b) NIOSH REL(g)

(as of 4/26/13)ACGIH® 2015

TLV® (h)

ppm (d)

mmg3

(e)

Up to 10-hour TWA, (ST) STEL, (C) Ceiling (f)

8-hour TWA, (ST) STEL, (C) Ceiling

Phosphoric acid 7664-38-2 N/A 11 mmg3

(ST) 3 mmg3

1 mmg3

(ST) 3 mmg3

Propane 74-98-6 1000 1800 1000 ppm N/A

n-Propyl alcohol 71-23-8 200 500 200 ppm (ST) 250 ppm 100 ppm

Sulfuric acid 7664-93-9 1 1 mmg3

0.2 mmg3

(Thoracic-size fraction)

1,1,1-Trichloroethane (methyl chloroform) 71-55-6 350 1900

350 ppm (ST) 450 ppm (C) 800 ppm

350 ppm (ST) 450 ppm

a. Columns 3 and 4 list PELs from OSHA Table Z-1 in 29 CFR 1910.1000. Columns 5 and 6 list other occupa-tional exposure limits (OELs) from NIOSH and ACGIH®.

b. Occupational Safety and Health Administration (OSHA) Permissible Exposure Limits (PELs) from 29 CFR 1910.1000 Z-1 Table [58 FR 35340, June 30, 1993; 58 FR 40191, July 27, 1993, as amended at 61 FR 56831, Nov. 4, 1996; 62 FR 1600, Jan 10,1997; 62 FR 42018, Aug. 4, 1997; 71 FR 10373, Feb. 28, 2006; 71 FR 16673, Apr. 3, 2006; 71 FR 36008, June 23, 2006.]. PELs are 8-hour time-weighted averages (TWAs), unless otherwise indicated. OSHA enforces these limits under section 5(a)(2) of the OSH Act. In addition to the values listed in this table, the Z tables in 29 CFR 1910.1000 list skin absorption designations.

c. The CAS number is for information only. Enforcement is based on the substance name. For an entry covering more than one metal compound measured as the metal, the CAS number for the metal is given—not CAS num-bers for the individual compounds.

d. Parts of vapor or gas per million parts of contaminated air by volume at 25 oC and 760 torr.e. Milligrams of substance per cubic meter of air. When entry is in this column only, the value is exact; when

listed with a ppm entry, it is approximate.f. TWA indicates a time-weighted average concentration. A short-term exposure limit (STEL) is designated by

ST preceding the value; unless noted otherwise, the STEL is a 15-minute TWA exposure that should not be exceeded at any time during a work day. A ceiling REL is designated by C preceding the value; unless noted otherwise, the ceiling value should not be exceeded at any time.

g. National Institute for Occupational Safety and Health (NIOSH) Recommended Exposure Limits (RELs) from the NIOSH Pocket Guide to Chemical Hazards (http://www.cdc.gov/niosh/npg) (NIOSH 2007). RELs are for up to 10-hour time weighted averages (TWAs) during a 40-hour work week, unless otherwise indicated. NIOSH has established occupational exposure limits for compounds not included in the OSHA Z Tables. Please see the NIOSH Pocket Guide for additional limits, skin absorption and other designations, and explanations.


396 NCEES

h. ACGIH® Threshold Limit Values (TLVs®) (ACGIH® 2015). TLVs® are listed in the order of 8-hour time-weighted averages (TWAs), STELs (ST), and Ceilings (C), if available. ACGIH® has established TLVs® for compounds not included in the OSHA Z Tables. Please see ACGIH® Documentation for additional limits, skin absorption and other designations, and explanations. The 2015 TLV® and BEI® Book and Documentation of the Threshold Limit Values on Chemical Substances, 7th Edition, are available through the ACGIH® website at http://www.acgih.org. The TLVs® and BEIs® are copyrighted by ACGIH® and are not publicly available. Permission must be requested from ACGIH® to reproduce the TLVs® and BEIs®.

Carcinogens

For carcinogens, the EPA considers an acceptable risk to an individual to be a lifetime excess cancer risk within the range of 10-4 to 10-6. The added risk of cancer is calculated as follows:

Risk = dose # toxicity = CDI # CSF

where

CDI = Chronic daily intake

CSF = Cancer slope factor, the slope of the dose-response curve for carcinogenic materials

RESPONSE

DOSE

X

X X

NO THRESHOLD LINEARAT LOW DOSE

CARCINOGENIC DOSERESPONSE CURVE

X

X

Noncarcinogens

For noncarcinogens, a hazard index (HI) characterizes the risk from all pathways and exposure routes. The EPA considers that an HI > 1.0 represents an unacceptable risk of an adverse effect occurring.

HI RfDCDInoncarcinogen=

where

CDInoncarcinogen = chronic daily intake of noncarcinogenic compound

RfD = reference dose

RESPONSE

DOSE

XX

X X

X

X

NONCARCINOGENIC DOSERESPONSE CURVE

THRESHOLD

RfD

NOAEL

Dose is expressed as body weight exposure time

mass of chemical#d n

NOAEL = No observable adverse effect level (the dose below which no harmful effects are apparent)


NCEES 397

Reference Dose

Reference dose (RfD) is determined from the noncarcinogenic dose-response curve using the NOAEL:

RfD = lifetime (i.e., chronic) dose that a healthy person could be exposed to daily without adverse effects

UFNOAELRfD

and

=

WSHD RfD UFNOAEL W#

#= =

where

SHD = safe human dose (mg/day)

NOAEL = threshold dose per kg of test animal kgdaymg

from the dose-response curve

UF = the total uncertainty factor, depending on nature and reliability of the animal test data

W = the weight of the adult male (typically 70 kg)

Exposure

Residential Exposure Equations for Various Pathways

Pathway Exposure Equation

Ingestion in drinking water CDI BW ATCW IR EF ED=^^^ ^^^h h

hhhh

Ingestion while swimming CDI BW ATCW CR ET EF ED=^ ^

^^^^ ^h h

hhhh h

Dermal contact with water AD BW ATCW SA PC ET EF ED CF=^ ^ ^

^^^^ ^ ^h h h

hhhh h h

Ingestion of chemicals in soil CDI BW ATCS IR CF FI EF ED=^ ^

^^ ^

^^ ^h h h

hhhh h

Dermal contact with soil AD BW ATCW CF SA AF ABS EF ED=^ ^ ^

^^^^ ^ ^h h h

hhhh h h

Inhalation of airborne (vapor phase) chemicals CDI BW ATCA IR ET EF ED

=^ ^

^^^^ ^h h

hhhh h

Ingestion of contaminated fruits, vegetables, fish, and shellfish CDI BW AT

CF IR FI EF ED=^ ^

^^^^ ^h hhhhh h


398 NCEES

where

ABS = absorption factor for soil contaminant is unitless

AD = absorbed dose in kg daymg:

AF = soil-to-skin adherence factor in

cmmg

2

AT = averaging time in days

BW = body weight in kg

CA = contaminant concentration in air in mmg3

CDI = chronic daily intake in kg daymg:

CF = volumetric conversion factor for water is 1000 cm1L

3

= conversion factor for soil in mgkg10 6-

CR = contact rate in hrL

CS = chemical concentration in soil in kgmg

CW = chemical concentration in water in Lmg

ED = exposure duration in years

EF = exposure frequency in yeardays

or yearevents

ET = exposure time in dayhr or event

hr

FI = fraction ingested is unitless

IR = ingestion rate in dayL or day

mg soilor meal

kg

= inhalation rate in hr

m3

PC = Chemical-specific dermal permeability constant in hrcm

SA = skin surface area available for contact in cm2

Source: U.S. Environmental Protection Agency, Risk Assessment Guidance for Superfund: Volume 1, Human Health Evaluation Manual (part A), EPA/540/1-89/002,1989.


NCEES 399

6.5.3.11 Intake Rates

EPA Recommended Values for Estimating IntakeParameter Standard Value

Average body weight, female adult 65.4 kgAverage body weight, male adult 78 kgAverage body weight, childa

6-11 months 9 kg1-5 years 16 kg6-12 years 33 kg

Amount of water ingested, adult 2.3 L/dayAmount of water ingested, child 1.5 L/dayAmount of air breathed, female adult 11.3 m3/dayAmount of air breathed, male adult 15.2 m3/dayAmount of air breathed, child (3-5 years) 8.3 m3/dayAmount of fish consumed, adult 6 g/dayWater swallowing rate, while swimming 50 mL/hrInhalation rates

adult (6-hr day) 0.98 m3/hradult (2-hr day) 1.47 m3/hrchild 0.46 m3/hr

Skin surface available, adult male 1.94 m2

Skin surface available, adult female 1.69 m2

Skin surface available, child3-6 years (average for male and female) 0.720 m2

6-9 years (average for male and female) 0.925 m2



15-18 years (female) 1.60 m2

15-18 years (male) 1.75 m2

Soil ingestion rate, child 1-6 years >100 mg/daySoil ingestion rate, persons > 6 years 50 mg/daySkin adherence factor, gardener's hands 0.07 mg/cm2

Skin adherence factor, wet soil 0.2 mg/cm2

Exposure durationLifetime (carcinogens; for noncarcinogens use, actual exposure duration) 75 yearsAt one residence, 90th percentile 30 yearsNational median 5 years

Averaging time (ED) (365 days/year)


400 NCEES

EPA Recommended Values for Estimating Intake (cont'd)Parameter Standard Value

Exposure Frequency (EF)Swimming 7 days/yearEating fish and shellfish 48 days/yearOral ingestion 350 days/year

Exposure time (ET)Shower, 90th percentile 12 minShower, 50th percentile 7 min

aData in this category taken from Copeland, T., A. M. Holbrow, J. M. Otan, et al. "Use of probabilistic methods to understand the conservatism in California's approach to assessing health risks posed by contaminants."

Journal of the Air and Waste Management Association, Vol. 44, pp. 1399–1413, 1994.

Source: U.S. Environmental Protection Agency, Risk Assessment Guidance for Superfund: Volume 1, Human Health Evaluation Manual (part A), EPA/540/1-89/002,1989.

6.5.3.12 Concentrations of Vaporized LiquidsVaporization rate (Qm, mass/time) from a liquid surface:

Q R TMKA P

g L

sat

ms= = G

where

M = molecular weight of volatile substance

K = mass transfer coefficient

As = area of liquid surface

Psat = saturation vapor pressure of the pure liquid at TL

Rg = ideal gas constant

TL = absolute temperature of the liquid

Mass flow rate of liquid from a hole in the wall of a process unit:

( )Q A C g P2H c gm 0½t=

where

AH = area of hole

C0 = discharge coefficient

ρ = density of the liquid

gc = gravitational constant

Pg = gage pressure within the process unit


NCEES 401

Concentration (Cppm) of vaporized liquid in ventilated space:

( )×C kQ PM

Q R T 10ppm

V

gm6

= > H

where

T = absolute ambient temperature

k = nonideal mixing factor

QV = ventilation rate

P = absolute ambient pressure

Sweep-through concentration change in a vessel:

lnQ t V C CC C––

V2 0

1 0= = Gwhere

QV = volumetric flow rate

t = time

V = vessel volume

C0 = inlet concentration

C1 = initial concentration

C2 = final concentration

6.5.3.13 Noise Pollution

SPL (dB) = 10 logPP

1002

2f p

SPLtotal = log10 101010SPLR

Point Source Attenuation: logSPL dB rr10 10 21D =^ dh n

Line Source Attenuation: logSPL dB rr10 10 21D =^ dh n

where

SPL (dB) = sound pressure level, measured in decibels

P = sound pressure (Pa)

P0 = reference sound pressure (2 × 10–5 Pa)

SPLtotal = sum of multiple sources

∆ SPL (dB) = change in sound pressure level with distance, measured in decibels

r1 = distance from source to receptor at point 1

r2 = distance from source to receptor at point 2


402 NCEES

6.5.3.14 Permissible Noise Exposure (per OSHA Regulations)Noise dose D should not exceed 100%.

%D TC100ii#= !

where

Ci = time spent at specified sound pressure level (SPL) in hours

Ti = time permitted at SPL in hours

Ci! = 8 (hours)

Permissible Noise Level vs. Permissible Time of Exposure

Noise Level (dBA)

Permissible Time (hr)

80 3285 1690 895 4100 2105 1110 0.5115 0.25120 0.125125 0.063130 0.031

If D > 100%, noise abatement is required.

If 50% ≤ D ≤ 100%, hearing conservation program is required.

Note: D = 100% is equivalent to 90 dBA time-weighted average (TWA). D = 50% is equivalent to TWA of 85 dBA.

Hearing conservation program requires: (1) testing employee hearing, (2) providing hearing protection at employee's request, and (3) monitoring noise exposure.

Exposure to impulsive or impact noise should not exceed 140 dB sound pressure level (SPL).


NCEES 403

6.5.4 Hazard Identification and Management

Terms and Definitions for Hazards Identification and ManagementTerm Definition

Alarm An audible and/or visible means of indication to the operator an equipment mal-function, process deviation, or abnormal condition requiring a timely response.

As Low as Reasonably Practicable (ALARP)

The concept that efforts to reduce risk should be continued until the incremental sacrifice (in terms of cost, time, effort, or other expenditure of resources) is grossly disproportionate to the incremental risk reduction achieved. The term as low as reasonably achievable (ALARA) is often used synonymously.

ConsequencesThe direct, undesirable result of an accident sequence usually involving a fire, ex-plosion, or release of toxic material. Consequence descriptions may be qualitative or quantitative estimates of the effects of an accident.

FrequencyNumber of occurrences of an event per unit time

e.g.,1 event in 1000 yr. 1 10 yrevents3#= −d n.

Failure Mode and Effect Analysis (FMEA)

A hazard identification technique in which all known failure modes of components or features of a system are considered in turn and undesired outcomes are noted. It is usually used in combination with fault tree analysis. It is a complicated proce-dure, usually carried out by experienced risk analysts.

Hazards and Operability Analysis (HAZOP)

A systematic qualitative technique to identify process hazards and potential operat-ing problems using a series of guide words to study process deviations. A HAZOP is used to question every part of a process to discover what deviations from the intention of the design can occur and what their causes and consequences may be. This is done systematically by applying suitable guide words. This is a systematic detailed review technique, for both batch and continuous plants, which can be applied to new or existing processes to identify hazards.

Independent Protection Layer (IPL)

A device, system, or action that is capable of preventing a postulated accident sequence from proceeding to a defined, undesirable endpoint. An IPL is indepen-dent of the event that initiated the accident sequence and independent of any other IPLs. IPLs are normally identified during layer of protection analysis.

Initiating Event

The minimum combination of failures or errors necessary to start the propagation of an incident sequence. It can be comprised of a single initiating cause, multiple causes, or initiating causes in the presence of enabling conditions. (The term initi-ating event is the usual term employed in Layer of Protection Analysis to denote an initiating cause or where appropriate, an aggregation of initiating causes with the same immediate effect, such as "BPCS failure resulting in high reactant flow.")

Layer of Protection Analysis (LOPA)

An approach that analyzes one incident scenario (cause-consequence pair) at a time, using predefined values for the initiating event frequency, independent protection layer failure probabilities, and consequence severity, in order to com-pare a scenario risk estimate to risk criteria for determining where additional risk reduction or more detailed analysis is needed. Scenarios are identified elsewhere, typically using a scenario-based hazard evaluation procedure such as the HAZOP study.

Lock-OutTag-Out (LOTO)Specific practices and procedures to safeguard employees from the unexpected energization or startup of machinery and equipment, or the release of hazardous energy during service or maintenance activities.


404 NCEES

Terms and Definitions for Hazards Identification and Management (cont'd)Term Definition

Process Hazard Analysis (PHA)

An organized effort to identify and evaluate hazards associated with processes and operations to enable their control. This review normally involves the use of qualita-tive techniques to identify and assess the significance of hazards. Conclusions and appropriate recommendations are developed. Occasionally, quantitative methods are used to help prioritized risk reduction.

Process Safety Management (PSM)

A management system that is focused on prevention of, preparedness for, mitiga-tion of, response to, and restoration from catastrophic releases of chemicals or energy from a process associated with a facility.

Quantitative Risk Analysis (QRA)

QRA is a technique that provides advanced quantitative means to supplement other hazard identification, analysis, assessment, control, and management meth ods to identify the potential for such incidents and to evaluate risk reduction and control strategies. QRA identifies those areas where operation, engineering, or manage-ment systems may be modified to reduce risk and may identify the most economi-cal way to do it. The primary goal of QRA is that appropriate management actions, based on results from a QRA study, help to make facilities handling haz ardous chemicals safer. QRA is one component of an organization's total process risk management. It allows the quantitative assessment of risk alternatives that can be balanced against other considerations.

Qualitative Risk Analysis (QRA)

The systematic development of numerical estimates of the expected frequency and/or consequence of potential accidents associated with a facility or operation. Using consequence and probability analyses and other factors such as population density and expected weather conditions, QRA predicts the fatality rate for a given event. This methodology is useful for eval uation of alternatives, but its value as an abso-lute measure of risk should be considered carefully.

Risk

A measure of human injury, environmental damage, or economic loss in terms of both the incident likelihood and the magnitude of the loss or injury. A simplified version of this relationship expresses risk as the product of the likelihood and the consequences (i.e., Risk = Consequence x Likelihood) of an incident.


NCEES 405

6.5.4.1 Layers of Protection

Typical Risk Reduction Methods Found in Process Plants

COMMUNITY EMERGENCY RESPONSEEMERGENCY BROADCASTING

PLANT EMERGENCY RESPONSEEVACUATION PROCEDURES

MITIGATIONMECHANICAL MITIGATION SYSTEMS

SAFETY INSTRUMENTED CONTROL SYSTEMSSAFETY INSTRUMENTED MITIGATION SYSTEMS

OPERATOR SUPERVISION

PREVENTIONMECHANICAL PROTECTION SYSTEM

PROCESS ALARMS WITH OPERATOR CORRECTIVE ACTION

SAFETY INSTRUMENTED CONTROL SYSTEMSSAFETY INSTRUMENTED PREVENTION SYSTEMS

CONTROL AND MONITORINGBASIC PROCESS CONTROL SYSTEMS

MONITORING SYSTEMS ( PROCESS ALARMS)OPERATOR SUPERVISION

PROCESS

Source: ISA 84.00.00.

Hierarchy of Controls

Source: Controls for Noise Exposure, Atlanta: The National Institute for Occupational Safety and Health (NIOSH), 2016.


406 NCEES

6.5.4.2 Elements of Risk-Based Process Safety

Commitment to process safety Process safety culture Compliance with standards Workforce involvement Stakeholder outreach

Understanding hazards and risk Process knowledge management Hazards identification and risk analysis

Managing risk Operating procedures Safe work practices Asset integrity and reliability Contractors management Training and performance assurance Management of change Operational readiness Conduct of operations Emergency management

Learning from experience Incident investigation Measurements and metrics Auditing Management review and continuous improvement

6.5.4.3 Safety Instrumented Systems

Definitions of Safety Integrity TermsTerm Definition

Architecture

Arrangement of hardware and/or software elements in a system; for example:

(1) Arrangement of safety instrumented system (SIS) subsystems (2) Internal structure of an SIS subsystem (3) Arrangement of software programs

Average Probability of Failure on Demand (PFDavg)

Average probability that a safety-instrumented function will fail in such a way that it cannot respond to a potentially dangerous condition. PFD or PFDavg is applied to repairable systems.

Basic Process Control System (BPCS)

System that responds to input signals from the process, its associated equipment, other programmable systems, and/or an operator and generates output signals caus-ing the process and its associated equipment to operate in the desired manner but that does not perform any safety-instrumented functions with a claimed SIL 1$ .

Common Cause Failure Failure that is the result of one or more events and that causes failure of two or more separate channels in a multiple-channel system, leading to system failure.

MooNSafety instrumented system, or part thereof, made up of N independent channels that are so connected that M channels are sufficient to perform the safety-instru-mented function.

Mean Time to Fail (MTTF) Mean time to random failure for a component population. MTTF is applied to items that are not repaired, such as bearings and transistors.

Mean Time to Trip Spurious (MTTFS) Mean time for a safety function to fail in a mode that causes a spurious trip.

Safe Failure Fraction (SFF) Fraction of the overall random hardware failure rate of a device that results in either a safe failure or a detected dangerous failure.


NCEES 407

Definitions of Safety Integrity Terms (cont'd)Term Definition

Safety Instrumented System (SIS)

Instrumented system used to implement one or more safety-instrumented func-tions.An SIS is composed of any combination of sensor(s), logic solver(s), and final element(s).

Safety Integrity Level (SIL)Discrete level (one out of four) for specifying the safety integrity requirements of the safety-instrumented functions to be allocated to the safety instrumented sys-tems. SIL 4 has the highest level of safety integrity; SIL 1, the lowest.

Safety Instrumented Function (SIF)

Safety function with a specified safety integrity level that is necessary to achieve functional safety and that can be either a safety instrumented protection function or a safety instrumented control function.

Systematic FailureFailure related in a deterministic way to a certain cause, which can only be elimi-nated by a modification of the design or of the manufacturing process, operational procedures, documentation, or other relevant factors.

Tolerable Risk Risk that is accepted in a given context based on the current values of society.

ValidationActivity of demonstrating that the safety-instrumented function(s) and safety in-strumented system(s) under consideration after installation meet in all respects the safety requirements specification.

VerificationActivity of demonstrating for each phase of the relevant safety life-cycle, by analy-sis and/or tests, that for specific inputs the outputs meet in all respects the objec-tives and requirements for the specific phase.

Source: The Instrumentation, Systems, and Automation Society (IHS), Functional Safety: Safety Instrumented Systems for the Process Industry Sector - Part 1: Framework, Definitions, System, Hardware and Software

Requirements (ANSI/ISA-84.00.01-2004 Part 1 IEC 61511-1 Mod), 2004.


408 NCEES

6.5.4.4 Functional Safety Life Cycle

SIS Safety Life-Cycle Phases and Functional Safety Assessment Stages

KEY:TYPICAL DIRECTION OF INFORMATION FLOW.

NO DETAILED REQUIREMENTS GIVEN IN THIS STANDARD.

REQUIREMENTS GIVEN IN THIS STANDARD.

NOTE 1 STAGES 1 THROUGH 5 INCLUSIVE ARE DEFINED IN 5.2.6.1.3.NOTE 2 ALL REFERENCES ARE TO PART 1 UNLESS OTHERWISE NOTED.

9

CLAUSES 7,12.4, AND

12.7

VERIFICATION

10 11

CLAUSE 5 CLAUSE 6.2

MANAGEMENT OF FUNCTION-AL SAFETY IN FUNCTIONAL

SAFETY ASSESSMENT AND AUDITING

SAFETY LIFE-CYCLE STRUCTURE

AND PLANNING 1

2

3

4

5

6

7

8

STAGE 4

STAGE 5DECOMMISSIONING

CLAUSE 18

MODIFICATIONCLAUSE 17

OPERATION AND MAINTENANCECLAUSE 16

INSTALLATION, COMMISSIONINGAND VALIDATION

CLAUSES 14 AND 15

DESIGN AND ENGINEERING OFSAFETY INSTRUMENTED SYSTEM

CLAUSES 11 AND 12

STAGE 3

STAGE 2

STAGE 1DESIGN AND DEVELOPMENT OF OTHER MEANS OF RISK

REDUCTIONCLAUSE 9

SAFETY REQUIREMENTS SPECIFICATION FOR SAFETY

INSTRUMENTED SYSTEM CLAUSES 10 AND 11

HAZARD AND RISK ASSESSMENT

CLAUSE 8

ALLOCATION OF SAFETY FUNCTIONS TO PROTEC-

TION LAYERSCLAUSE 9

Source: The Instrumentation, Systems, and Automation Society (IHS), Functional Safety: Safety Instrumented Systems for the Process Industry Sector - Part 1: Framework, Definitions, System, Hardware and Software

Requirements (ANSI/ISA-84.00.01-2004 Part 1 IEC 61511-1 Mod), 2004.


NCEES 409

6.5.4.5 SIS Safety Life-Cycle Overview

The Safety Instrumented System (SIS) Safety Life-CycleSafety Life-Cycle Phase

or ActivityObjectives

Requirements Clause or Subclause

Inputs OutputsBox # in Previous

ImageTitle

1 Hazard and Risk Assessment

To determine the hazards and hazardous events of the process and associated equipment, the sequence of events leading to the hazard-ous event, the process risks associated with the hazardous event, the requirements for risk reduction, and the safety functions required to achieve the necessary risk reduction

8 Process design, layout, work force arrange-ments, safety targets

Description of hazards of the required safety function(s) and their associated risk reduction(s)

2 Allocation of Safety Functions to Protection Layers

Allocation of safety functions to protection layers and the associated safety integrity level for each safety-instru-mented function

9 Description of required safety-instrumented function(s) and associated safety integrity require-ments

Description of allocation of safety requirements (see Clause 9)

3 SIS Safety Requirements Specification

To specify the requirements for each SIS, in terms of the required safety-instrumented functions and their associated safety integrity, in order to achieve the required function-al safety

10 Description of allocation of safety require-ments (see Clause 9)

SIS safety require-ments; software safety require-ments

4 SIS Design and Engineering

To design the SIS to meet the requirements for safety-instrumented functions and safety integrity

11, 12.4 SIS safety requirements; software safety requirements

Design of the SIS in conformance with the SIS safety requirements; planning for the SIS integration test

5 SIS Installation Commissioning and Validation

To integrate and test the SIS

To validate that the SIS meets in all respects the require-ments for safety in terms of the required safety-instru-mented functions and the required safety integrity

12.3, 14, 15 SIS design

SIS integration test plan

SIS safety requirements

Plan for the safety validation of the SIS

Fully functioning SIS in confor-mance with the SIS design results of SIS integration tests

Results of the installation, commissioning, and validation activities


410 NCEES

SIS Safety Life-Cycle Overview (cont'd)Safety Life-Cycle Phase

or ActivityObjectives

Requirements Clause or Subclause

Inputs OutputsBox # in Previous

ImageTitle

6 SIS Operation and Maintenance

To ensure that the functional safety of the SIS is main-tained during operation and maintenance

16 SIS requirements

SIS design

Plan for SIS operation and maintenance

Results of the operation and maintenance activities

7 SIS Modification To make corrections, en-hancements, or adaptations to the SIS, ensuring that the required safety integrity level is achieved and maintained

17 Revised SIS safety require-ments

Results of SIS modification

8 Decommission-ing

To ensure proper review and sector organization, and to ensure SIF remains appropri-ate

18 As-built safety requirements and process informa-tion

SIF placed out of service

9 SIS Verification To test and evaluate the outputs of a given phase to ensure correctness and con-sistency with respect to the products and standards pro-vided as inputs to that phase

7, 12.7 Plan for the verification of the SIS for each phase

Results of the veri-fication of the SIS for each phase

10 SIS Functional Safety Assessment

To investigate and arrive at a judgment on the functional safety achieved by the SIS

5 Planning for SIS functional safety assessment

SIS safety requirement

Results of SIS functional safety assessment

6.5.4.6 Safety Integrity Levels: Probability of Failure on Demand

Demand Mode of OperationSafety Integrity

Level (SIL)Target Average Probability

of Failure on Demand Target Risk Reduction

4 to10 105 41$- - , ,to10 000 100 0002 #

3 to10 104 31$- - 1000 to 10,0002 #

2 to10 103 21$- - 100 to 10002 #

1 to10 102 11$- - to10 1002 #


NCEES 411

6.5.4.7 Functional Safety Equations

Average Probability of Failure on Demand (PFDavg)

( )PF T PF t dt1

avg

T

0

= # (Rigorous version)

PF t

2avgm= (Approximation)

Safe Failure Fraction (SFF)

SFF

SD SU DD DU

SD SU DDm m m mm m m= + + +

+ +

where

l = failure rate (failures/year)

and subscripts indicate failure mode:

SD = safe detected

SU = safe undetected

DD = dangerous detected

DU = dangerous undetected

6.5.4.8 Management of ChangeManagement of Change (MOC)—A management system to identify, review, and approve all modifications to equip-ment, procedures, raw materials, and processing conditions, other than replacement in kind, prior to implementation, to help ensure that changes to processes are properly analyzed (for example, for potential adverse impacts), documented, and communicated to affected employees.

Key Principles:

• Maintain a dependable practice• Identify potential change situations• Evaluate possible impacts• Decide whether to allow the change• Complete follow-up activities


412 NCEES

6.5.4.9 Hazardous Waste Compatibility

Hazardous Waste Compatibility Chart

HEAT GENERATIONFIREINNOCUOUS & NON-FLAMMABLE GASTOXIC GAS GENERATIONFLAMMABLE GAS GENERATION EXPLOSIONPOLYMERIZATIONSOLUBILIZATION OF TOXIC MATERIALMAY BE HAZARDOUS BUT UNKNOWN

HFGGTGFEPSU

KEY

REACTIVITYCODE CONSEQUENCES

HEAT GENERATIONFIRE, AND TOXIC GASGENERATION

HF

GT

EXAMPLE

REACTIVITYGROUP

NAME

ACID, MINERALSNON-OXIDIZING

ACIDS, MINERALSOXIDIZING

ACIDS,ORGANIC

ALCOHOLS & GLYCOLS

AMINES ALIPHATIC &AROMATIC

CAUSTICS

CYAMIDES

CARBAMATES

AZO COMPOUNDS,DIAZO COMP, HYDRAZINES

DITHIOCARBAMATES

ESTERS

ETHERS

FLUORIDES, INORGANIC

CARBONS, AROMATIC

ISOCYANATES

KEYTONES

ORGANIC SULFIDESMETAPHORS & OTHER

OXIDIZING AGENTS,STRONG

REDUCING AGENTS,STRONG

EXTREMELY REACTIVE! DO NOT MIX WITH ANY CHEMICAL OR WASTE MATERIAL

WATER & MIXTURESCONTAINING WATER

WATER REACTIVESUBSTANCES

U.S. ENVIRONMENTAL PROTECTION AGENCY. APRIL 1980 EPA – 600/2–80–076

1 2 3 4 5 6 7 8 9 10 11

11

10

9

8

7

HS

S

SS

S

S

H H H H

HHH

H

H HG

HG

HG

HG

HG

GH

HG

HF

F

HF

HF

HF

F

H

H

HG

HT

HF

HF

HF

HFH

F

H

HG HH

G

G

G

H

EH

H

GH

EH

G

G

H

GH

GH

GH

GH

G GFH

G

GT

GF

GT GT

GT GT GT

GFGF GFGF

HGF

HGF

HGF

GTGTGFGFGFGF

GTGTGT

GT

HGT

HGT

HH H H

HH

H

H

GT

GFGFGF

H

H

H

GH H

FH

FH

FH

HFH

FH

FH

F UH

FH

FH

FH

FH

F

F F

HFH

FH

F

F

H

H

GTFH

H

H H

H

H

H

GF

GTGF

GF

FHGF

F

F

HGF

FHGF

FHGF

FHGF

HGF

GTHFGT

HFGT

GT

GT

GF

GF

HFGT GT

HFGT

HFGT

GTHGFH

H

GFGFHH

GFH

GFH

GFH

GFH

GFH

H H H

6

5

4

3

2

1

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22 23 24 25 26 27 28 29 30 31 32 33 34

METAL, ALKALI & ALKALINEEARTH, ELEMENTAL

HALOGENATED ORGANICS

AMIDES

ALDEHYDES

NO.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

104

105

106

107

101 102 103 104

104

105

105

106

106

107

107

Source: U.S. Environmental Protection Agency, EPA 600/2-80-076, April 1980.


NCEES 413

6.5.4.10 OSHA Highly Hazardous ChemicalsThe following is from 29 CFR 1910.119, Appendix A. It contains a list of toxic and reactive highly hazardous chemicals that present a potential for a catastrophic event at or above the threshold quantity.

Highly Hazardous ChemicalsChemical Name CAS* TQ**

Acetaldehyde 75-07-0 2500Acrolein (2-Propenal) 107-02-8 150Acrylyl Chloride 814-68-6 250Allyl Chloride 107-05-1 1000Allylamine 107-11-9 1000Alkylaluminum Varies 5000Ammonia, Anhydrous 7664-41-7 10,000Ammonia solutions (greater than 44% ammonia by weight) 7664-41-7 15,000Ammonium Perchlorate 7790-98-9 7500Ammonium Permanganate 7787-36-2 7500Arsine (also called Arsenic Hydride) 7784-42-1 100Bis (Chloromethyl) Ether 542-88-1 100Boron Trichloride 10294-34-5 2500Boron Trifluoride 7637-07-2 250Bromine 7726-95-6 1500Bromine Chloride 13863-41-7 1500Bromine Pentafluoride 7789-30-2 2500Bromine Trifluoride 7787-71-5 15,0003-Bromopropyne (also called Propargyl Bromide) 106-96-7 100Butyl Hydroperoxide (Tertiary) 75-91-2 5000Butyl Perbenzoate (Tertiary) 614-45-9 7500Carbonyl Chloride (see Phosgene) 75-44-5 100Carbonyl Fluoride 353-50-4 2500Cellulose Nitrate (concentration greater than 12.6% nitrogen) 9004-70-0 2500Chlorine 7782-50-5 1500Chlorine Dioxide 10049-04-4 1000Chlorine Pentrafluoride 13637-63-3 1000Chlorine Trifluoride 7790-91-2 1000Chlorodiethylaluminum (also called Diethylaluminum Chloride) 96-10-6 50001-Chloro-2,4-Dinitrobenzene 97-00-7 5000Chloromethyl Methyl Ether 107-30-2 500Chloropicrin 76-06-2 500Chloropicrin and Methyl Bromide mixture None 1500Chloropicrin and Methyl Chloride mixture None 1500Cumene Hydroperoxide 80-15-9 5000Cyanogen 460-19-5 2500Cyanogen Chloride 506-77-4 500


414 NCEES

Highly Hazardous Chemicals (cont'd)Chemical Name CAS* TQ**

Cyanuric Fluoride 675-14-9 100Diacetyl Peroxide (concentration greater than 70%) 110-22-5 5000Diazomethane 334-88-3 500Dibenzoyl Peroxide 94-36-0 7500Diborane 19287-45-7 100Dibutyl Peroxide (tertiary) 110-05-4 5000Dichloro Acetylene 7572-29-4 250Dichlorosilane 4109-96-0 2500Diethylzinc 557-20-0 10,000Diisopropyl Peroxydicarbonate 105-64-6 7500Dilauroyl Peroxide 105-74-8 7500Dimethyldichlorosilane 75-78-5 10001,1-Dimethylhydrazine 57-14-7 1000Dimethylamine, Anhydrous 124-40-3 25002,4-Dinitroaniline 97-02-9 5000Ethyl Methyl Ketone Peroxide (also Methyl Ethyl Ketone Peroxide; concentration greater than 60%) 1338-23-4 5000

Ethyl Nitrite 109-95-5 5000Ethylamine 75-04-7 7500Ethylene Fluorohydrin 371-62-0 100Ethylene Oxide 75-21-8 5000Ethyleneimine 151-56-4 1000Fluorine 7782-41-4 1000Formaldehyde (Formalin) 50-00-0 1000Furan 110-00-9 500Hexafluoroacetone 684-16-2 5000Hydrochloric Acid, Anhydrous 7647-01-0 5000Hydrofluoric Acid, Anhydrous 7664-39-3 1000Hydrogen Bromide 10035-10-6 5000Hydrogen Chloride 7647-01-0 5000Hydrogen Cyanide, Anhydrous 74-90-8 1000Hydrogen Fluoride 7664-39-3 1000Hydrogen Peroxide (52% by weight or greater) 7722-84-1 7500Hydrogen Selenide 7783-07-5 150Hydrogen Sulfide 7783-06-4 1500Hydroxylamine 7803-49-8 2500Iron, Pentacarbonyl 13463-40-6 250Isopropylamine 75-31-0 5000Ketene 463-51-4 100Methacrylaldehyde 78-85-3 1000Methacryloyl Chloride 920-46-7 150Methacryloyloxyethyl Isocyanate 30674-80-7 100


NCEES 415


Methyl Acrylonitrile 126-98-7 250Methylamine, Anhydrous 74-89-5 1000Methyl Bromide 74-83-9 2500Methyl Chloride 74-87-3 15,000Methyl Chloroformate 79-22-1 500Methyl Ethyl Ketone Peroxide (concentration greater than 60%) 1338-23-4 5000Methyl Fluoroacetate 453-18-9 100Methyl Fluorosulfate 421-20-5 100Methyl Hydrazine 60-34-4 100Methyl Iodide 74-88-4 7500Methyl Isocyanate 624-83-9 250Methyl Mercaptan 74-93-1 5000Methyl Vinyl Ketone 79-84-4 100Methyltrichlorosilane 75-79-6 500Nickel Carbonyl (Nickel Tetracarbonyl) 13463-39-3 150Nitric Acid (94.5% by weight or greater) 7697-37-2 500Nitric Oxide 10102-43-9 250Nitroaniline (para Nitroaniline) 100-01-6 5000Nitromethane 75-52-5 2500Nitrogen Dioxide 10102-44-0 250Nitrogen Oxides (NO; NO(2); N2O4; N2O3) 10102-44-0 250Nitrogen Tetroxide (also called Nitrogen Peroxide) 10544-72-6 250Nitrogen Trifluoride 7783-54-2 5000Nitrogen Trioxide 10544-73-7 250Oleum (65% to 80% by weight; also called Fuming Sulfuric Acid) 8014-95-7 1000Osmium Tetroxide 20816-12-0 100Oxygen Difluoride (Fluorine Monoxide) 7783-41-7 100Ozone 10028-15-6 100Pentaborane 19624-22-7 100Peracetic Acid (concentration greater 60% Acetic Acid; also called Peroxyacetic Acid) 79-21-0 1000

Perchloric Acid (concentration greater than 60% by weight) 7601-90-3 5000Perchloromethyl Mercaptan 594-42-3 150Perchloryl Fluoride 7616-94-6 5000Peroxyacetic Acid (concentration greater than 60% Acetic Acid; also called Peracetic Acid) 79-21-0 1000

Phosgene (also called Carbonyl Chloride) 75-44-5 100Phosphine (Hydrogen Phosphide) 7803-51-2 100Phosphorus Oxychloride (also called Phosphoryl Chloride) 10025-87-3 1000Phosphorus Trichloride 7719-12-2 1000Phosphoryl Chloride (also called Phosphorus Oxychloride) 10025-87-3 1000


416 NCEES


Propargyl Bromide 106-96-7 100Propyl Nitrate 627-3-4 2500Sarin 107-44-8 100Selenium Hexafluoride 7783-79-1 1000Stibine (Antimony Hydride) 7803-52-3 500Sulfur Dioxide (liquid) 7446-09-5 1000Sulfur Pentafluoride 5714-22-7 250Sulfur Tetrafluoride 7783-60-0 250Sulfur Trioxide (also called Sulfuric Anhydride) 7446-11-9 1000Sulfuric Anhydride (also called Sulfur Trioxide) 7446-11-9 1000Tellurium Hexafluoride 7783-80-4 250Tetrafluoroethylene 116-14-3 5000Tetrafluorohydrazine 10036-47-2 5000Tetramethyl Lead 75-74-1 1000Thionyl Chloride 7719-09-7 250Trichloro (chloromethyl) Silane 1558-25-4 100Trichloro (dichlorophenyl) Silane 27137-85-5 2500Trichlorosilane 10025-78-2 5000Trifluorochloroethylene 79-38-9 10,000Trimethyoxysilane 2487-90-3 1500

* Chemical abstract service number ** Threshold quantity in pounds (amount necessary to be covered by OSHA CFR 1910.119 standard)


NCEES 417

6.5.4.11 Hazardous Classification Based on NFPA 70

NFPA Hazardous Classification

GROUP AACETYLENE

CLASS IGASES OR VAPOR

CLASS IICOMBUSTIBLE DUST

DIVISION 2HAZARDOUS VAPORSCONTAINED BUT MAY

BE PRESENT

DIVISION 1HAZARDOUS VAPORS

PRESENTZONE 0, 1, OR 2

DIVISION 2STORED OR HANDLED

OTHER THANMANUFACTURE

DIVISION 1HANDLED,

MANUFACTURED ORUSED

DIVISION 2SURFACE

ACCUMULATED – NONAIR SUSPENDED

DIVISION 1AIR SUSPENDED

CLASS IIIFIBERS

GROUP BFLAMMABLE GAS, FLAMMABLE

OR COMBUSTIBLE VAPORMESG ≤ 0.45 MM MIC RATIO ≤ 0.40

GROUP CFLAMMABLE GAS, FLAMMABLE

OR COMBUSTIBLE VAPOR0.45 MM ≤MESG ≤ 0.75 MM 0.45 MM ≤ MIC RATIO ≤ 0.80

GROUP DFLAMMABLE GAS, FLAMMABLE

OR COMBUSTIBLE VAPOR0.75MM ≤ MESG

0.80MM ≤ MIC RATIO CLASS 1, ZONE 0: IGNITABLE CONCENTRATIONS PRESENT CONTINUOUSLY OR FOR LONG PERIODS OF TIMECLASS 1, ZONE 1: IGNITABLE CONCENTRATIONS LIKELY TO EXIST UNDER NORMAL OPERATIONCLASS 1, ZONE 2: IGNITABLE CONCENTRATIONS NOT LIKELY TO EXIST UNDER NORMAL OPERATION

MSEG: MAXIMUM EXPERIMENTAL SAFE GAPMIC: MINIMUM IGNITING CURRENT RATIO

GROUP GCOMBUSTIBLE DUSTS NOT

INCLUDED ELSEWHERE

GROUP FCOMBUSTIBLE CARBONACEOUS

DUSTS CONTAINING >8%AND TRAPPED VOLATILES

GROUP ECOMBUSTIBLE METAL DUSTS

Source: National Fire Protection Association, NFPA 70, Chapters 500 and 505, 2011.

Maximum Experimental Safe Gap (MESG): The maximum clearance between two parallel metal surfaces that has been found, under specified test conditions, to prevent an explosion in a test chamber from being propagated to a secondary chamber containing the same gas or vapor at the same concentration.

Minimum Igniting Current (MIC) Ratio: The ratio of the minimum current required from an inductive spark dis-charge to ignite the most easily ignitable mixture of a gas or vapor, divided by the minimum current required from an inductive spark discharge to ignite methane under the same test conditions.


418 NCEES

6.5.4.12 FlammabilityFlammable describes any solid, liquid, vapor, or gas that will ignite easily and burn rapidly. A flammable liquid is defined by NFPA and USDOT as a liquid with a flash point below 100°F (38°C). Flammability is further defined with lower and upper limits:

LFL = lower flammability limit (volume % in air) UFL = upper flammability limit (volume % in air)

A vapor-air mixture will only ignite and burn over the range of concentrations between LFL and UFL. Examples:

Compound LFL UFLEthyl alcohol 3.3 19Ethyl ether 1.9 36Ethylene 2.7 36Methane 5 15Propane 2.1 9.5

Predicting Lower Flammable Limits of Mixtures of Flammable Gases (Le Chatelier's Rule)

Based on an empirical rule developed by Le Chatelier, the lower flammable limit of mixtures of multiple flam-mable gases in air can be determined. A generalization of Le Chatelier's rule is

LFLC 1

i

i

i

n

1

$=

a k/where

Ci = the volume percent of fuel gas i in the fuel/air mixture

LFLi = the volume percent of fuel gas i at its lower flammable limit in air alone

If the indicated sum is greater than unity, the mixture is above the lower flammable limit. This can be restated in terms of the lower flammable limit concentration of the fuel mixture (LFLm):

C100LFLLFL

m

i

fi

i

n

1

=

=

a k/

where Cfi = the volume percent of fuel gas i in the fuel gas mixture.

Predicting Lower Flammable LimitsSATURATED VAPOR-AIR MIXTURES

MIST FLAMMABLEMIXTURES

TEMPERATURETL AITTU

UPPERLIMIT

B

A

AUTO-IGNITION

COMB

USTA

BLE

CONC

ENTR

ATIO

N

THE SFPE HANDBOOK OF FIRE PROTECTION ENGINEERING, NATIONAL FIRE PROTECTION ASSOCIATION. 1988. WITH PERMISSION FROM THE SOCIETY OF FIRE PREVENTION ENGINEERS.

*

LOWERLIMIT

Source: National Fire Protection Association, The SFPA Handbook of Fire Protection Engineering, 1988. Used by permission of the Society of Fire Prevention Engineers.


NCEES 419

6.5.4.13 Fundamental Burning Velocities

Fundamental Burning Velocities of Selected Gases and Vapors

GasFundamental

Burning Velocity

scma k

GasFundamental

Burning Velocity

scma k

Acetone 54 Cyclobutane 67Acetylene 166* ethyl- 53Acrolein 66 isopropyl- 46Acrylonitrile 50 methyl- 52Allene (propadiene) 87 Cyclohexane 46Benzene 48 methyl- 44

n-butyl- 37 Cyclopentadiene 46tert-butyl- 39 Cyclopentane 441,2-dimethyl- 37 methyl- 421,2,4-trimethyl- 39 Cyclopropane 56

1,2-Butadiene (methylallene) 68 cis-1,2-dimethyl- 551,3-Butadiene 64 trans-1,2-dimethyl- 55

2,3-dimethyl- 52 ethyl- 562-methyl- 55 methyl- 58

n-Butane 45 1,1,2-trimethyl- 522-cyclopropyl- 47 trans-Decalin (decahydronaphthalene) 362,2-dimethyl- 42 n-Decane 432,3-dimethyl- 43 1-Decene 442-methyl- 43 Diethyl ether 472,2,3-trimethyl- 42 Dimethyl ether 54

Butanone 42 Ethane 471-Butene 51 Ethene (ethylene) 80*

2-cyclopropyl- 50 Ethyl acetate 382,3-dimethyl 46 Ethylene oxide 1082-ethyl- 46 Ethylenimine 462-methyl- 46 Gasoline (100-octane) 403-methyl- 49 n-Heptane 462,3-dimethyl-2-butene 44 Hexadecane 44

2-Buten 1-yne (vinylacetylene) 89 1,5-Hexadiene 521-Butyne 68 n-Hexane 46

3,3-dimethyl- 56 1-Hexene 502-Butyne 61 1-Hexyne 57Carbon disulfide 58 3-Hexyne 53Carbon monoxide 46 HFC-23 (Difluoromethane) 6.7


420 NCEES

Fundamental Burning Velocities of Selected Gases and Vapors (cont'd)

GasFundamental

Burning Velocity

scma k

GasFundamental

Burning Velocity

scma k

HFC-143 (1,1,2-Trifluoroethane) 13.1 1-Pentene 50HFC-143a (1,1,1-Trifluoroethane) 7.1 2-methyl- 47HFC-152a (1,1-Difluoroethane) 23.6 4-methyl- 48Hydrogen 312* 1-Pentene 63Isopropyl alcohol 41 4-methyl- 53Isopropylamine 31 cis-2-Pentene 51Jet fuel, grade JP-1 (average) 40 2-Pentyne 61Methane 40* 4-methyl- 54

diphenyl- 35 Propane 46*Methyl alcohol 56 2-cyclopropyl- 50Methylene 61 1-deutero- 401,2-Pentadiene (ethylallene) 61 1-deutero-2-methyl- 40cis-1,3-Pentadiene 55 2-deutero-2-methyl- 40trans-1,3-Pentadiene (piperylene) 54 2,2-dimethyl- 39

2-methyl-(cis or trans) 46 2-methyl- 411,4-Pentadiene 55 2-cyclopropyl- 532,3-Pentadiene 60 2-methyl- 44n-Pentane 46 Propionaldehyde 58

2,2-dimethyl- 41 Propylene oxide (1,2-epoxypropane) 822,3-dimethyl- 43 1-Propyne 822,4-dimethyl- 42 Spiropentane 712-methyl- 43 Tetrahydopyran 483-methyl- 43 Tetralin (tetrahydronaphthalene) 392,2-trimethyl- 41 Toluene (methylbenzene) 41

* Gases that were critically examined as to their fundamental burning velocities, in studies by Andrews and Bradley (Andrews, G.E., and D. Bradley, "Determination of Burning Velocities: a Critical Review," Combustion and Flame,

Vol. 18, New York: Elsevier Scientific Publishing Co., 1972, pp. 133–153) or by France and Pritchard (France, D.H., and R. Pritchard, "Burning Velocity Measurements of Multicomponent Fuel Gas Mixtures," Gas Warnie International, Vol. 26,

No. 12, 1977).

Source: National Fire Protection Association 68, Standard on Explosion Protection by Deflagration Venting, 2013 ed., pp. 65–66. Used by permission.


NCEES 421

The table below compares values from the Andrews/Bradley and France/Pritchard studies to those in the table above.

Comparison of Fundamental Burning Velocities for Selected Gases

Fundamental Burning Velocity scma k

Gas From Table AboveAndrews and Bradley France and

Pritchard (in Air)In Air In OxygenAcetylene 166 158 1140 -Ethylene 80 79 - 0Hydrogen 312 310 1400 347Methane 40 45 450 43Propane 46 - - 46

Flammability Properties of Gases 5L (0.005 m3) Sphere; E = 10J, normal conditions*

Flammable Material Pmax (bar)Acetophenonea 7.6Acetylene 10.6Ammoniab 5.4b-Naphtholc 4.4Butane 8.0Carbon disulfide 6.4Diethyl ether 8.1Dimethyl formamidea 8.4Dimethyl sulfoxidea 7.3Ethanea 7.8Ethyl alcohol 7.0Ethyl benzenea 7.4Hydrogen 6.8Hydrogen sulfide 7.4Isopropanola 7.8Methane 7.1Methanola 7.5Methylene chloride 5.0Methyl nitrite 11.4Neopentane 7.8Octanola 6.7Octyl chloridea 8.0


422 NCEES

Flammability Properties of Gases 5L (0.005 m3) Sphere; E = 10J, normal conditions* (cont'd)

Flammable Material Pmax (bar)Pentanea 7.8Propane 7.9South African crude oil 6.8–7.6Toluenea 7.8

a. Measured at elevated temperatures and extrapolated to 25°C (77°F) at normal conditionsb. E = 100J - 200Jc. 200°C (392°F)

* W. Bartknecht, "Explosions-Schutz: Grundlagen und Anwendung," Springer-Verlag, Berlin, 1993 (German only).

Source: National Fire Protection Association 68, Standard on Explosion Protection by Deflagration Venting, 2013 ed., pp. 65–66.

6.5.4.14 Combustible DustCombustible dust is a solid material composed of distinct particles or pieces, regardless of size, shape, or chemical composition, that presents a fire or deflagration hazard when suspended in air or some other oxidizing medium over a range of concentrations. Combustible dusts are often either organic or metal dusts that are finely ground into very small particles, fibers, fines, chips, chunks, flakes, or a small mixture of these.

According to OSHA's Safety and Health Information Bulletin (SHIB) "Combustible Dust in Industry: Preventing and Mitigating the Effects of Fire and Explosions," dust particles with an effective diameter of less than 420 microns (those passing through a U.S. No. 40 standard sieve) should be deemed to meet the criterion of the defini-tion. However, larger particles can still pose a deflagration hazard (for instance, as larger particles are moved, they can abrade each other, creating smaller particles). In addition, particles can stick together (agglomerate) due to electrostatic charges accumulated through handling, causing them to become explosible when dispersed.

Types of dusts include, but are not limited to:

• Metal dust, such as aluminum and magnesium

• Wood dust

• Plastic or rubber dust

• Biosolids

• Coal dust

• Organic dust, such as flour, sugar, paper, soap, and dried blood

• Dusts from certain textiles

Kst is the dust deflagration index, which measures relative explosion severity compared to other dusts. The larger the value for Kst, the more severe the explosion. Kst provides the best "single number" estimate of the anticipated behavior of a dust deflagration.

MIE, the minimum ignition energy, predicts the ease and likelihood of ignition of a dispersed dust cloud.

MEC, the minimum explosible concentration, measures the minimum amount of dust dispersed in air required to spread an explo sion. The MEC is analogous to the Lower Flammable Limit (LFL) or Lower Explosive Limit (LEL) for gases and vapors in air.


NCEES 423

Examples of Kst Values for Different Types of Dusts

Dust Explosion Class* Kst bar sm:c m* Characteristic Typical materials**

St 0 0 No explosion SilicaSt 1 > 0 and < 200 Weak explosion Powered milk, charcoal, sulfur, sugar, zincSt 2 > 200 and < 300 Strong explosion Cellulose, wood flour, poly methyl acrylateSt 3 > 300 Very strong explosion Anthraquinone, aluminum, magnesium

* OSHA CPL 03-00-008 - Combustible Dust National Emphasis Program ** NFPA 68, Standard on Explosion Prevention by Deflagration Venting

Source: U.S. Department of Labor, OSHA, "Hazard Communication Guidance for Combustible Dusts," OSHA 3371-08, 2009.

The actual class is sample-specific and will depend on varying characteristics of the material, such as particle size or moisture.

Source for next five tables: National Fire Protection Association 68, Standard on Explosion Protection by Deflagration Venting, 2013 ed., pp. 67–69. Used by permission.

Agricultural Products

MaterialMass Median

Diameter (mm)

Minimum Flammable

Concentration

mg3c m

barPmax _ i bar smKst :c m

Dust Hazard Class

Cellulose 33 60 9.7 229 2Cellulose pulp 42 30 9.9 62 1Cork 42 30 9.6 202 2Corn 28 60 9.4 75 1Egg white 17 125 8.3 38 1Milk, powdered 83 60 5.8 28 1Milk, nonfat, dry 60 - 8.8 125 1Soy flour 20 200 9.2 110 1Starch, corn 7 - 10.3 202 2Starch, rice 18 60 9.2 101 1Starch, wheat 22 30 9.9 115 1Sugar 30 200 8.5 138 1Sugar, milk 27 60 8.3 82 1Sugar, beet 29 60 8.2 59 1Tapioca 22 125 9.4 62 1Whey 41 125 9.8 140 1Wood Flour 29 - 10.5 205 2


424 NCEES

Carbonaceous Dusts

MaterialMass Median

Diameter (mm)

Minimum Flammable

Concentration

mg3c m

barPmax _ i bar smKst :c m Dust Hazard

Class

Charcoal, activated 28 60 7.7 14 1Charcoal, wood 14 60 9.0 10 1Coal, bituminous 24 60 9.2 129 1Coke, petroleum 15 125 7.6 47 1Lampblack <10 60 8.4 121 1Lignite 32 60 10.0 151 1Peat, 22% H2O - 125 84.0 67 1

Soot, pine <10 - 7.9 26 1

Chemical Dusts

MaterialMass Median

Diameter (mm)

Minimum Flammable

Concentration

mg3c m


Class

Adipic acid <10 60 8.0 97 1Anthraquinone <10 - 10.6 364 3Absorbic acid 39 60 9.0 111 1Calcium acetate 92 500 5.2 9 1Calcium acetate 85 250 6.5 21 1Calcium stearate 12 30 9.1 132 1Carbonyl- methyl- cellulose 24 125 9.2 136 1

Dextrin 41 60 8.8 106 1Lactose 23 60 7.7 81 1Lead stearate 12 30 9.2 152 1Methyl cellulose 75 60 9.5 134 1Paraformaldehyde 23 60 9.9 178 1Sodium ascorbate 23 60 8.4 119 1Sodium stearate 22 30 8.8 123 1Sulfur 20 30 6.8 151 1


NCEES 425

Metal Dusts

MaterialMass Median

Diameter (mm)

Minimum Flammable

Concentration

mg3c m


Class

Aluminum 29 30 12.4 415 3Bronze 18 750 4.1 31 1Iron, carbonyl <10 125 6.1 111 1Magnesium 28 30 17.5 508 3Phenolic resin 55 - 7.9 269 2Zinc 10 250 6.7 125 1Zinc <10 125 7.3 176 1

Plastic Dusts

MaterialMass Median

Diameter (mm)

Minimum Flammable

Concentration

mg3c m


Dust Hazard Class

(poly) Acrylamide 10 250 5.9 12 1(poly) Acrylonitrile 25 - 8.5 121 1(poly) Ethylene (low-pressure process) <10 30 8.0 156 1

Epoxy resin 26 30 7.9 129 1Melamine resin 18 125 10.2 110 1Melamine, molded (wood flour and mineral filled phenol-formaldehyde) 15 60 7.5 41 1

Melamine, molded (phenol- cellulose) 12 60 10.0 127 1

(poly) Methyl acrylate 21 30 9.4 269 2(poly) Methyl acrylate, emulsion polymer 18 30 10.1 202 2

Phenolic resin <10 15 9.3 129 1(poly) Propylene 25 30 8.4 101 1Terpene-phenol resin 10 15 8.7 143 1Urea-formaldehyde/cellulose, molded 13 60 10.2 136 1

(poly) Vinyl acetate/ethylene copolymer 32 30 8.6 119 1

(poly) Vinyl alcohol 26 60 8.9 128 1(poly) Vinyl butyral 65 30 8.9 147 1(poly) Vinyl chloride 107 200 7.6 46 1


426 NCEES

Plastic Dusts (cont'd)

MaterialMass Median

Diameter (mm)

Minimum Flammable

Concentration

mg3c m


Dust Hazard Class

(poly) Vinyl chloride/vinyl acetylene emulsion copolymer

35 60 8.2 95 1

(poly) Vinyl chloride/ethylene/vinyl acetylene suspension copolymer

60 60 8.3 98 1

Ignition and Reaction Temperatures of Metal-Powder Layers in an Air, Carbon Dioxide, or Nitrogen Atmosphere

Line No.

Sample No. Material

Ignition Temperature, °C Reaction Temperature, °C

Air Carbon Dioxide Nitrogen Carbon

Dioxide Nitrogen

35 701 Aluminum, atomized 900 -- -- 900 75021 897 Aluminum, atomized 490 540 -- -- 80080 702 Aluminum, flake 590 660 -- -- 700

102 705 Chromium 670 -- -- (1) 700110 706 Copper 270 -- -- -- 700120 712 Iron, hydrogen-reduced 290 -- -- (1) 200136 716 Lead 210 -- -- 870 400151 725 Magnesium 490 630 530 -- --154 727 Magnesium 510 -- 510 -- --156 729 Magnesium 520 -- 520 -- --157 730 Magnesium 490 -- 500 -- --159 1020 Magnesium 490 600 550 -- --164 734 Magnesium 480 -- 490 -- --165 733 Magnesium 480 -- 500 -- --168 736 Magnesium 420 -- -- 700 900176 737 Silicon 950 -- -- 1000 1000190 1652 Thorium 280 450 500 -- --191 1653 Thorium hydride 20 340 330 -- --193 739 Tin 430 -- 900 720 --195 1555 Titanium 480 900 900 -- --198 740 Titanium 460 680 -- -- 900199 1556 Titanium, copper-coated 430 900 900 -- --201 864 Titanium 470 470 500 -- --204 1649 Titanium hydride 500 710 750 -- --211 1625 Uranium 100 350 410 -- --212 1626 Uranium hydride 20 360 210 -- --217 744 Zinc 460 480 -- -- 600225 745 Zirconium 210 560 530 -- --228 1632 Zirconium 190 620 790 -- --


NCEES 427

Ignition and Reaction Temperatures of Metal-Powder Layers in an Air, Carbon Dioxide, or Nitrogen Atmosphere (cont'd)

Line No.

Sample No. Material

Ignition Temperature, °C Reaction Temperature, °C

Air Carbon Dioxide Nitrogen Carbon

Dioxide Nitrogen

229 1633 Zirconium 300 710 -- -- --233 1627 Zirconium hydride 340 650 -- -- --247 1021 Aluminum-magnesium 460 660 550 -- --248 746 Aluminum-magnesium 470 700 550 -- --249 748 Aluminum-magnesium 480 670 630 -- --

1 No reaction at 850°C

Source: Jacobson, M., A.R. Cooper, and J. Nagy, Explosibility of Metal Powders, Bureau of Mines Report of Investigations 6516, Washington, D.C.: United States Department of the Interior, Bureau of Mines, 1964.

6.5.4.15 Relief Vent Sizing

Relief-Venting Flammable Liquids

20 200

14,090,0009,950,000

4,000,000

400,000

1000 2800EXPOSED WITH A SURFACE AREA, A (FT2)

HEAT

ABS

ORPT

ION,

Q (B

TU/H

R)

Q = 20,00

0A

Q = 21,000 (A)0.82

Q = 14,090,000

Q = 20,00

0A

Q = 199,300 (A)0.566Q = 963,400 (A)0.338

Q = 199,300 (A)0.566Q = 963,400 (A)0.338

Q = 21,000 (A)0.82

Q = 14,090,000

Source: National Fire Prevention Association, NFPA 30: Flammable and Combustible Liquid Code, 2008 ed., p. 110. Used by permission.


428 NCEES

Estimation of Emergency Relief Venting for Specific Liquids

.CFH

L MQ70 5=

where

CFH = cubic feet of free air per hour

70.5 = factor for converting pounds of gas to ft3 of air

Q = total heat input per hour (Btu)

L = latent heat of vaporization lbBtuc m

M = molecular weight

6.5.4.16 Pressure Relief Variables and Constants

Pressure Relief Variables and ConstantsSymbol Description Units (U.S.) Units (metric)

A Required effective discharge area of the device in2 mm2

C A function of the ratio of the ideal gas-specific heats k CCv

p=e o of the gas or vapor at inlet-relieving temperature lbf hr

lbm lbmole R-

- -cmm hr K Pakg kgmol K

2 : :

: :

Cp Specific heat at constant pressure lb FBtuc kgK

KJ

Cv Specific heat at constant volume lb FBtuc kgK

KJ

F2 Coefficient of subcritical flow

GlSpecific gravity of a liquid at flowing temperature referred to water at standard conditions

k Ratio of the specific heats CCv

pe o for an ideal gas at relieving tempera-

ture. The ideal-gas to specific-heat ratio is independent of pressure.dimensionless

Kb

Capacity correction factor due to back pressure; can be obtained from manufacturer's literature or estimated for preliminary sizing. The back-pressure correction factor applies to balanced-bellows valves only. For conventional and pilot-operated valves, use a value for Kb equal to 1.0.

dimensionless

Kc

Combination correction factor for installations with a rupture disk upstream of the pressure relief valve. Equals 1.0 when a rupture disk is not installed; equals 0.9 when a rupture disk is installed in com-bination with a PRV and the combination does not have a certified value.

dimensionless


NCEES 429

Pressure Relief Variables and Constants (cont'd)Symbol Description Units (U.S.) Units (metric)

Kd for gas,

vapor, steam

Rated coefficient of discharge that should be obtained from the valve manufacturer. For preliminary sizing, an effective discharge coeffi-cient can be used as follows:

• 0.65 when a PRV is installed with or without a rupture disk in combination

• 0.62 when a PRV is not installed and sizing is for a rupture disk with minimum net flow area

dimensionless

Kd for liquid

Effective coefficient of discharge. For preliminary sizing, use the following values:

• 0.975 when a PRV is installed with or without a rupture disk in combination

• 0.62 when a PRV is not installed and sizing is for a rupture disk with minimum net flow area

dimensionless

KN Correction factor for the Napier equation (KN = 1.0) dimensionless

KSH

Superheat correction factor; can be obtained from the "Superheat Correction Factors" table on page 432. For saturated steam at any pressure, KSH = 1.0. For temperatures above 1200°F, use the critical vapor sizing equations.

dimensionless

Kv Correction factor due to viscosity dimensionless

KW

Correction factor due to back pressure. If the back pressure is atmo-spheric, use a value for KW of 1.0. Balanced-bellows valves in back-pressure service require the correction determined from the figure "Capacity Correction Factor, KW, Due to Back Pressure on Balanced-Bellows PRVs in Liquid Service." Conventional and pilot-operated valves require no special correction.

dimensionless

M

Molecular weight of the gas or vapor at inlet-relieving conditions. Various handbooks carry tables of molecular weights of materials; however, the composition of the flowing gas or vapor is seldom the same as that listed in such tables. This composition should be obtained from the process data.

P1Upstream relieving pressure; set pressure plus allowable overpres-sure plus atmospheric pressure psia kPa

P2 Back pressure psia kPa

Q Flow rate . .min

U S galminL

r Ratio of back pressure to upstream relieving pressure, PP1

2 dimensionless

Re Reynolds number dimensionlessT Relieving temperature of the inlet gas or vapor °R (°F + 460) K (°C + 273)m Absolute viscosity at the flowing temperature cPU Viscosity at the flowing temperature Saybolt universal seconds

V Required flow through the devicescfm at

14.7 psia and 60°F

minnormalm3 at 0°C

and 101.325 kPa


430 NCEES

Pressure Relief Variables and Constants (cont'd)Symbol Description Units (U.S.) Units (metric)

W Required flow through the device. hlb

hkg

Z Compressibility factor for the deviation of the actual gas from a perfect gas, evaluated at inlet-relieving conditions. dimensionless

Pressure Relief EquationsDescription Units (U.S.)

(units per previous table)Units (metric)

(units per previous table)

Coefficient C C k k520 12 k

k11

= +−+

c^^m

hh .C k k0 03948 1

2 kk11

= +−+

c^^m

hh

Correction Factor KN

KN = 1.0

where , psiaP 1 5001 #

KN = 1.0

where , kPaP 10 3391 #

. ,

. ,K P

P0 2292 1 0610 1906 1 000

N1

1= −−

where P1 > 1,500 psia and , psia3 200#

. ,

. ,K P

P0 03324 1 0610 02764 1 000

N1

1= −−

where P1 > 10,339 kPa and , kPa22 057#

Coefficient F2F k

k rr

r1 1

1k kk

22 1

= − −−

−c c cm m m> H

Sizing for Gas or Vapor Service at Critical Flow Conditions

A C K P K KW

MT Z

d b c1=

Sizing for Subcritical Flow: Gas or Vapor, Conventional and Pilot-Operated PRVs

When the ratio of back pressure to inlet pressure exceeds the critical pressure ratio Pcf /P1, the flow through the pressure-relief device is subcritical. These equations may be used to calculate the required effective discharge area for a conventional PRV whose spring setting is adjusted to com-pensate for superimposed back pressure. Equations may also be used for sizing a pilot-operated PRV.

( )A F K KW

M P P PT Z

735 d c2 1 1 2= −

.( )A F K K

WM P P P

T Z17 9d c2 1 1 2

= −

Sizing for Steam-Relief Operating at Critical Flow Conditions .A P K K K K K

W51 5 d b c N SH1

= .A P K K K K KW190 5

d b c N SH1=


NCEES 431

Pressure Relief Equations (cont'd)Description Units (U.S.) Units (metric)

Sizing for Liquid Relief: PRVs Requiring Capacity Certification

The ASME Code requires that capacity certification be obtained for PRVs de-signed for liquid service. The procedure for obtaining capacity certification includes testing to determine the rated coefficient of discharge for the liquid PRVs at 10% overpressure.

The sizing equations for pressure-relief devices in liquid service provided here as-sume that the liquid is incompressible (i.e., the density of the liquid does not change as the pressure decreases from the relieving pressure to the total back pressure).

Valves in liquid service that are designed in accordance with the ASME Code may be initially sized using these area equations.

A K K K KQ

P PG

38 d w c v 1 2

1= −.

A K K K KQ

P PG11 78

d w c v 1 2

1= −

Kv: Correction Factor Due to Viscosity . . .Re ReK 0 9935 2 878 342 75

. .

.

v 0 5 1 5

1 0= + +

−

d n

Re = Reynolds Number

When a PRV is sized for viscous liquid ser-vice, it should first be sized as if it were for a nonviscous application (i.e., Kv = 1.0), so that a preliminary required discharge area A can be obtained from the liquid relief area equations above.

From API 526 standard orifice sizes, use the next orifice size larger than A to deter-mine the Reynolds Number, Re, from either of the following relationships:

Second equation is not recommended for viscosities less than 100 Saybolt universal seconds (SSU)

After determining the Reynolds Number, Re, obtain the factor KV. Apply KV in the liquid relief area equations above to correct the preliminary required discharge area. If the corrected area exceeds the chosen standard orifice area, repeat the above calculations using the next larger standard orifice size.

( , )Re

AQ G2 800 l

n= ,

ReU A

Q12 700=

Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008.


432 NCEES

Superheat Correction Factors, KSH

Superheat Correction Factors

Set Pressure psig (kPag)

Temperature °F (°C)300

(149)400

(204)500

(260)600

(316)700

(371)800

(427)900

(482)1000 (538)

1100 (593)

1200 (649)

15 (103) 1.00 0.98 0.93 0.88 0.84 0.80 0.77 0.74 0.72 0.7020 (138) 1.00 0.98 0.93 0.88 0.84 0.80 0.77 0.74 0.72 0.7040 (276) 1.00 0.99 0.93 0.88 0.84 0.81 0.77 0.74 0.72 0.7060 (414) 1.00 0.99 0.93 0.88 0.84 0.81 0.77 0.75 0.72 0.7080 (551) 1.00 0.99 0.93 0.88 0.84 0.81 0.77 0.75 0.72 0.70100 (689) 1.00 0.99 0.94 0.89 0.84 0.81 0.77 0.75 0.72 0.70120 (827) 1.00 0.99 0.94 0.89 0.84 0.81 0.78 0.75 0.72 0.70140 (965) 1.00 0.99 0.94 0.89 0.85 0.81 0.78 0.75 0.72 0.70160 (1103) 1.00 0.99 0.94 0.89 0.85 0.81 0.78 0.75 0.72 0.70180 (1241) 1.00 0.99 0.94 0.89 0.85 0.81 0.78 0.75 0.72 0.70200 (1379) 1.00 0.99 0.95 0.89 0.85 0.81 0.78 0.75 0.72 0.70220 (1516) 1.00 0.99 0.95 0.89 0.85 0.81 0.78 0.75 0.72 0.70240 (1654) -- 1.00 0.95 0.90 0.85 0.81 0.78 0.75 0.72 0.70260 (1792) -- 1.00 0.95 0.90 0.85 0.81 0.78 0.75 0.72 0.70280 (1930) -- 1.00 0.96 0.90 0.85 0.81 0.78 0.75 0.72 0.70300 (2068) -- 1.00 0.96 0.90 0.85 0.81 0.78 0.75 0.72 0.70350 (2413) -- 1.00 0.96 0.90 0.86 0.82 0.78 0.75 0.72 0.70400 (2757) -- 1.00 0.96 0.91 0.86 0.82 0.78 0.75 0.72 0.70500 (3446) -- 1.00 0.96 0.92 0.86 0.82 0.78 0.75 0.73 0.70600 (4136) -- 1.00 0.97 0.92 0.87 0.82 0.79 0.75 0.73 0.70800 (5514) -- -- 1.00 0.95 0.88 0.83 0.79 0.76 0.73 0.701000 (6893) -- -- 1.00 0.96 0.89 0.84 0.78 0.76 0.73 0.711250 (8616) -- -- 1.00 0.97 0.91 0.85 0.80 0.77 0.74 0.71

1500 (10,339) -- -- -- 1.00 0.93 0.86 0.81 0.77 0.74 0.711750 (12,063) -- -- -- 1.00 0.94 0.86 0.81 0.77 0.73 0.702000 (13,786) -- -- -- 1.00 0.95 0.86 0.80 0.76 0.72 0.692500 (17,232) -- -- -- 1.00 0.95 0.85 0.78 0.73 0.69 0.663000 (20,679) -- -- -- -- 1.00 0.82 0.74 0.69 0.65 0.62



NCEES 433

Capacity Correction Factor, KW, Due to Back Pressure on Balanced-Bellows PRVs in Liquid Service1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.500 10

PERCENT OF GAUGE BACKPRESSURE = (PB /PS) x 10020

K w

Kw = CORRECTION FACTOR DUE TO BACK PRESSURE.= BACK PRESSURE, IN PSIG.= SET PRESSURE, IN PSIG.

PBPS

30 40 50

NOTE: THE CURVE ABOUT REPRESENTS VALUES RECOMMENDED BY VARIOUS MANUFACTURERS.THIS CURVE MAY BE USED WHEN THE MANUFACTURER IS NOT KNOWN.OTHERWISE, THE MANUFACTURER SHOULD BE CONSULTED FOR THE APPLICABLE CORRECTION FACTOR.


6.5.5 Environmental Considerations

6.5.5.1 Air PollutionConcentrations in air can be converted from ppb to

mg3n

as follows:

mg

ppbMWRT

P3n =

_ i

where

ppb = parts per billion

P = pressure, in atm

R = ideal gas law constant = 0.0821 mol Kliter atm

::

T = absolute temperature, K = 273.15 + °C

MW = molecular weight, in molg


434 NCEES

6.5.5.2 Atmospheric Dispersion Modeling (Gaussian)σy and σz are functions of downwind distance and stability class:

exp exp expC uQ y z H z H

2 21

21

21

y z y z z2

2

2

2

2

2

r v v v v v= − −

−+ −

+f f ^ f ^p h p h p> Hwhere

C = steady-state concentration at a point (x, y, z) in mg3n

Q = emissions rate in sgn

σy = horizontal dispersion parameter, in meters

σz = vertical dispersion parameter, in meters

u = average wind speed at stack height in sm

x = downwind distance along plume center line, in meters

y = horizontal distance from plume center line, in meters

z = vertical distance from ground level, in meters

H = effective stack height (m) = h + ∆h

where h = physical stack height

∆h = plume rise

Maximum concentration at ground level and directly downwind from an elevated source:

expC uQ H

21

max y z z2

2

r v v v= −f _ i p

where variables are as above except for

Cmax = maximum ground-level concentrationH2zv = for neutral atmospheric conditions


NCEES 435

6.5.5.3 Characteristic Hazardous WasteA waste is a characteristic waste if it meets any of the characteristics identified in 40 CFR 261 Subpart C (D code waste).

Hazardous Waste CharacteristicsCharacteristic

(D Code) [Subpart #] Definition

Ignitability (D001) [40 CFR 261.21]

(1) A liquid (other than an aqueous solution containing <24% alcohol by volume) that has flash point <140oF [Method Pensky-Martens or Setaflash].

(2) A nonliquid that is capable (under STP) of causing fire through friction, absorption of moisture, or spontaneous chemical changes and, when ignited, burns so vigorously and persistently that it creates a hazard.

(3) An ignitable compressed gas.

Corrosivity (D002) [40 CFR 261.22]

(1) An aqueous solution with a pH .or2 12 5# $ [Method 9040C in SW-846].

(2) A liquid that corrodes steel (SAE 1020) at a rate of > 1/4 inch per year at a test temperature of 130oF [Method 1110A in SW-846].

Reactivity (D003) [40 CFR 261.23]

(1) Normally unstable and readily undergoes violent change without detonating.

(2) Reacts violently with water.

(3) Forms potentially explosive mixtures with water.

(4) When mixed with water, generates toxic gases, vapors, or fumes in a quantity sufficient to present a danger to human health or the environment.

(5) A cyanide- or sulfide-bearing waste that, when exposed to pH conditions between 2 and 12.5, can generate toxic gases, vapors, or fumes in a quantity sufficient to present a danger to human health or the environment.

(6) Capable of detonation or explosive reaction if subjected to a strong initiating source or if heated under confinement.

(7) Readily capable of detonation or explosive decomposition or reaction at standard temperature and pressure.

(8) A forbidden explosive as defined in 49 CFR 173.54, or a Division 1.1, 1.2, or 1.3 explosive as defined in 49 CFR 173.50 and 173.53.

Toxicity (D004 to D043) [40 CFR 261.24]

A waste that contains constituents above the regulatory threshold listed in Table 1 of 40 CFR 261.24 using the Toxicity Characteristic Leaching Procedure (TCLP) test [Method 1311 in SW846].

Constituents: arsenic, barium, benzene, cadmium, carbon tetrachloride, chlordane, chlorobenzene, chloroform, chromium, ocresol, m-cresol, p-cresol, total cresols, 2,4-D, 1,4-dichlorobenzene, 1,2-dichloroethane, 1,1-dichloroethylene, 2,4-dinitrotoluene, endrin, heptachlor (and its epoxide), hexachlorobenzene, hexachlorobutadiene, hexa-chloroethane, lead, lindane, mercury, methoxychlor, methyl ethyl ketone, nitrobenzene, pentachlorophenol, pyridine, selenium, silver, tetrachloroethylene, toxaphene, trichloro-ethylene, 2,4,5-trichlorophenol, 2,4,6-trichlorophenol, 2,4,5-TP (silvex), and vinyl chloride.


436 NCEES

Atmospheric Stability Under Various ConditionsSurface Wind Speeda in s

mDay: Solar Insulation Night: Cloudinesse

Strongb Moderatec Slightd Cloudy (<4/8) Clear (<3/8)<2 A A-Bf B E F2-3 A-B B C E F3-5 B B-C C D E5-6 C C-D D D D> 6 C D D D D

Source: Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed., Florida: Lewis Publishing/CRC Press, 1994.

a. Surface wind speed is measured at 10 m above the ground. b. Corresponds to a clear summer day with sun higher than 60° above the horizon. c. Corresponds to a summer day with a few broken clouds, or clear day with sun 35–60° above the horizon. d. Corresponds to a fall afternoon or a cloudy summer day with the sun 15–35°. e. Cloudiness is defined as the fraction of sky covered by the clouds. f. For A - B, B - C, or C - D conditions, average the values obtained for each.

A = Very unstable B = Moderately unstable C = Slightly unstable D = Neutral E = Slightly stable F = Stable Regardless of wind speed, Class D should be assumed for overcast conditions, day or night.


NCEES 437

Standard Deviations of a Plume

Source: D.B. Turner, Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed. Florida: Lewis Publishing/CRC Press, 1994.

σ yST

ANDA

RD D

EVIA

TION

, MET

ERS

DISTANCE DOWNWIND, x, METERS

ABCDEF

HORIZONTAL STANDARD DEVIATION OF A PLUME

ABCDEF

------

MODERATELY UNSTABLEEXTREMELY UNSTABLESLIGHTLY UNSTABLENEUTRALSLIGHTLY STABLEMODERATELY STABLE

102 103

103

104

104

102

10

105543254325

5

432

5432

5432

5432

1

σ zST

ANDA

RD D

EVIA

TION

, MET

ERS

DISTANCE DOWNWIND, x, METERS

VERTICAL STANDARD DEVIATION OF A PLUME

102 103

103

104

102

10

105543254325

5

4

4

3

3

2

2

5432

5432

1

AB

CD

EF


438 NCEES

Effective Stack Height

10-7 10-6

100 200180

200

200

200

200

200

250

250

250

250

250

300

300

300

300

300

150

150100

10070 EFFECTIVE STACK HEIGHT, H

7050

5040

40

150

150150

150

100

100100

100

70

707070

6050

505050

40

4040

40

30

3030

3030

30

20

2020202020

151515

1515

101010

8

88

7

7 54

F

E

D

C

B

A

200180

200

200

200

200

200

250

250

250

250

250

300

300

300

300

300

150

150100

10070 EFFECTIVE STACK HEIGHT, H

7050

5040

40

150

150150

150

100

100100

100

70

707070

6050

505050

40

4040

40

30

3030

3030

30

20

2020202020

151515

1515

101010

8

88

7

7 54

A - EXTREMELY UNSTABLEB - MODERATELY UNSTABLEC - SLIGHTLY UNSTABLED - NEUTRALE - SLIGHTLY STABLEF - MODERATELY STABLE

10

F

E

D

C

B

A1x ma

x km

0.110-5 10-4 10-3 10-2

(Cu/Q)max’ m-2

Source: Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed., CRC Press (Lewis Publishing), 1994.

Effective stack height is shown on curves numerically.

xmax = distance along plume center line to the point of maximum concentration

(Cu/Q)max = e[ ( ) ( ) ( ) ]ln ln lna b H c H d H2 3+ + +

H = effective stack height, stack height + plume rise, in meters

Values of Curve-Fit Constants for Estimating (Cu/Q)max from H as a Function of Atmospheric Stability

StabilityConstants

a b c dA –1.0563 –2.7153 0.1261 0B –1.8060 –2.1912 0.0389 0C –1.9748 –1.9980 0 0D –2.5302 –1.5610 –0.0934 0E –1.4496 –2.5910 0.2181 –0.0343F –1.0488 –3.2252 0.4977 –0.0765

Source: Table 1, Ranchoux, R.J.P., "Determination of Maximum Ground Level Concentration," Journal of the Air Pollution Control Association, vol. 26, no. 11, Lexington: Taylor & Francis Ltd, 1976, p. 1089, reprinted by permission of the Air

& Waste Management Association, www.awma.org, and Taylor & Francis Ltd, http://www.tandfonline.com. Journal's website can be found at htpp://informaworld.com.


NCEES 439

6.5.5.4 Incineration

%DRE WW W 100

in

in out #=-

where

DRE = destruction and removal efficiency (%)

Win = mass feed rate of a particular POHC*, in hrkgor hrlb

Wout = mass emission rate of the same POHC*, in hrkgor hrlb

*POHC = principal organic hazardous contaminant

%CE 100CO COCO2

2 #=+

where

CO2 = volume concentration (dry) of CO2 , in parts per million (volume: ppmv)

CO = volume concentration (dry) of CO, in ppmv

CE = combustion efficiency

6.5.5.5 Kiln Formula .t S N

DL2 28

=

where

t = mean residence time, in minutes

L/D = internal length-to-diameter ratio

S = kiln rake slope, in ftin. of length

N = rotational speed, in minrev

Energy Content of Waste

Typical Waste Values Moisture (%) Energy lbBtuc m

Food waste 70 2000Paper 6 7200Cardboard 5 7000Plastics 2 14,000Wood 20 8000Glass 2 60Bimetallic cans 3 300

PE C

hemical R

eference Handbook

440

NC

EES

6.6 Flammability Data

Chemical CAS No.Class I

Division Group

TypeaFlash Point (°C)

AIT (°C)

% LFL

% UFL

Vapor Density (Air=1)

Vapor Pressureb

(mm Hg)

Class 1 Zone Groupc

MIE (mJ)

MIC Ratio

MESG (mm)

Acetaldehyde 75-07-0 Cd I −38 175 4 60 1.5 874.9 IIA 0.37 0.98 0.92Acetic Acid 64-19-7 Dd II 39 426 19.9 2.1 15.6 IIA 2.67 1.76Acetone 67-64-1 Dd I –20 465 2.5 12.8 2 230.7 IIA 1.15 1 1.02Acetylene 74-86-2 Ad GAS 305 2.5 100 0.9 36,600 IIC 0.017 0.28 0.25Acrylic Acid 79-10-7 D II 54 488 2.4 8 2.5 4.3 IIB 0.86Acrylonitrile 107-13-1 Dd I 0 481 3 17 1.8 108.5 IIB 0.16 0.78 0.87Allyl Alcohol 107-18-6 Cd I 22 378 2.5 18 2 25.4 IIB 0.84Allyl Chloride 107-05-1 D I −32 485 2.9 11.1 2.6 366 IIA 1.33 1.17Ammonia 7664-41-7 Dd,f GAS 651 15 28 0.6 7498 IIA 680 6.85 3.17Aniline 62-53-3 D IIIA 70 615 1.2 8.3 3.2 0.7 IIABenzene 71-43-2 Dd I –11 498 1.2 7.8 2.8 94.8 IIA 0.2 1 0.99n-Butane 3583-47-9 Dd,g GAS 288 1.9 8.5 2 IIA 0.25 0.94 1.071,3-Butadiene 106-99-0 B(D)d,e GAS 420 2 11.5 1.9 IIB 0.13 0.76 0.791-Butanol 71-36-3 Dd I 36 343 1.4 11.2 2.6 7 IIA 0.91Butylene 25167-67-3 D I 385 1.6 10 1.9 2214.6 IIA 0.94Carbon Monoxide 630-08-0 Cd GAS 609 12.5 74 0.97 IIB 0.54Cumene 98-82-8 D I 36 424 0.9 6.5 4.1 4.6 IIA 1.05Cyclohexane 110-82-7 D I −17 245 1.3 8 2.9 98.8 IIA 0.22 1 0.94Cyclopropane 75-19-4 Dd I 503 2.4 10.4 1.5 5430 IIA 0.17 0.84 0.91Diethyl Ether (Ethyl Ether) 60-29-7 Cd I −45 160 1.9 36 2.6 538 IIB 0.19 0.88 0.83

Ethane 74-84-0 Dd GAS −29 472 3 12.5 1 IIA 0.24 0.82 0.91Ethanol (Ethyl Alcohol) 64-17-5 Dd I 13 363 3.3 19 1.6 59.5 IIA 0.88 0.89Ethylene 74-85-1 Cd GAS 490 2.7 36 1 IIB 0.07 0.53 0.65Ethylene Dichloride 107-06-2 Dd I 13 413 6.2 16 3.4 79.7Ethylene Oxide 75-21-8 B(C)d,e I −20 429 3 100 1.5 1314 IIB 0.065 0.47 0.59Ethyl Acetate 141-78-6 Dd I −4 427 2 11.5 3 93.2 IIA 0.46 0.99Ethyl Alcohol 64-17-5 Dd I 13 363 3.3 19 1.6 59.5 IIA 0.88 0.89

C


peration

NC

EES

441


Division Group


AIT (°C)

% LFL

% UFL


Vapor Pressureb

(mm Hg)

Class 1 Zone

Groupc

MIE (mJ)

MIC Ratio

MESG (mm)

Ethyl Benzene 100-41-4 D I 15 432 0.8 6.7 3.7 9.6Ethyl Chloride 75-00-3 D GAS −50 519 3.8 15.4 2.2Ethyl Mercaptan 75-08-1 Cd I −18 300 2.8 18 2.1 527.4 IIB 0.9 0.9Formaldehyde (Gas) 50-00-0 B GAS 430 7 73 1 IIB 0.57Formic Acid 64-18-6 D II 50 434 18 57 1.6 42.7 IIA 1.86

Fuel Oil 1 (Jet Fuel) 8008-20-6 D II or IIIAk 38–72k 210 0.7 5

Fuel Oil 2 (Diesel) II or IIIAk 52–96k 257

Gasoline 8006-61-9 Dd I −46 280 1.4 7.6 3n-Heptane 142-82-5 Dd I −4 204 1 6.7 3.5 45.5 IIA 0.24 0.88 0.91n-Hexane 110-54-3 Dd,g I −23 225 1.1 7.5 3 152 IIA 0.24 0.88 0.93Hydrogen 1333-74-0 Bd GAS 500 4 75 0.1 IIC 0.019 0.25 0.28Hydrogen Sulfide 7783-06-4 Cd GAS 260 4 44 1.2 IIB 0.68 0.9Isobutane 75-28-5 Dg GAS 460 1.8 8.4 2 IIA 0.95Isoprene 78-79-5 Dd I −54 220 1.5 8.9 2.4 550.6Isopropyl Ether 108-20-3 Dd I −28 443 1.4 7.9 3.5 148.7 IIA 1.14 0.94Kerosene 8008-20-6 D II 72 210 0.7 5 IIALiquefied Petroleum Gas 68476-85-7 D I 405

Methanol (Methyl Alcohol) 67-56-1 Dd I 12 385 6 36 1.1 126.3 IIA 0.14 0.82 0.92

Methyl Chloride 74-87-3 D GAS −46 632 8.1 17.4 1.7 IIA 1Methyl Ether 115-10-6 Cd GAS −41 350 3.4 27 1.6 IIB 0.85 0.84Methyl Ethyl Ketone 78-93-3 Dd I −6 404 1.4 11.4 2.5 92.4 IIB 0.53 0.92 0.84Naptha (Petroleum) 8030-30-6 Dd,h I 42 288 1.1 5.9 2.5 IIAn-Octane 111-65-9 Dd,g I 13 206 1 6.5 3.9 14 IIA 0.94n-Pentane 109-66-0 Dd,g I −40 243 1.5 7.8 2.5 513 IIA 0.28 0.97 0.93Process Gas > 30% H2 1333-74-0 Bi GAS 520 4 75 0.1 0.019 0.45Propane 74-98-6 Dd GAS 450 2.1 9.5 1.6 IIA 0.25 0.82 0.97

PE C

hemical R

eference Handbook

442

NC

EES


Division Group


AIT (°C)

% LFL

% UFL


Vapor Pressureb

(mm Hg)

Class 1 Zone

Groupc

MIE (mJ)

MIC Ratio

MESG (mm)

1-Propanol 71-23-8 Dd I 15 413 2.2 13.7 2.1 20.7 IIA 0.89Propylene 115-07-1 Dd GAS 460 2.4 10.3 1.5 IIA 0.28 0.91Styrene 100-42-5 Dd I 31 490 0.9 6.8 3.6 6.1 IIA 1.21Tetrahydrofuran 109-99-9 Cd I −14 321 2 11.8 2.5 161.6 IIB 0.54 0.87Toluene 108-88-3 Dd I 4 480 1.1 7.1 3.1 28.53 IIA 0.24Triethylamine 121-44-8 Cd I –9 249 1.2 8 3.5 68.5 IIA 0.75 1.05Vinyl Acetate 108-05-4 Dd I −6 402 2.6 13.4 3 113.4 IIA 0.7 0.94Vinyl Chloride 75-01-4 Dd GAS −78 472 3.6 33 2.2 IIA 0.96Xylene 1330-20-7 Dd I 25 464 0.9 7 3.7 IIA 0.2 1.09

a. Type designates whether the material is a gas, flammable liquid, or combustible liquid.b. Vapor Pressure is reflected in units of mm Hg at 25°C (77°F), unless stated otherwise.c. Class I Zone Groups are based on 1996 IEC TR3 60079-20, Electrical apparatus for explosive gas atmospheres—Part 20: Data for flammable gases

and vapors, relating to the use of electrical apparatus, which contains additional data on MESG and group classifications.d. Material has been classified by test.e. When all conduits run into explosion-proof equipment are provided with explosion-proof seals installed within 450 mm (18 in.) of the enclosure,

equipment for the group classification shown in parentheses is permitted.f. For classification of areas involving ammonia, see ASHRAE 15, Safety Code for Mechanical Refrigeration, and ANSI/CGA G2.1, Safety Require-

ments for the Storage and Handling of Anhydrous Ammonia.g. Commercial grades of aliphatic hydrocarbon solvents are mixtures of several isomers of the same chemical formula (or molecular weight). The

autoignition temperatures of the individual isomers are significantly different. The electrical equipment should be suitable for the AIT of the solvent mixture.h. [deleted]i. Petroleum naphtha is a saturated hydrocarbon mixture whose boiling range is 20°C to 135°C (68°F to 275°F). It is also known as benzine, ligroin,

petroleum ether, and naphtha.j. Fuel and process gas mixtures found by test not to present hazards similar to those of hydrogen may be grouped based on the test results.k. [deleted]

Source: NFPA 497: "Recommended Practice for the Classification of Flammable Liquids, Gases, or Vapors and of Hazardous (Classified) Locations for Electrical Installations in Chemical Process Areas," 2008 ed., Table 4.4.2. Used by permission.

443

7 GENERAL INFORMATION

7.1 Terms, Symbols, and Definitions


A Area or surface area ft2 m2

a Acceleration secft2 s

m2

ci Molar concentration ftlb mole

3 mmol3

cp Heat capacitylbm FBtu-c kg K

Js Km2

2

: :=

D Diameter ft or in. m

DAB Mass diffusivity hrft2

sm2

d Distance or diameter or diagonal ft or in. m

f Moody friction factor dimensionless

f Frequency sec1

s1

g Gravitational accelerationsecft2 s

m2

h Height ft or in. m

h Convection heat-transfer coefficient hr ft FBtu- -2 c m K

Ws Kkg

2 3: :=

hm Mass-transfer coefficient hrft

sm

Dhfusion Latent heat of fusionlbmBtu

kgJ

sm2

2=

Dhvap Latent heat of vaporizationlbmBtu

kgJ

sm2

2=


444 NCEES


k Thermal conductivity - -hr ft FBtuc m K

Ws Kkg m3: :

:=

L Length ft or in. m

MW Molecular weight lbmolelbm

molkg

N Number of moles lbmole molm Mass lbm kg

P Pressure inlbf2 Pa

mN

m skg

2 2:= =

P Perimeter ft or in. m

P Probability dimensionless

r, R Radius ft or in. m

R Universal gas constant lb mole Rpsi ft

lb mole RBtuor-

--

3

c c mol KJ:

T Temperature °F or °R °C or Kt Time hr or sec s

u Velocity secft

sm

V Volume ft3 m3

Wi Mass ratio dimensionless

wi Mass fraction or weight fraction dimensionless

Xi Molar ratio dimensionless

xi Mole fraction dimensionless

x Distance ft or in. ma, b, q,

f, j Angle degree or radians

a Thermal diffusivityhrft2

sm2

β Coefficient of thermal expansion R1c K

1

gi Mass concentrationftlbm3 m

kg3

g Surface tension in.lbf

mN

skg2=

λ Molecular mean free path ft or in. m

μ Dynamic viscosity cP or -secft

lbf2 Pa s m s

kg: :=

n Kinematic viscosityhrft2

sm2

r Density ftlbm3 m

kg3

Chapter 7: General Information

NCEES 445


t Shear stress inlbf2 m

Nm skg

2 2:=

ji Volume fraction dimensionless

fi Volume concentrationftft3

3

mm3

3

7.1.1 Constants

Physical ConstantsSymbol Value Units Description

co

6.706 • 108hrmiles

Speed of light2.998 • 108 s

m

G3.44 • 10–8

lbf secft- 4

4

Gravitational constant6.674 • 10–11

kgN m

2

2:

g32.174

secft2 Gravitational acceleration

(earth)9.8067 s

m2

gc 32.174 -lbf seclbm ft- 2

Gravitational conversion factor

k5.66 • 10–24

Rft lbf-c

Boltzmann constant 1.3806 • 10–23

KJ

s Kkg m2

2

:

:=

NA

2.731 • 1026lb mole1

Avogadro's Number6.022 • 1023

mol1


446 NCEES

Physical Constants (cont'd)Symbol Value Units Description

R

8.314 mol KJ

mol Km Pa3

: ::=

Universal gas constant

83.14mol Kcm bar3

::

8314kmol Km Pa3

::

82.06mol Kcm atm3

::

0.0821 mol Kliter atm

::

62.36 mol Kliter Torr

::

62,360mol Kcm Torr3

::

10.73lb mole Rpsi ft

-- 3

c

1.987 lb mole RBtu

mol Kcal

- :c=

1545 lb mole Rft lbf

--c

0.7302lb mole Ratm ft

-- 3

c

v

1.71 • 10–9ft hr RBtu- -2 4c

Stefan-Boltzmann constant (radiation)

5.67 • 10–8m KW

s Kkg

2 4 3 4: :=

Mathematical ConstantsSymbol Value Description

p 3.14159 Archimedes constant (Pi)e 2.71828 Base of the natural logg 0.57722 Euler's constant


NCEES 447

Standard ValuesNote: The definitions for STP (standard temperature and pressure) vary between industries.

The table below contains several conditions as specified.Property Conditions U.S. Units SI Units

Molar standard volume, ideal gas (STP)

P = 1 atm = 14.696 psia T = 0°C = 32°F lb mole

ft3593 .

.

molm

molliter

0 0224

22 41

3

Molar standard volume, ideal gas (ambient)

P = 1 atm = 14.696 psia T = 15°C = 59°F

. molm0 023653

. molliter23 645

Standard cubic foot (scf) P = 1 atm = 14.696 psia T = 15.56°C = 60°F

. lbmoleft379 493

Density of air (STP) P = 1 atm = 14.696 psia T = 0°C = 32°F

.ftlbm0 0805 3 .

mkg

1 29 3

Density of air (ambient) P = 1 atm = 14.696 psia T = 15.6°C = 60°F .

ftlbm0 0764 3 .

mkg

1 22 3

Density of air (ambient) P = 1 atm = 14.696 psia T = 20°C = 68°F

.ftlbm0 0749 3 .

mkg

1 20 3

Density of mercury P = 1 atm = 14.696 psia T = 20°C = 68°F ft

lbm848 3 ,mkg

13 579 3

Density of water P = 1 atm= 14.696 psia T = 4°C = 32.9°F .

ftlbm62 4 3 1000

mkg3

Density of water P = 1 atm= 14.696 psia T = 15.6°C = 60°F .

ftlbm62 37 3 .

mkg

999 0 3

Atmospheric pressure Sea level .inlbm14 696 2 . Pa1 013 105:

Triple point of water32.02 F0.0887 psia

c 0.01109 C0.6123 kPa

c

Speed of sound in air (STP) P = 1 atm= 14.696 psia T = 0°C = 32°F 1090 sec

ftsm330

Speed of sound in air (ambient) P = 1 atm= 14.696 psia T = 20°C = 69°F 1130 sec

ftsm343

Energy of visible light Wavelength: 555 nm .cd sr hrBtu1 4 98 10 3: := − * .cd sr W1 1 46 10 3: := −

* cd • sr = candela steradian; see derived SI units for definition

7.1.2 Dimensional AnalysisA dimensionally homogeneous equation has the same dimensions on the left and the right sides of the equation. Dimensional analysis involves the development of equations that relate dimensionless groups of variables to describe physical phenomena.


448 NCEES

7.1.2.1 Buckingham Pi TheoremThe number of independent dimensionless groups that may be used to describe a phenomenon known to involve n variables is equal to the number (n-r ), where r is the number of basic dimensions (e.g., mass, length, time) needed to express the variables dimensionally.

7.1.2.2 SimilitudeTo use a model to simulate the conditions of the prototype, the model must be geometrically, kinematically, and dynamically similar to the system that is modeled. Systems that have the same dimensionless numbers are similar.

Dimensionless Numbers1

Symbol Definition Name Description

Ar g D p f2

3

n

t t t−` jp f

p f Archimedes Ratio of buoyancy forces to viscous forces for a particle (p) in a fluid (f)

Bi kh L or k A

h V Biot Ratio of internal thermal resistance of a solid body to its surface thermal resistance (used for heat transfer)

Bim Dh LAB

m Biot (mass transfer)

Ratio of the internal species transfer resistance to the boundary layer species transfer resistance (used for mass transfer)

Bo ( ) g Lv12

ct t- Bond Ratio of buoyancy force to surface tension (used for boiling and

condensation)

Brk Tu2nD

Brinkman Ratio of viscous dissipation to enthalpy change (for use in high-speed flow)

Cf u21 2t

x Drag or friction coefficient

Ratio of surface shear stress to free-stream kinetic energy; dimension-less surface shear stress

Ca uReWe

cn = Capillary Ratio of viscous forces to surface tension (for use in two-phase flow)

Cauu Masound2

22= Cauchy Ratio of inertia forces to compression forces (for use in compressible

flow)

Ec c Tup

2

DEckert Kinetic energy of flow relative to boundary-layer enthalpy difference

(for use in high-speed flow)

Eu uP

2tD

Euler Ratio of pressure to inertia force

FoLD tAB

2 Fourier Dimensionless time; ratio of rate of heat conduction to rate of internal energy storage in a solid (for use in transient heat transfer problems)

Fom Lt2a Fourier

(mass transfer)Dimensionless time; ratio of rate of heat conduction to rate of internal energy storage in a solid (for use in transient mass transfer problems)

Frg Lu2

Froude Ratio of flow inertia to gravitational forces (for flow with a free surface)

f21

DL u

P2t

DFriction factor Ratio of shear force to inertia force; dimensionless pressure drop for

internal flow

Gavg L2

3Galilei Ratio of gravitational forces to viscous forces

Grv

g T L2

3bD Grashoff Ratio of buoyancy to viscous forces (for use in natural convection)


NCEES 449

Dimensionless Numbers (cont'd)Symbol Definition Name Description

GzDx

Re Pr

Dx

u La

= Graetz Ratio of enthalpy flow rate to axial heat conduction

Jal hc T.

vap

p l

D

D

Jakob Ratio of sensible heat to latent heat (for use in film condensation and boiling)

Jav hc T.

vap

p v

D

D

jH St Pr 32 Colburn factor

(heat) Dimensionless heat transfer coefficient

jm St Scm 32 Colburn factor

(mass) Dimensionless mass transfer coefficient

Ka g3

4

tc

n Kapitza Ratio of surface tension forces to viscous forces (used for waves on a liquid film)

Kn Lm Knudsen Ratio of mean free path to a characteristic length (for use in non-

continuum flow)

Le DABa Lewis Ratio of molecular thermal diffusivity to mass diffusivity

Ma uusound Mach Dimensionless velocity; ratio of velocity to speed of sound (for use in

compressible flow)

Nukh L Nusselt

Dimensionless heat transfer coefficient; ratio of convection heat trans-fer to conduction in a fluid layer of thickness L (for use in convective heat transfer)

Pe u L Re Pra =3 Peclet Ratio of enthalpy flow rate to heat conduction rate (for use in forced convection heat transfer)

Pem Du L Re ScAB

=3 Peclet (mass transfer)

Ratio of enthalpy flow rate to heat conduction rate (for use in forced convection mass transfer)

Prkcpn Prandtl

Relative effectiveness of molecular transport of momentum and energy within the boundary layer; ratio of molecular momentum dif-fusivity to thermal conductivity (for use in convective heat transfer)

Rav

g T LPr2

3bD Raleigh Product of Grashoff and Prandtl numbers (for use in natural convec-tion)

Re u Dnt Reynolds Ratio of inertia and viscous forces (for use in forced convection and

fluid flow)

Sc DvAB Schmidt Ratio of molecular momentum diffusivity to mass diffusivity (for use

in convective mass transfer)

Sh Dh LAB

m Sherwood Ratio of convection mass transfer to diffusion in a slab of thickness L (for use in convective mass transfer)

Sk uP LnD Stokes Ratio of pressure force to viscous force

St Re PrNu

u chpt

=Stanton

Dimensionless heat transfer coefficient, ratio of actual convection heat flux to enthalpy energy heat flux (for use in forced convection heat transfer)

Stm Re ScSh

uhm=

Stanton (mass)

Dimensionless mass transfer coefficient (for use in forced convection mass transfer)


450 NCEES

Dimensionless Numbers (cont'd)Symbol Definition Name Description

Stehc Tfusion

p

D

D Stefan Ratio of sensible heat to latent heat for the solid/liquid transition (for use in melting and solidification)

Sr uL f Strouhal Time characteristics of fluid flow (for use in oscillating flow)

We u L2

ct Weber Ratio of inertial to surface tension forces (for use in liquid/vapor

phase change)

1Verify whether gravitational constant (gc) is required before using.

7.2 Units of Measurement

7.2.1 Metric Prefixes

Metric Prefixes and Their SymbolsMultiple Prefix Symbol

10–18 atto a10–15 femto f10–12 pico p10–9 nano n10–6 micro μ10–3 milli m10–2 centi c10–1 deci d101 deka da102 hecto h103 kilo k106 mega M109 giga G1012 tera T1015 peta P1018 exa E

7.2.2 Base and Derived SI Units

Base SI UnitsQuantity Name Symbol

Length meter mMass kilogram kgTime second sElectric current ampere ATemperature Kelvin KAmount of a substance mol molLuminous intensity candela cd


NCEES 451

Derived SI Units With Special NamesQuantity Unit

Name Symbol Name Symbol Definition

Electric capacitance C farad F F VC

JA s

kg mA s2 2

2

2 4:::= = =

Electric charge Q coulomb C C A s:=

Electric conductance G siemens S S 1VA

JA s

kg mA s2

2

2 3:::

X= = = =

Energy or work or heat H joule J J N m skg m

2

2

::

= =

Force F newton N N skg m

2:

=

Frequency f hertz Hz Hz s1=

Inductance L henry H H s AV s

A skg m2 2

2

::

:

:X= = =

Electric potential E volt V V A sJ

A skg m2 3

2

: :

:= =

Power or energy flux P watt W W sJ

sN m

skg m

3

2: :

= = =

Pressure or stress P pascal Pa Pa mN

m skg

2 2:= =

Electric resistance R ohm Ω AV

A skg m2 3

2

:

:X = =

Illuminance lux lx lx mlm

mcd sr

2 2:= =

Luminous flux VU lumen lm lm cd sr:=

Magnetic flux UE weber Wb Wb V s s Akg m2

2

::

:= =

Magnetic flux density tesla T T mWb

mV s

s Akg

2 2 2:

:= = =

Note: Steradian or square radian (sr) is dimensionless and represents a solid angle in three-dimensional space (angle at the tip of a cone).


452 NCEES

7.2.3 Unit Conversion Tables (U.S. and Metric)

TimeTime Second (sec) Minute (min) Hour (hr) Day Week Year

1 sec = 1 0.01667 2.7778E–04 1.1574E–05 1.6534E–06 3.1710E–081 min = 60 1 0.01667 6.9444E–04 9.9206E–05 1.9026E–061 hr = 3600 60 1 0.04167 5.9524E–03 1.1416E–041 day = 8.6400E+04 1440 24 1 0.14286 2.7397E–031 week = 6.0480E+05 1.0080E+04 168 7 1 0.019181 year = 3.1536E+07 5.2560E+05 8760 365 52.143 1

Additional Unit Conversions for Time1 fortnight = 3.4560 • 105 sec = 14 days

7.2.3.1 Angle

Conversion Table for the Most Commonly Used Units of an AngleAngle Degree (°) rad Minute (') Second (") Revolution

1° = 1 0.01745 60 3600 2.7778E–031 rad = 57.296 1 3437.7 2.0626E+05 0.159151' = 0.01667 2.9089E–04 1 60 4.6296E–051" = 2.7778E–04 4.8481E–06 0.01667 1 7.7161E–071 rev = 360 6.2832 2.1600E+04 1.2960E+06 1

7.2.3.2 Length

Conversion Table for the Most Commonly Used Units of LengthLength m in ft yd mile mil

1 m = 1 39.370 3.2808 1.0936 6.2135E–04 3.9370E+041 in = 0.0254 1 0.0833 0.02778 1.5782E–05 10001 ft = 0.3048 12 1 0.3333 1.8939E–04 1.2000E+041 yd = 0.9144 36 3 1 5.6816E–04 3.6000E+041 mile = 1609.4 6.3362E+04 5280.2 1760.1 1 6.3362E+071 mil = 2.5400E–05 0.001 8.3333E–05 2.7778E–05 1.5782E–08 1


NCEES 453

Additional Unit Conversions for Length1 league = 4828.2 m = 3 miles

1 m (micron) = 1 • 10–6 m = 3.937 • 10–5 in.1 mile (nautical) = 1853.3 m = 1.1515 miles1 nautical league = 5559.9 m = 3 nautical miles

1 furlong = 201.17 m = 81 mile

1 perch = 1 rod = 1 pole = 5.292 m = 5.5 yds = 41 chain

1 fathom = 1.8288 m = 6 ft = 2 yds1 cable length (U.S. Survey) = 219.456 m = 120 fathoms = 240 yd

1 chain (U.S. Survey) = 20.117 m = 0.1 furlong1 link = 0.2012 m = 0.001 furlong

1 cubit = 0.4572 m = 21 yard = 18 in.

1 bolt = 36.576 m = 40 yd1 skein = 109.728 m = 120 yd1 span = 0.2286 m = 9 in.

1 hand (horses) = 0.1016 m = 4 in.

1 caliber = 2.54 • 10–4 m = 1001 in.

1 Å (Angström) = 1 • 10–10 m = 3.937 • 10–9 in.1 fermi = 1 • 10–15 m = 3.937 • 10–14 in.

1 astronomical unit = 1.496 •1011 m = 9.2954 • 107 miles1 light year = 9.4605 • 1015 m = 5.8783 • 1012 miles

1 mm = 0.001 m = 0.03937 in.1 cm = 0.01 m = 0.3937 in.1 km = 1000 m = 0.62135 mile

7.2.3.3 Area

Conversion Table for the Most Commonly Used Units of AreaArea m2 in2 ft2 yd2 acre sq mile

1 m2 = 1 1550 10.764 1.196 2.4710E–04 3.8610E–091 in2 = 6.4516E–04 1 6.9444E–03 7.7160E–04 1.5942E–07 2.4910E–121 ft2 = 0.09290 144 1 0.1111 2.2957E–05 3.5870E–101 yd2 = 0.83613 1296 9 1 2.0661E–04 3.2283E–091 acre = 4046.9 6.2727E+06 4.3560E+04 4840 1 1.5625E–051 sq mile = 2.5900E+06 4.0145E+09 2.7879E+07 3.0976E+06 640 1


454 NCEES

Additional Unit Conversions for Area

1 circ mil = 5.067 • 10–10 m2 = 4r sq.mil = 7.8539 • 10–7 in2

1 circ inch = 5.0671 • 10–4 m2 = 4r in2 = 0.78539 in2

1 ha (hectare) = 1 • 104 m2 = 2.471 acres1 township = 9.324 • 107 m2 = 144 homesteads

1 homestead = 6.475 • 105 m2 = 160 acres1 rood = 1011.725 m2 = 0.25 acre

1 sq rod = 25.2926 m2 = 30.25 sq. yd1 section = 2.59 • 108 m2 = 1 sq. mile

1 barn (bn) = 1 • 10–28 m2 = 100 fm2 (femtometer)1 are = 100 m2 = 119.6 sq. yd

1 centiare = 1 m2 = 10.764 ft2

1 mm2 = 1 • 10–6 m2 = 1.55 • 10–3 in2

1 cm2 = 1 • 10–4 m2 = 0.155 in2

1 km2 = 1 • 106 m2 = 0.3861 sq. mile

7.2.3.4 Volume

Conversion Table for the Most Commonly Used Units of VolumeVolume m3 in3 ft3 gal barrel (oil) liter

1 m3 = 1 6.1024E+04 35.314 264.20 6.2901 10001 in3 = 1.6387E–05 1 5.7870E–04 4.3295E–03 1.0308E–04 0.016391 ft3 = 0.02832 1728 1 7.4814 0.17812 28.3171 gal = 3.7850E–03 231 0.13367 1 0.02381 3.78501 barrel = 0.15898 9701.6 5.6143 42.0 1 158.981 liter = 0.001 61.024 0.03531 0.2642 6.2901E–03 1


NCEES 455

Additional Unit Conversions for Volume1 yd3 = 0.7646 m3 = 27 ft3

1 register ton = 2.8317 m3 = 100 ft3

1 dry gal (U.S.) = 4.405 • 10–3 m3 = 1.164 gal (U.S.)1 U.S. bushel = 0.0353 m3 = 8 dry gal (U.S.) = 9.31 gal (U.S.)

1 quart (U.S.) = 9.4625 • 10–4 m3 = 41 gal (U.S.)

1 pint (U.S.) = 4.7313 • 10–4 m3 = 81 gal (U.S.) = 2

1 quart (U.S.)

1 cup (U.S.) = 2.3656 • 10–4 m3 = 21 pint = 16

1 gal (U.S.)

1 gill (U.S.) = 1.1828 • 10–4 m3 = 41 pint = 32

1 gal (U.S.)

1 fl oz (U.S.) = 2.9570 • 10–5 m3 = 81 cup = 128

1 gal (U.S.)

1 fl dram (U.S.) = 3.6963 • 10–6 m3 = 81 fl oz = 1024

1 gal (U.S.)

1 minim (U.S.) = 6.1605 • 10–8 m3 = 601 dram = 480

1 fl oz

1 cm3 = 1 ml = 1 • 10–6 m3 = 0.06102 in3

1 mm3 = 1 • 10–9 m3 = 6.1024 • 10–5 in3

1 hectoliter = 0.1 m3 = 26.42 gal (U.S.)1 hogshead = 0.2385 m3 = 63 gal (U.S.)

1 UK bushel = 0.0364 m3 = 8 dry gal (UK)1 Imperial gal (UK) = 0.0045 m3 = 1.201 gal (U.S.)

1 quarter (UK) = 0.291 m3 = 64 gal (UK)1 peck (UK) = 0.0091 m3 = 2 gal (UK)

1 quart (UK) = 0.0011 m3 = 41 gal (UK)

1 pint (UK) = 5.6826 • 10–4 m3 = 81 gal (UK)

1 barrel (UK) = 0.1637 m3 = 36 gal (UK) = 43 gal (U.S.)1 barrel (U.S. liq) = 0.1192 m3 = 31.503 gal (U.S.) = 26 gal (UK)

1 barrel (U.S. dry) = 0.1156 m3 = 30.55 gal (U.S.)1 cord (lumber) = 3.625 m3 = 128 ft3

1 stere (lumber) = 1 m3 = 1.308 yd3

1 boardfoot (lumber) = 2.3597 • 10–6 m3 = 121 ft3

U.S. Conversion for Liquid Volume1 gal (U.S.) = 4 quarts

1 quart = 2 pints1 pint = 2 cups1 cup = 8 fl oz


456 NCEES

U.S. Conversion for Dry Volume1 cup = 16 tablespoons (Tbsp)

1 Tbsp = 3 teaspoons (tsp)1 tsp = 8 pinches

1 pinch = 2 dashes7.2.3.5 Mass

Conversion Table for the Most Commonly Used Units of MassMass kg lbm oz ton (short) ton (long) slug

1 kg = 1 2.2046 35.273 1.1023E–03 9.8420E–04 0.068521 lbm = 0.45359 1 16 5.0000E–04 4.4642E–04 0.031081 oz = 0.02835 0.0625 1 3.1251E–05 2.7902E–05 1.9426E–031 ton (short) = 907.18 2000 3.1999E+04 1 0.89285 0.621621 ton (long) = 1016.1 2240 3.5840E+04 1.12 1 69.6221 slug = 14.594 32.174 514.78 0.01608 0.014363 1

Additional Unit Conversions for Mass1 hundredweight (short) = 45.3592 kg = 100 lbm1 hundredweight (long) = 50.8023 kg = 112 lbm

1 tonne (metric) = 1000 kg = 2204.6 lbm1 centner = 100 kg = 220.5 lbm

1 dram = 1.7719 • 10–3 kg = 0.0625 oz1 grain = 6.4799 • 10–5 kg = 2.2857 • 10–3 oz1 carat = 2.0000 • 10–4 kg = 7.0547 • 10–3 oz

1 atomic mass unit = 1.6605 • 10–27 kg = 3.6608 • 10–27 lbm

1 mkgf s2: = 9.8067 kg = 21.62 lbm

1 stone = 6.3503 kg = 14 lbm1 firkin = 40.8231 kg = 90 lbm

1 lb (apothecary/troy) = 0.3732 kg = 13.166 oz = 12 oz (ap/troy) = 0.8229 lbm1 oz (apothecary/troy) = 3.1103 • 10–2 kg = 1.0971 oz

1 dram (apothecary) = 3.8879 • 10–3 kg = 0.13714 oz1 scruple (apothecary) = 1.2960 • 10–3 kg = 0.04571 oz

1 grain (apothecary/troy) = 6.4799 • 10–5 kg = 2.2857 • 10–3 oz = 1.4286 • 10–4 lbm1 carat (troy) = 2.0500 • 10–4 kg = 7.231 • 10–3 oz

1 pennyweight (troy) = 1.5552 • 10–3 kg = 0.05486 oz1 mite (troy) = 3.2400 • 10–6 kg = 1.1428 • 10–4 oz1 doite (troy) = 1.3500 • 10–7 kg = 4.7618 • 10–6 oz


NCEES 457

Apothecary Measures1 lb = 373.242 grain1 lb = 12 oz1 oz = 8 drams

1 dram = 3 scruples1 scruple = 20 grains

Troy Measures1 lb = 373.242 grain1 lb = 12 oz (ozt)

1 ozt = 20 pennyweight (dwt)1 dwt = 24 grains

1 grain = 20 mites1 mite = 24 doites

7.2.3.6 Density

Conversion Table for the Most Commonly Used Units of Density

Densitymkg3 ft

lbm3 gal

lbmliterkg

inlbm

3 ydton

3

mkg

1 3 = 1 0.06243 8.3452E–03 0.001 3.6128E–05 7.5250E–04

ftlbm1 3 = 16.018 1 0.13367 0.01618 5.7870E–04 0.01205

gallbm1 = 119.83 7.481 1 0.11983 4.3292E–03 0.09017

literkg

1 = 1000 62.43 8.3452 1 0.036128 0.7525

inlbm1 3 = 2.7679E+04 1728 231 27.679 1 20.829

ydton1 3 = 1328.9 82.963 11.09 1.3289 0.048011 1


458 NCEES

Additional Unit Conversions for Density

ftslug1 3 = .

mkg

515 379 3 = .ftlbm32 175 3

literg

1 =mkg1 3 = .

ftlbm0 06243 3

galoz1 = .

mkg

7 4906 3 = .ftlbm0 46764 3

ftgrain1 3 = .

mkg

0 0023 3 = .ftlbm1 4286 10 43:

-

UK gallbm1 = .

mkg

99 978 3 = .ftlbm6 2416 3

Specific gravity (also called relative density): The ratio of the density of a substance to the density of water at 4°C (39°F):

SG1000

mkg 62.4

ftlbm

3 3

t t= =

API gravity:

. . ; ..API SG SG API

141 5 131 5 131 5141 5

FF

6060= − = +cc

7.2.3.7 Specific Volume

Conversion Table for the Most Commonly Used Units of Specific Volume

Specific Volume kg

m3

kgliter

lbmft3

lbmgal

lbmin3

kgft3

kgm13

= 1 1000 16.018 119.76 2.7680E+04 35.314

kgliter1 = 0.001 1 0.01602 0.11976 27.68 0.03531

lbmft13

= 0.06243 62.428 1 7.4764 1728 2.2046

lbmgal

1 = 8.3500E–03 8.35 0.13375 1 231 0.29488

lbmin13

= 3.6127E–05 0.03613 5.7870E–04 4.3266E–03 1 1.2758E–03

kgft13

= 0.02832 28.317 0.45359 3.3913 783.81 1


NCEES 459

7.2.3.8 Velocity

Conversion Table for the Most Commonly Used Units of Velocity

Velocity sm

secft

minft

hrmiles

hrkm knots

sm1 = 1 3.2808 196.85 2.2369 3.6 1.9423

secft1 = 0.3048 1 60 0.68182 1.0973 0.592

minft1 = 5.0800E–03 0.01667 1 0.01136 0.018288 9.8667E–03

hrmile1 = 0.44704 1.4667 88 1 1.6093 0.86827

hrkm1 = 0.27778 0.91134 54.681 0.62137 1 0.53952

1 knot = 0.51486 1.6892 101.35 1.1517 1.8535 1

7.2.3.9 Acceleration

Conversion Table for the Most Commonly Used Units of Acceleration

Accelerationsm2 sec

ft2

.secin2 s

cm2

ghr skm:

sm1 2 = 1 3.2808 39.37 0.01 0.10197 3.569

secft1 2 = 0.3048 1 12 3.0480E–03 0.03108 1.0878

.1secin2 = 0.0254 0.08333 1 2.5400E–04 2.5901E–03 0.09065

scm1 2 = 100 328.08 3937 1 10.197 356.9

1 g = 9.8067 32.174 386.09 0.09807 1 35

hr skm1 :

= 0.28019 0.91926 11.031 2.8019E–03 0.02857 1


460 NCEES

7.2.3.10 Volumetric Flow

Conversion Table for the Most Commonly Used Units of Volumetric FlowVolumetric

Flow sm3

mingal

hrft3 *

daybarrel **

dayMMgal

secft3

sm13

= 1 1.5851E+04 1.2713E+05 5.4345E+05 22.8 35.314

mingal

1 = 6.3089E–05 1 8.0207 34.286 1.4384E–03 2.2280E–03

hrft13

= 7.8658E–06 0.12468 1 4.2747 1.7934E–04 2.7778E–04

daybarrel1 = 1.8401E–06 0.02917 0.23394 1 4.1954E–05 6.4982E–05

dayMMgal

1 = 0.04386 695.2 5576 2.3835E+04 1 1.5489

secft13

= 0.02832 448.84 3600 1.5389E+04 0.64563 1

* 1 barrel of oil = 42 gallons ** million gallons

Additional Unit Conversions for Volumetric Flow

minft13

= . sm4 7195 10 43

:- = .

. .minU S gal

7 4807

hrgal1 = . s

m1 0515 10 63

:- = .

. .minU S gal

0 01667

minUK gal1 = . s

m7 5766 10 53

:- = .

. .minU S gal

1 201

hrUK gal1 = . s

m1 2628 10 63

:- = .

. .minU S gal

0 02

( )day

MMgal UK1 = . s

m0 05263 = .

. .minU S gal

834 01

hrm13

= 3600 hrm3 = .

. .minU S gal

5 7062 107:

sliter1 = . s

m0 0013

= .. .minU S gal

951 04

minliter1 = . s

m0 063

= .. .minU S gal

15 851

sliter1n = s

m10 93

- = .. .minU S gal

1 5851 10 5:-

smliter1 = s

m10 63

- = .. .minU S gal

0 01585


NCEES 461

7.2.3.11 Mass Flow

Conversion Table for the Most Commonly Used Units of Mass Flow

Mass Flow skg

hrlbm

minlbm

hrkg *

yearMMlbm ( )

dayton short

skg1 = 1 7936.5 132.28 3600 69.524 95.238

hrlbm1 = 1.2600E–04 1 0.01667 0.4536 8.7600E–03 0.012

minlbm1 = 7.5600E–03 60 1 27.216 0.5256 0.72

hrkg1 = 2.7778E–04 2.2046 0.03674 1 0.01931 0.02646

yearMMlbm1 = 0.01438 114.16 1.9026 51.781 1 1.3699

( )day

ton short1 = 0.0105 83.33 1.3889 37.8 0.73 1

* million pounds

Additional Unit Conversions for Mass Flow

( )day

ton long1 = . s

kg0 0118 = , hr

lbm930 333

( )hr

ton short1 = . s

kg0 2520 = 2000 hr

lbm

( )hr

ton long1 = . s

kg0 2822 = 2240 hr

lbm

hrslug1 = . s

kg4 0539 10 3:

- = . hrlbm32 174

seclbm1 = . s

kg0 4536 = 3600 hr

lbm


462 NCEES

7.2.3.12 Mass Flux

Conversion Table for the Most Commonly Used Units of Mass Flux

Mass Fluxs mkg

2: hr mkg

2: s cmg

2: -hr ftlbm

2 -sec ftlbm

2 sec inlbm

- 2

1s mkg

2:= 1 3600 0.1 737.35 0.20482 1.4223E–03

1hr mkg

2:= 2.7778E–04 1 2.7778E–05 0.20482 5.6894E–05 3.9510E–07

1s cmg

2:= 10 3.6000E+04 1 7373.5 2.0482 0.01422

hr ftlbm1

- 2 = 1.3562E–03 4.8823 1.3562E–04 1 2.7777E–04 1.9290E–06

sec ftlbm1

- 2 = 4.8824 1.7577E+04 0.48824 3600 1 6.9444E–03

sec inlbm1

- 2 = 703.07 2.5310E+06 70.307 5.1841E+05 144 1

7.2.3.13 Force

Conversion Table for the Most Commonly Used Units of Force

Force Ns

kg m2:

= lbf -pdlslb ftecm

2= dynes

g cm2:

= kg kilopond (kp)f = ozf

1 N = 1 0.22481 7.233 1.0000E+05 0.10197 3.59691 lbf = 4.4482 1 32.174 4.4482E+05 0.45359 161 pdl = 0.13825 0.03108 1 1.3825E+04 0.01410 0.49731 dyne = 1.0000E–05 2.2481E–06 7.2330E–05 1 1.0197E–06 3.5969E–051 kgf = 9.8067 2.2046 70.932 9.8067E+05 1 35.2741 ozf = 0.27801 0.0625 2.0109 2.7801E+04 0.02835 1

Additional Unit Conversions for Force

1s

kg mDyne12

:= = 1 N = 0.22481 lbf

1 dyne = N1 10 5:- = . lbf0 22481 10 5:

-

1 ton (long)f = 9964 N = 2240 lbf

1 ton (short)f = 8896.44 N = 2000 lbf

1 kip 1 kilo lbf= = 4448.2 N = 1000 lbf1 pond = 1 p = 0.0098 N = 2.2046 • 10–3 lbf


NCEES 463

7.2.3.14 Pressure/Stress

Conversion Table for the Most Commonly Used Units of Pressure

Pressure Pam skg

2:= psi

inlbf2= * Torr = mmHg in w. c.** bar atm

1 Pa = 1 1.4504E–04 7.5008E–03 4.0148E–03 1.0000E–05 9.8717E–061 psi*= 6894.8 1 51.716 27.681 0.06895 0.068061 Torr = 133.32 0.01934 1 0.53525 1.3332E–03 1.3161E–031 in w. c.** = 249.08 0.03613 1.8683 1 2.4908E–03 2.4588E–031 bar = 1.0000E+05 14.504 750.08 401.48 1 0.987171 atm = 1.0130E+05 14.696 759.83 406.7 1.013 1

*0 psig (gauge) = 14.696 psia (absolute) = 1 atm = 1.013 • 105 Pa ** inches water column

Additional Unit Conversions for Pressure and Stress

mN

m skg

1 12 2:= = 1 Pa = 1.4504 • 10–4 psi

1 in Hg = 3386.6 Pa = 0.49118 psi

ftlbf1 2 = 47.8803 Pa = 6.9444 • 10–3 psi

atcmkgf

1 1 2= = 9.8067 • 104 Pa = 14.223 psi

. .mm w cmkgf

1 1 2= = 9.8067 Pa = 1.4223 • 10–3 psi

1 ft w. c. = 2988.98 Pa = 0.4335 psi

cmdyne1 2 = 0.1 Pa = 1.4504 • 10–5 psi

ftpdl1 2 = 1.4882 Pa = 2.1584 • 10–4 psi

mpdl1 2 = 0.1383 Pa = 2.0052 • 10–5 psi

( )in

tonf long1 2 = 1.5444 • 107 Pa = 2240 psi

1 intonf (short)

2 = 1.3790 • 107 Pa = 2000 psi

cmN1 2 = 1 • 104 Pa = 1.4504 psi

ftlbm g1

-2 = 47.88 Pa = 6.9444 • 10–3 psi

1 bar =cmdyne

1 106 2: = 0.98692 atm


464 NCEES

7.2.3.15 Energy and Torque

Conversion Table for the Most Commonly Used Units of Energy (Work or Heat)

Energy Js

kg m2

2:= Btu kcal kWh ft-lbf hp-hr

1 J = 1 9.4778E–04 2.3885E–04 2.7778E–07 0.73757 3.7251E–071 Btu = 1055.1 1 0.25201 2.9308E–04 778.21 3.9303E–041 kcal = 4186.8 3.9682 1 1.1630E–03 3088.1 1.5596E–031 kWh = 3.6000E+06 3412 859.85 1 2.6553E+06 1.3411 ft-lbf = 1.3558 1.2850E–03 3.2383E–04 3.7661E–07 1 5.0504E–071 hp-hr = 2.6845E+06 2544.3 641.19 0.7457 1.9800E+06 1

Additional Unit Conversions for Energy (Work or Heat) and Torque

skg m

N m W s1 1 12

2:: := = = 1 J = 9.4778 • 10–4 Btu

1 therm = 1.0551 • 108 J = 105 Btu1 cal = 0.001 kcal = 4.1868 J = 3.9682 • 10–3 Btu

1 CHU = 1899.1 J = 1.8 Btu1 ton-hr (refrigeration) = 1.2661 • 107 J = 1.2 • 104 Btu

1 PS • hr (metric) = 2.6478 • 106 J = 2509.5 Btu1 kgf • m = 9.8067 J = 9.2946 • 10–3 Btu

1 dyne • cm = 1 erg = 1 • 10–7 J = 9.4778 • 10–11 Btu1 Dyne • m = 1 J = 9.4778 • 10–4 Btu

1 lbf -in = 0.113 J = 1.0708 • 10–4 Btu1 ft-pdl = 0.0421 J = 3.9938 • 10–5 Btu

1 ton (explosives) = 4.1840 • 109 J = 3.9655 • 106 Btu1 eV = 1.6022 • 10–19 J = 1.5185 • 10–22 Btu

1 hp-hr (UK) = 2.5645 • 106 J = 2430.6 Btu1 psi-ft3 = 195.2401 J = 0.18504 Btu

1 atm • cm3 = 0.1013 J = 9.601 • 10–5 Btu


NCEES 465

7.2.3.16 Specific Enthalpy

Conversion Table for the Most Commonly Used Units of Specific Enthalpy Specific

Enthalpy kgJ

lbmBtu

kgkcal -

lbmhp hr

kgkWh

lbmlbf ft-

kgJ1 = 1 4.2992E–04 2.3885E–04 1.6897E–07 2.7778E–07 0.33456

lbmBtu1 = 2326 1 0.55556 3.9301E–04 6.4611E–04 778.18

kgkcal1 = 4186.8 1.8 1 7.0743E–04 1.1630E–03 1400.7

-lbmhp hr1 = 5.9184E+06 2544.4 1413.6 1 1.644 1.9800E+06

kgkWh1 = 3.6000E+06 1547.7 859.85 0.60828 1 1.2044E+06

-lbmlbf ft1 = 2.989 1.2851E–03 7.1392E–04 5.0505E–07 8.3029E–07 1

Additional Unit Conversions for Specific Enthalpy

kgkcal

lbmCHU

gcal1 1 1= = = . kg

J4186 8 = 1.8 lbmBtu

kgkgf m1

: = . kgJ9 8067 = 4.2161 • 10–3 lbm

Btu

-lbmpsi ft1

3= . kg

J430 4329 = 0.18505 lbmBtu

gatm cm1

3: = . kgJ101 3 = 0.04355 lbm

Btu

7.2.3.17 Calorific Value

Conversion Table for the Most Commonly Used Units of Calorific Value Calorific

Value mJ3 ft

Btu3 m

kcal3 ft

therm3 gal

thermftCHU

3

mJ1 3 = 1 2.6838E–05 2.3885E–04 2.6838E–10 3.5971E–11 1.4910E–05

ftBtu1 3 = 3.7260E+04 1 8.8994 1.0000E–05 1.3403E–06 0.55556

mkcal1 3 = 4186.8 0.11237 1 1.1237E–06 1.5060E–07 0.06243

fttherm1 3 = 3.7260E+09 1.0000E+05 8.8994E+05 1 0.13403 5.5556E+04

galtherm1 = 2.7800E+10 7.4611E+05 6.6399E+06 7.4611 1 4.1451E+05

ftCHU1 3 = 6.7067E+04 1.8 16.019 1.8000E–05 2.4125E–06 1


466 NCEES

7.2.3.18 Entropy

Conversion Table for the Most Common Units of Entropy

Entropy KJ Btu

cF Ckcal Clausiusc

= CCHUc

kcalcF

KJ1 = 1 5.2654E–04 2.3885E–04 5.2654E–04 4.2992E–04

FBtu1 o = 1899.2 1 0.45361 1 0.8165

Ckcal1 o = 4186.8 2.2045 1 2.2045 1.8

CCHU1 o = 1899.2 1 0.45361 1 0.8165

kcal1 o =F 2326.0 1.2247 0.5556 1.2247 1

7.2.3.19 Power

Conversion Table for the Most Commonly Used Units of Power

Power W hrBtu

hrkcal hp hr

therm ton refrigeration

1 W = 1 3.4120 0.85985 1.3404E–03 3.4120E–05 2.8434E–04

hrBtu1 = 0.29308 1 0.252 3.9285E–04 1.0000E–05 8.3335E–05

hrkcal1 = 1.1630 3.9682 1 1.5589E–03 3.9682E–05 3.3069E–04

1 hp = 746.04 2545.5 641.48 1 0.02546 0.21213

hrtherm1 = 2.9308E+04 1.0000E+05 2.5200E+04 39.285 1 8.3335

1 ton refrigeration = 3516.9 1.2000E+04 3024.0 4.7141 0.12 1


NCEES 467

Additional Unit Conversions for Power

sJ V A

skg m

1 3

2

::= = = 1 W = 3.412 hr

Btu

skgf m1

: = 9.8067 W = 33.461 hrBtu

hratm m1

3: = 28.15 W = 96.049 hrBtu

1 PS (metric) = 735.48 W = 2509.5 hrBtu

serg1 = 1 • 10–7 W = 3.412 • 10–7 hr

Btu

hrCHU1 = 0.5275 W = 1.8 hr

Btu

minlbf ft1 - = 0.0226 W = 0.0771 hr

Btu

seclbf ft1 - = 1.3558 W = 4.626 hr

Btu

secpdl ft1

- = 0.0421 W = 0.14378 hrBtu

1 hp (British) = 756.7 W = 2581.9 hrBtu

1 hp (Boiler) = 9809.5 W = 3.347 • 104 hrBtu

7.2.3.20 Heat Flux

Conversion Table for the Most Commonly Used Units of Heat Flux

Heat FluxmW2 ft hr

Btu-2 m hr

kcal2 : cm s

cal2 : ft hr

kcal-2 ft hr

CHU-2

mW1 2 = 1 0.317 0.85985 2.3885E–05 0.07989 0.17611

ft hrBtu1

-2= 3.1546 1 2.7125 7.5346E–05 0.25201 0.55554

m hrkcal1 2 :

= 1.163 0.36867 1 2.7778E–05 0.09291 0.20481

cm scal1 2 :

= 4.1868E+04 1.3272E+04 3.6000E+04 1 3344.6 7372.2

ft hrkcal1

-2= 12.518 3.9682 10.764 2.9899E–04 1 2.2045

ft hrCHU1

-2= 5.6784 1.8 4.8825 1.3563E–04 0.45362 1


468 NCEES

7.2.3.21 Dynamic Viscosity

Conversion Table for the Most Commonly Used Units of Dynamic ViscosityViscosity

(dynamic) Pa • s cP Poise secft

lbf -2 in

lbf sec-2 ft sec

lbm-

1 Pa • s = 1 1000 10 0.02089 1.4504E–04 0.67195

1 cP = 0.001 1 0.01 2.0885E–05 1.4504E–07 6.7195E–04

1 Poise = 0.1 100 1 2.0885E–03 1.4504E–05 0.06720

secft

lbf1 -2 = 47.88 4.7880E+04 478.8 1 6.9444E–03 32.173

secin

lbf1 -2 = 6894.8 6.8948E+06 6.8948E+04 144 1 4633

secftlbm1 - = 1.4882 1488.2 14.882 0.03108 2.1585E–04 1

Additional Unit Conversions for Dynamic Viscosity

Poise cm sg

cmdyne s

1 1 1 2::= = = 0.1 Pa • s = 2.0885 • 10–3

ftlbf sec-

2

--ft

lbf secft sslug

1 12 = = 47.8803 Pa • s = 1 secft

lbf -2

--

ft slbm

ftpdl s

1 2= = 1.4882 Pa • s = 0.03108 secft

lbf -2

-ft hrlbm1 = 4.1338 • 10–4 Pa • s = 8.6336 • 10–6 sec

ftlbf -

2

mkgf s1 2

: = 9.8067 Pa • s = 0.20482 secft

lbf -2

mkgf hr1 2

: = 3.5320 • 10–4 Pa • s = 7.3767 • 10–6 secft

lbf -2

ft hrkg

1 : = 9.1134 • 10–4 Pa • s = 1.9034 • 10–5 secft

lbf -2


NCEES 469

7.2.3.22 Diffusion Coefficient, Thermal Diffusivity, and Kinematic Viscosity

Conversion Table for the Most Commonly Used Units of the Diffusion Coefficient, Thermal Diffusivity, and Kinematic Viscosity

Diffusivity sm2

scmSt

*2= sec

ft2hrft2

secin2

in. hrliter

-

sm12

= 1 1.0000E+04 10.764 3.8751E+04 1550 9.1441E+04

scmSt1

*2= = 1.0000E–04 1 1.0764E–03 3.8751 0.155 9.1441

secft12

= 0.09290 929.03 1 3600 144 8495.2

hrft12

= 2.5806E–05 0.25806 2.7777E–04 1 0.04 2.3597

secin12

= 6.4516E–04 6.4516 6.9444E–03 25 1 58.994

1 in. hrliter

- = 1.0936E–05 0.10936 1.1771E–04 0.42378 0.01695 1

* St = Stokes

7.2.3.23 Heat Capacity and Specific Entropy

Conversion Table for the Most Commonly Used Units of Heat Capacity and Specific Entropy

Heat Capacity m KW: Flbm

Btu-c lbm R

lbf ft--c

=

m kW1 :

= 1 2.3885E–04 0.18586

F1 lbmBtu

-c = 4186.8 1 778.17

1 lbm Rlbf ft

--c

= 5.3803 1.2851E–03 1

F1 lbmBtu 1 kg C

kcal 1 g Ccal 1 lbm C

CHU- -: :c c c c

= = =


470 NCEES

7.2.3.24 Thermal Conductivity

Conversion Table for the Most Commonly Used Units of Thermal ConductivityThermal

Conductivity m KW: hr ft F

Btu- -c hr ft F

Btu in- -

-2 c hr m C

kcal: : c s cm C

cal: : c

m KW1 :

= 1 0.57777 6.9334 0.85985 2.3885E–03

1 hr ft FBtu- -c = 1.7308 1 12 1.4882 4.1339E–03

1hr ft FBtu in- -

-2 c

= 0.14423 0.08333 1 0.12402 3.4449E–04

1 hr m Ckcal: : c

= 1.163 0.67194 8.0635 1 2.7778E–03

1 s cm Ccal: : c

= 418.68 241.9 2902.9 360 1

1 hr ft FBtu 1 hr ft C

CHU- - - -c c

=

7.2.3.25 Heat-Transfer Coefficient

Conversion Table for the Most Commonly Used Units of the Heat-Transfer CoefficientHeat-Transfer

Coefficient m KW2 : hr ft F

Btu- -2 c sec ft F

Btu- -2 c hr m C

kcal2: : c s cm C

cal2: : c hr ft C

kcal- -2 c

m KW1 2 :

= 1 0.1761 4.8919E–05 0.85985 2.3885E–05 0.07989

1hr ft FBtu- -2 c

= 5.6785 1 2.7779E–04 4.8826 1.3563E–04 0.45363

1sec ft FBtu- -2 c

= 2.0442E+04 3599.8 1 1.7577E+04 0.48824 1633

1hr m Ckcal

2: : c= 1.1630 0.20481 5.6893E–05 1 2.7778E–05 0.09291

1s m Ccal2: : c

= 4.1868E+04 7373.1 2.0482 3.6000E+04 1 3344.6

1hr ft Ckcal- -2 c

= 12.518 2.2045 6.1237E–04 10.764 2.9899E–04 1

1hr ft FBtu 1

hr ft CCHU

- - - -2 2c c=


NCEES 471

7.2.3.26 Surface Tension

Conversion Table for the Most Commonly Used Units of Surface TensionSurface Tension m

Nin.lbf

ftlbf

cmg

cmdyne

.inpdl

mN1 = 1 5.7101E–03 4.7585E–04 1.0197 1000 0.18372

.1 inlbf = 175.13 1 0.08333 178.58 1.7513E+05 32.174

ftlbf1 = 2101.5 12 1 2143 2.1015E+06 386.09

cmg

1 = 0.98067 5.5997E–03 4.6665E–04 1 980.67 0.18017

cmdyne1 = 0.001 5.7101E–06 4.7585E–07 1.0197E–03 1 1.8372E–04

.1 inpdl = 5.4431 0.03108 2.5901E–03 5.5504 5443.1 1

7.2.3.27 Cubic Expansion Coefficient

Conversion Table for the Most Commonly Used Units of Cubic Expansion

Cubic Expansion m K

kg3 : m F

lbm-3 c cm C

g3 : c

m Kkg

1 3 := 1 0.03468 0.001

1m Flbm

-3 c= 28.833 1 0.02883

1cm Cg3 : c

= 1000 34.682 1

7.2.3.28 Temperature

Conversion Table for Temperature UnitsKelvin (K) Celsius (°C) Rankine (°R) Fahrenheit (°F)

T(K) = T(K) T(°C) + 273.15 95 T(°R) 9

5 T(°F) + 255.37

T(°C) = T(K) – 273.15 T(°C)95 T(°R) – 273.15 9

5 T(°F) – 17.78

T(°R) = 59 T(K) 5

9 T(°C) + 491.67°R T(°R) T(°F) + 459.67

T(°F) = 59 T(K) + 459.67 5

9 T(°C) + 32 T(°R) – 459.67 T(°F)


472 NCEES

7.3 General Engineering Relations

7.3.1 Measures of Composition

7.3.1.1 Fractions

Mole Fraction (or mole%): xi

x N

NA

A= N Nii=/ x 1ii =/

For binary systems:

x N NN

NN

11

AA B

a

a

B= + =

+ N x N1 1A B B= −c m x x 1A B+ =

Mass Fractions (Weight Fraction or wt%): wi

w m

mA

A= m mii=/ w 1ii =/

For binary systems:

w m mm

mm

11

AA B

A

AB

= + =+

m w m1 1A B B= −c m w w 1A B+ =

Conversion Between Mole Fraction and Mass Fraction

MW N

mA A

A= m N MWA A A= N MWm

A A

A=

xm MWMW

m

w MWMWw

A A

A

A

A

ii i i ii

= =/ /

wN MWMW

N

x MWMWx

A

A

A

A

A

ii

i ii

i

= =/ /

For binary systems:

xm m MW

MWm

w MWMW

1 1 1

1A

A B B

A

A

A B

A=

+=

+ −c m w

N N MWMW

N

x MWMW

1 1 1

1A

A B A

B

A

A A

B=

+=

+ −c m

Volume Fraction (%vol): i{

VV

*

*

ii{ = where V Vii=[ [/ 1ii{ =/

Volume fraction is the volume of a constituent of a mixture prior to mixing Vi[` j divided by the sum of volumes of all constituents prior to mixing V [` j.For mixtures of ideal gases: φi = xi

For ideal solutions (no volume change due to mixing): wi i i{ t

t=


NCEES 473

Density and Average Molecular Weight (MW) of a Mixture:

MW x MWi ii=/

For ideal solutions (no change in volume due to mixing): w1ii

it t=/For solutions of components with similar densities (assume volume of the solution is proportional to the mass):

wi iit t=/

7.3.1.2 Ratios or Loading

Mole Ratio: Xi

Ratios are used primarily for dilute solution or when one component is not affected by the process. For solutions with a solvent it is also called "solute-free basis" and for combustion gases "dry basis."

Note: Component A is the basis (the solvent, the inert, or the predominant component).

X NN

xx

A Aii i= = X N

N 1AA ii = −

!/ X 1A =

For binary systems (A: Solvent, B: Solute):

X xx

xx1 1 1

1 1 1BB

B

BA

= − =−

= − xX1 11

B

B

=+

x X11

AB

= +

For dilute systems with xA→1: Xi→xi

Mass Ratio: Wi

W m

mww

A Aii i= = W m

m 1AA ii = −

!/ WA = 1

For binary systems (A: Solvent, B: Solute):

W w

w

ww1 1 1

1 1 1BB

B

BA

= − =−

= − wW1 11

B

B

=+

w W11

AB

= +

For dilute systems with wA→1: Wi→wi

Conversion Between Mole Ratio and Mass Ratio

W X MW

MWAi ii= X W MW

MWAi i i=

7.3.1.3 Concentrations

Molar Concentration: ci or [i]

c V

Ni

i=

For ideal gases: c x RTp

i i=


474 NCEES

Mass Concentration: gi

Vm

wiiic t= =

Volume Concentration: fi

VV

iiz =[

Volume fraction is the volume of a constituent of a mixture prior to mixing V *i divided by the volume of the mix-

ture (V).

For mixtures in which volume decreases on mixing:

V V*mixii 2/ 1ii 2z/

Ideal solution (no volume change due to mixing):

wi i i iz { t

t= =

1iiz =/ (ideal solutions only)

7.3.1.4 Molarity and Molality

Molarity (M)

Molarity Liters of solutionmoles of solute=

Note that molarity is temperature-dependent.

Molality (m)

Molality kg of solvent

moles of solute=

Note that molality is temperature-independent.


NCEES 475

7.3.1.5 Special Measures of Composition

Normality (N)

Normality liters of solution

equivalent grams of the solute=

Gram equivalent weight is a measure of the reactive capacity of a given molecule and thus is reaction-dependent.

Note that normality is temperature-dependent.

pH and pOH

logpH H10=− +7 A or logpH H O10 3=− +8 BlogpOH OH10=− −7 A

and

logpK pH pOH K10= + =− where K H O OH3= + −8 7B AFor water at 20 Cc : K 10 14= − and pK = 14

Note that all concentrations are in moles/liter.

Proof (for Alcohol Content)

Proof abv ml of solution

ml of pure ethanol2 200= =

abv = alcohol % by volume (volume concentration)

For Dilute Solution (Can Be Based on Mass, Molar, or Volume)

ppm = parts per million = 10–6

ppb = parts per billion = 10–9

ppt = parts per trillion = 10–12

Percent: 1% = 10,000 ppm

Permil: 1a = 1000 ppm

PE C

hemical R

eference Handbook

476

NC

EES

7.3.1.6 Conversion Table Between Different Measures of Concentration

Multicomponent SystemsMole

Fraction xi

Mass Fraction

wi

Mole Ratio Xi

Mass Ratio Wi

Molar concentration

ci

Mass concentration

gi

Mole Fraction

xi =xi w MW

MWw

j j

ij

i

/ XX

1 A jj

i

+!/ MW

MWW MWMW

W

A Ai

j j

ij

i

+!

/ c MWit MW

MWi

itc

Mass Fraction

wi =x MWMWx

jj i

j

i

/ wi MW X MWX MW

A j jj A

i i+

!/ W

W1 jj A

i+

!/ c MWi i

titc

Mole Ratio Xi = x

xAi

wwMWMW

A A

i i Xi W MWMWAi i

ccAi

MWMW

A

A

i

icc

Mass Ration Wi = x

xMWMW

AAi

i ww

Ai X MW

MWAii Wi c MW

c MWA A

i iAicc

Molar concentration

ci = MWxit

MWw

i

it X cAi MWW A

i

ic ci MWiic

Mass concentration

gi = MWx MWi it wit X MW cAi i w Ai c c MWi i gi

Avg. MW MW = x MWj jj/ MW

w1

j

jj/ X

MW X MW1 A

A A

jj

j jj

+

+

!

!

//

MW X MWW

W1A A

A

j j

jj

jj

+!

!

//

Avg.* Density

r =x MWMW

i

j jj t/

w1

j

jj t/

*Ideal solutions only

C

hapter 7: General Inform

ation

NC

EES

477

Binary SystemsMole

Fraction xB

Mass Fraction

wB

Mole Ratio XB

Mass Ratio WB

Molar concentration

cB

Mass concentration

gB

Mole Fraction

xB =xB w w MW

MWw

1B BA

B

B

+ −_ i XX

1 B

B+ MW

MWW

W

A

BB

B

+c MWBt MW

MWB

Btc

Mass Fraction

wB = x x MWMW

x

1B BB

A

B

+ −_ i wBMWMW

X

X

B

AB

B

+ WW1 B

B+

c MWB Bt

Btc

Mole Ratio XB = x

x1 B

B- w

wMWMW

1 B

B

B

A- XB W MW

MWB B

A

ccAB

MWMW

A B

B Acc

Mass Ratio WB = x

xMWMW

1 B

B

A

B- w

w1 B

B- X MW

MWB A

B WB c MWc MWA A

B B

ABcc

Molar concentration

cB = MWxBt

MWw

B

Bt X cB A MWW

B

B Ac cB MWB

Bc

Mass concentration

gB = MWx MWB Bt wBt X c MWB A B wB Ac c MWB B gB

Avg. MW MW = x MW x MW1B B B A+ −_ i w w MW

MWMW

1B BA

B

B

+ −_ i XMW X MW

1 B

A B B+

+MW MW

WW

11

A B

B

B

+

+

Avg.* Density

r = x x MWMW

MWMW

1B BB

AAB

B B

tt

t

+ −_ i w w1B B AB

B

tt

t

+ −_ i X MWMWMWMW X

B B AB

B B

A

B

tt

t

+

+d n

W

W1

BA

B

B B

ttt

+

+_ i

*Ideal solutions only

Note: For mole and mass ratios, "A" is the basis component (e.g., the solvent).


478 NCEES

7.3.2 Density Definitions

7.3.2.1 Density and Relative DensityDensity is

Vm

t =

Relative density is

RDreftt=

where reft = density of a reference material

7.3.2.2 Specific Gravity

Specific Gravity (Relative Density) of Gas

SG

ir at ef emp, ress

as

a r t p

gt

t=

The reference temperatures are commonly either 0°C or 60°F and the reference pressure is commonly 14.696 psia (101,325 Pa).

For ideal gas:

28.96SG

molgMW

MW MWair

gas gas==

Specific Gravity (Relative Density) of Liquid

SGH O at ref temp2tt=

where 62.4ftlbm 1000

mkg

H O, ref 3 32t = =

The reference temperatures are commonly either 4°C or 60°F.

Specific Gravity (Realtive Density) in Baumé

For liquids lighter than water, using degrees Baumé or B°: BSG 130140= + c

For liquids heavier than water, using degrees Baumé or B°: 145 B145SG = − c

Specific Gravity (Relative Density) for Hydrocarbon Liquid

131.5 API141.5SG60 F = +c API 141.5 131.5SG60 F

= −c

where API = American Petroleum Institute gravity or API gravity


NCEES 479

Specific Gravity (Relative Density) for Slurries

Bulk density and specific gravity of solids and liquid mixtures (slurries) are1 1 1 1bulk liquid solids solids liquidt t \ t t= + −d n

SG SG SG SG1 1 1 1bulk liquid

solids solids liquid\= + −e o

7.4 Mathematics

7.4.1 Algebra

7.4.1.1 Linear Algebra

Straight Line

General form: A x + B y + C = 0

Standard form: y = m x + b

Point-slope form: y - y1 = m (x - x1)

Two-point form: x xy y

x xy y

1

1

2 1

2 1−−

= −−

Intercept form: xx

yy

1 00

+ − =0

, where intercepts x0 ≠ 0, y0 ≠ 0

Slope: 2m x xy y2 1

= −− 1

Angle between lines with slopes m1 and m2: arctan m mm m1 2 1

2 1−a = +e o

Distance between two points (two-dimensional space): d y y x x12

2 12−= + −2` _j i

Intersection of two straight lines: x m mb b

y m mm b m b

i i1 2

2 1

1 2

1 2 2 1= −−

= −−

7.4.1.2 Polynomials

Quadratic Equation

Standard form: a x2 + b x + c = 0

Normal form: x2 + p x + q = 0

Roots: cx ab

ba

ab b a c

2 1 1 42

4,1 2 2

2!

!= − − =− −d n

xp p

q2 4,1 2

2

!= −

Vieta's Rule: p = – (x1 + x2) q = x1 x2

If (b2 – 4 a c) > 0, the roots are real and unequal.

If (b2 – 4 a c) = 0, the roots are real and equal.

If (b2 – 4 a c) < 0, the roots are imaginary and unequal.

If (b2 – 4 a c) = n2 (perfect square), the roots are rational and unequal.


480 NCEES

Expansion of General Algebraic Expressions

(a ± b)2 = a2 ± 2 a b + b2

(a ± b)3 = a3 ± 3 a2 b + 3 a ∙ b2 ± b3

(a ± b)4 = a4 ± 4 a3 b + 6 a2 b2 ± 4 a b3 + b4

a2 – b2 = (a + b) (a – b)

a3 + b3 = (a + b) (a2 – a b + b2)

a3 – b3 = (a – b) (a2 + a b + b2)

a4 + b4 = (a2 + b2) (a2 – b2) = (a2 + a b 2 + b2) (a2 – a b 2 + b2)

Quadratic Surface (Sphere)

Standard form: (x – h)2 + (y – k)2 + (z – m)2 = r2

Distance between two points in three-dimensional space: d x x y y z z2 12

2 12

2 12= − + − + −_ ` _i j i

7.4.1.3 Logarithms, Exponents, and Roots

Logarithms

General definition: logb(x) = c where: x = bc

Natural logarithm: ln(x) = c where: x = ec (base: e = 2.71828)

Base 10 logarithm: log(x) = c where: x = 10c (base: 10)

To change from one base to another:

( ) ( )( )

log loglog

x bx

ba

a=

ln( ) log ( )

log ( )2.302585 log ( )x e

xx

10

1010= =

log( ) ln(10)

ln( )0.4343 ln( )x

xx= =

Identities:

logb(1) = 0

logb(b) = 1

logb(bn) = n

logb(xc) = c logb(x)

( ) ( )log log log logx x c x c x1 1

b c bc

b b= = − =−c cm m

( ) ( )log log logx x c x1b c b b

c1

= =_ i 8 B

( ) ( ) ( )log log logx y x yb b b= +

( ) ( )log log logyx x yb b b= −d n


NCEES 481

b x( )logn x nb = b x

( )lognx

n1b

=

Rules for Exponents and Radicals

a0 = 1

a1 = a

Identities:

p an ± q an = (p ± q) an

an am = an+m

aa amn

n m= −

( ) ( )a a am n n m n m= =

a a a1 1nn

n= =− c m

an bn = (a b)n

ba

ba

nn n

= c m

( )a an n1=

( )a a amn n mnm

= =` j

a am xn x mn=

( )p a q a p q an n n+ = +` ` `j j j

a a am n n m= +` `j j

ab a bn n n= +

ba

ba

ba

n

n n1

= =n c m

7.4.1.4 ProportionsDirectly proportional (4th proportional):

a

c

b x

x c\

a : b = c : x

x abc=

If ba

xc= then: b

a bxc x+ = + and b

a bxc x− = − and a b

a bc xc x

+− = +

−


482 NCEES

Square proportional (3rd proportional): 90°

b

a x

x b2\

a : b = b : x

x ab2

=

Mean proportional:

b

x

90°

a

x b\

a : x = x : b

x a b=

Inversely proportional:

x b1\

Inversely square proportional:

xb12\

7.4.1.5 Complex NumbersRectangular form: z a i b= +

where 1i -=

a = real component

b = imaginary component

Polar form: cos sinz c c i c ei+i i i= = + = i_ i

tan

cossin

c a b

ab

a cb c

2 2

1i

i

i

= +

=

==

− c m

Addition and Subtraction (in rectangular form): ( )z z a a i b b1 2 1 2 1 2! ! != + _ iMultiplication and Division (in polar form):

z z c c

zz

cc

z a i b c nn n n

1 2 1 2 1 2

21

21

1 2

+

+

+

i i

i i

i

= +

= −

= + =_

d_

__

^ni

iii

h


NCEES 483

Complex Conjugate:

z a i bz z a b2 2

= −= +

)

)

Euler's Identity:

cos sincos sin

cos

sin

e ie i

e e

i e e

21

21

i

i

i i

i i

i i

i i

i

i

= += −

= +

= −

i

i

i i

i i

−

−

−

__

ii

7.4.2 Geometry and Trigonometry

7.4.2.1 Circular Transcendental FunctionsTrigonometric functions are defined using a right triangle:

r

θ

x

y

sin

csc

sec

cot

,

,

,

arcsin

arccos

arctan

arc

arc

arc

ry

yr

rx

xr

xy

yx

i i

i i

i i

= =

= =

= =

c

cb

d

d

c

m

ml

n

n

m

Law of Sines

B

A

c

b

a

C

sin sin sinAa

Bb

Cc= =

Law of Cosinesa2 = b2 + c2 – 2bc cos A b2 = a2 + c2 – 2ac cos B c2 = a2 + b2 – 2ab cos C

Law of Tangents

( )

( )

( )

( )

( )

( )

tan

tan

tan

tan

tan

tan

a ba b

A B

A B

b cb c

B C

B C

a ca c

A C

A C

2121

2121

2121

+− =

+

−

+− =

+

−

+− =

+

−


484 NCEES

Trigonometric Functions in a Unit Circle

θ

θθ

θθ

θ

θ

(0, 1)

(1,0)

cot

costan

csc

sec

sin

Trigonometric Identities

sin (–θ) = –sin θ cos (–θ) = cos θ tan (–θ) = –tan θ

cos sin sin

sin cos cos

csc sin

sec cos

tan cossin

cot tan

2 2

2 21

1

1

i ir

ir

i ir

ir

ii

ii

iii

ii

= + =− −

= − =− +

=

=

=

=

c

c c

cm

m m

m

sin cos 12 2i i+ =

tan sec12 2i i+ =

cot csc12 2i i+ =


NCEES 485

Double-Angle Formulas

sin sin cos2 2a a a=

cos cos sin sin cos2 1 2 2 12 2 2 2a a a a a= − = − = −

tantantan2

12

2aaa=

− cot cot

cot2 212

a aa= −

Two-Angle Formulas

( )

( )

( ) ( )( )

( ) ( )( )

( )

( )

( ) ( )( )

( ) ( )( )

sin sin cos cos sin

cos cos cos sin sin

tan tan tantan tan

cot cot cotcot cot

sin sin cos cos sin

cos cos cos sin sin

tan tan tantan tan

cot cot cotcot cot

1

1

1

1

a b a b a b

a b a b a b

a ba ba b

a ba ba b

a b a b a b

a b a b a b

a ba ba b

a bb aa b

+ = +

+ = −

+ = −+

+ = +−

− = −

− = +

− = +−

− = −+

Half-Angle Formulas

( )

( )

( )( )

( )( )

sincos

coscos

tan coscos

cot coscos

2 21

2 21

2 11

2 11

!

!

!

!

a a

a a

aaa

aaa

=−

=+

= +−

= −+

c

c

c

c

m

m

m

m


486 NCEES

Combination of the Trigonometric Functions of Different Angles

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

sin sin cos cos

cos cos cos cos

sin cos sin sin

sin sin sin cos

sin sin cos sin

cos cos cos cos

cos cos sin sin

21

21

21

2 21

21

2 21

21

2 21

21

2 21

21

a b a b a b

a b a b a b

a b a b a b

a b a b a b

a b a b a b

a b a b a b

a b a b a b

= − − +

= − + +

= + + −

+ = + −

− = + −

+ = + −

− =− + −

c

c

c

c

c

c

c

c

m

m

m

m

m

m

m

m

8

8

8

<

<

<

<

<

<

<

<

F

F

F

F

B

B

B

F

F

F

F

Miscellaneous Formulas

sin sin cos cos2 2

121

21 2

i i ii= = −c cm m

cos cos sin cos21

21

21 22 2i i i

i= − = +c cm m

tantan

tan

cos sin

cos

1 21

2 21

21

21

2 21

21

2 2 2i

i

i

i i

i i=

−=

−

c

c

c

c

c

c

m

m

m

m

m

m

tan coscos

cossin

sincos

1 21 2

1 22

21 2

iii

ii

ii= +

− = + = −

cot

cot

cot

cos

cos sin

2 2121 1

2 21

21

21

212 2 2

ii

i

i i

i i=

−=

−c

c c

c

c

cm

m m

m

m

m

cot coscos

sincos

cossin

1 21 2

21 2

1 22

iii

ii

ii= −

+ = + = −

7.4.2.2 Planar Geometry—Area and PerimeterA = area

P = perimeter (circumference)

a,b,c = lengths of sides

d = diagonal(s) or diameter

h = height


NCEES 487

Square

a dA = a2

P = 4 a

d a 2=

Rectangle

b d

a

A = a b

P = 2 (a + b)

d a b2 2= +

Parallelogram

b

h

d1

d2

a

α

( )

( )( )

( )

sin

sincotcot

A a h ab

P a b a h

d a h hd a h hd d a b

2 2

2

12 2

22 2

12

22 2 2

a

a

a

a

= =

= + = +

= + +

= − +

+ = +

c m

Trapezoid

h

b

a

m

A a b h mh

m a b2

2

= + =

= +

Triangle (oblique)

h

a

bc

r i

( ) ( ) ( )

P a b c

r Pa

Pb

Pc

A a h r P

A P P a P b P c

1 2 1 2 1 2

21

21

21 2 2 2

i

1

= + +

= − − −

= =

= − − −

c c cm m m

Triangle (equilateral)

P a

A a a h

h a

3

43

21

23

2=

= =

=

h

a

a


488 NCEES

Triangle (right)

a

hb

P a b h

A a h

b a h21

2 2

= + +

=

= +

Regular Polygon (n equal sides)

a

rφ

θ( )

tan

P na

A n r a

a r

n

nn

2

2 22

2

z

zr

ir

=

=

=

=

=−

c m= G

Circle

d r

P r d

A r d

d r

2

42

22

r r

rr

= =

= =

=

Annulus

D

b

d

( ) ( ) ( ) ( )A D d D d D d b b d

b D d4 4

2

2 2r rr= − = + − = +

= −


NCEES 489

Sector of a Circle s

r

φ

( )

A r s r

s rP r s r

2 2

2 2

2z

z

z

= =

== + = +

Segment of a Circle

d

A

φ

s

r

b

( )

sin

arccos

sin

b r

rs

rr d

Ar

2 2

2

22

z

z

z z

=

= = −

=−

cc

mm

( )A dd d b

r dhb

6 3 4

2 8

2 2

2

= +

= +

cos tan

sin

d r b

P s b r

1 2 2 4

2 2

z z

zz

= − =

= + = +

c

c

cm

m

m=

=

G

G

Ellipse a

b

(h, k)

y '

x '

P a b

A ab

2 2approx

2 2r

r

= +

=

Parabola

A i

A o

b

h

A bh

A bh32

3

i

o

=

=


490 NCEES

7.4.2.3 Cubic Geometry—Volume and Surface AreaA = surface area

V = volume

a,b,c = lengths of sides

d = diagonal(s) or diameter

h = height

Cube

α

a

σ d

V aA ad a

63

3

2

===

Cuboid

b

c d

a

( )V abcA ab a c bcd a b c

22 2 2

== + += + +

Parallelepiped

A

h

base

V A hbase=

Pyramid

h

A base

VA h3base=


NCEES 491

Frustum of Pyramid

A 1

A 2

hV h A A A A

V hA A

for A A

3

2

1 2 1 2

1 21 2. .

= + +

+

_ i

Right Circular Cylinder

h

d

r

( )

V d h

A r hA r r h

42

2mantle

2r

r

r

=

== +

Hollow Cylinder

dh

D

( )V h D d42 2r= −

Right Circular Cone

hx

A2

A1

m

r

( )

: :

V r h d h

A r mA r r mm h rA A x h

3 12mantle

2 2

2 2

1 22 2

r r

r

r

= =

== += +

=

Frustum of Cone

h

d

dm

p

m—2

( )

( )

V h D Dd d

A m D d pm

m h D d

12

2 2

2

mantle

2 2

22

r

rr

= + +

= + =

= + −c m


492 NCEES

Sphere

V r d

A r d34

61

4

3 3

2 2

r r

r r

= =

= =

Zone of a Sphere

h

a

rb

( )

( )

V h a b h

A r hA r h a b

6 3 3

22

mantle

2 2 2

2 2

r

r

r

= + +

=

= + +

Segment of a Sphere (Spherical Cap)

h

rs

( )

( )( )

cos

V h s h h r h

A r h s h

A rs h r h

6 43

3

2 4 4

2 12 2

cap

cap

2 2 2

2 2

20

rr

rr

r i

= + = −

= = +

= −= −

c cm m

q0 is the angle of the cutout, rotated from the center of the radius.

Sector of a Sphere

h

r

s

( )

V r h

A r h s

32

2 4

2r

r

=

= +


NCEES 493

Sphere with Cylindrical Boring

h

r

R

( )

V h

A h R rh R r

62

3

2 2

r

r

=

= += −

Sphere with Conical Boring

Rh

D

( )

V R h

A h R D

D R h

32

2 22

2

2 2

r

r

=

= +

= −

Torus

d

D

V Dd

A Dd42

2

2

r

r

=

=

Sliced Cylinder

h

d

V d h42r=

Ungula

h

r

V r h

A r h

A r rh

rh

32

2

2 2 1 1

mantle

2

22

2r

=

=

= + + +e o> H


494 NCEES

Barrel

h

d

D

( )V h D d12 2 2 2.r +

Prismoid

A1

A2

A

h

h/2

( )V h A A A6 41 2= + +

Regular Polyhedra

Name No. of Faces Form of Faces Total Surface Area VolumeTetrahedron 4 Equilateral triangle . a1 7321 2 . a0 1179 3

Cube 6 Square a6 2 a3

Octahedron 8 Equilateral triangle . a3 4641 2 . a0 4714 3

Dodecahedron 12 Regular pentagon . a20 6457 2 . a7 6631 3

Icosahedron 20 Equilateral Triangle . a8 6603 2 . a2 1817 3

The radius of a sphere inscribed within a regular polyhedron is:

r AV3=

Paraboloid of Revolution d

h

V hd82r=


NCEES 495

7.4.3 Calculus

7.4.3.1 DifferentiationFor any function y = f(x), the derivative D y dx

dyyx= = = l

itlimy xy

x 0 DD=

"Dl d n

itlimx

f x x f xx 0

-

D

D=+

"D

_^

^ih

h8 B* 4

where the slope of the curvey f x=l ^ h

Test for a Maximum

y f x= ^ h is a maximum for ,x a= if f a 0=l^ h and f a 01m^ h

Test for Minimum

y f x= ^ h is a minimum for ,x a= if f a 0=l^ h and f a 02m^ h

Test for a Point of Inflection

y = f(x) has a point of inflection at x = a, if ,f a 0=m^ h and if f xm^ h changes sign as x increases through x = a

L'Hôpital's Rule

If the fractional function g xf x^^hh assumes one of the indeterminate forms 0

0 or 33 (where a is finite or infinite), then:

itlim g xf x

x" a

^^hh

is equal to the first of the expressions

it it itlim lim limg xf x

g xf x

g xf x

x x x" " "a a al

l

m

m

n

n

^^

^^

^^

hh

hh

hh

which is not indeterminate, provided such first indicated limit exists.

Curvature K of a Function

P

s

+ Δ

ΔΔ

ααα

α

Y

O X

Q

y = f (x)

=

The curvature K of a curve at point P is the limit of its average curvature for the arc PQ as Q approaches P. This is also expressed as:

The curvature of a curve at a given point is the rate of change of its inclination with respect to its arc length.

itlimK s dsd

s 0

a aDD= =

"D


496 NCEES

Curvature in Rectangular Coordinates

Ky

y

1 2 23=

+ l

m

_ i9 CWhen it may be easier to differentiate the function with respect to y rather than x, the notation xlwill be used for the derivative.

x dydx=l

Kx

x

1 2 23=

+

−

l

m

^ h8 B

Radius of Curvature

The radius of curvature R at any point on a curve is defined as the absolute value of the reciprocal of the curvature K at that point.

R K1= K 0!_ i

Ryy1 2 2

3

= +m

l_ i9 C y 0!m_ i

List of Derivatives

u, v, and w represent functions of x.

a, c, and n represent constants.

Arguments of trigonometric functions are in radians. The following definitions are used:

arcsin u = sin-1 (u), sin sinu u

11 =−^ h

1. dxdc 0=

2. dxdx 1=

3. dxd cu c dx

du=^ h

4. dxd u v w

dxdu

dxdv

dxdw+ −

= + −_ i

5. dxd uv u dx

dv v dxdu= +

^ h

6. dxd uvw u v dx

dw uw dxdv v w dx

du= + +^ h

7. dxd vu

vv dxdu u dx

dv

2=−c m

8. dxd u

n u dxdun

n 1= −_ i


NCEES 497

9. dxd f u

dud f u

dxdu=

^ ^h h7 7A A) 3

10. dxdu

dudx1=c m

11. log

logdxd u

e u dxdu1a

a=_ _i i

12. lndx

d uu dxdu1=

^ h

13. lndxd a a a dx

duuu=

_ ^i h

14. dxd e

e dxduu

u=_ i

15. lndxd u

vu dxdu u u dx

dvvv v1= +−_ ^i h

16. sin

cosdxd u

u dxdu=

^ h

17. cos

sindxd u

u dxdu= −

^ h

18. tan

secdxd u

u dxdu2=

^ h

19. cot

cscdxd u

u dxdu2= −

^ h

20. sec

sec tandxd u

u u dxdu=

^ h

21. csc

csc cotdxd u

u u dxdu= −

^ h

22. sindx

d uu dxdu

111

2=

−

−_ i sin u2 2

1# #r r- -c m

23. cosdx

d uu dxdu

111

2=−

−

−_ i cos u0 1# # r

-_ i

24. tandx

d uu dxdu

111

2=+

−_ i tan u2 2

11 1r r- -c m

25. cotdx

d uu dxdu

111

2= −+

−_ i cot u0 11 1 r-_ i

26. secdx

d uu u dx

du1

11

2=

−

−_ i sec secandu u0 2 2

1 11 # #r

rr- -- -c cm m

27. cscdx

d uu u dx

du1

11

2= −

−

−_ i csc cscandu u0 2 2

1 11 1# #r

rr- -- -c cm m


498 NCEES

Parametric Form of the Derivative

y x t dx

dydtdydxdt

xy= = =l oo_ ^ hi

y x tdxd y

xx y y x

2

2= =

−m p

o p o p_ ^ ^hi h

where

y dtdy

ydtd y

2

2

=

=

o

p

Derivative of Inverse Functions

The equation y = f(x) solved for x gives the inverse function x y{= _ i.f x

y1{

=ll

^ _h i7.4.3.2 Integration

The indefinite integral F(x) is a function such that F x f x=l] ]g g .f x dx F x C= +^ ^h h#

C is an unknown constant which disappears on differentiation.

The definite integral:

iti 1=

( )lim f x x f x dx F x F b F an

i i a

babD = = = −

"3

n

_ ^ ^ ^i h h h/ # Also, x 0i "D for all i.

To find the integral: Use the list of indefinite integrals (below), integration by parts (equation #6 in the list), integra-tion by substitution, and separation of rational fractions into partial fractions.

List of Indefinite Integrals

u, v, and w represent functions of x.

a, c, and n represent constants.

Arguments of trigonometric functions are in radians. The following definitions are used:

,sin sin sin sinarc u u u u11 1= =− −^ ^h h

Note: A constant of integration should be added to the integrals.

1. d f x f x=^ ^h h#2. dx x=#3. a f x dx a f x dx=^ ^h h##4. u x v x dx u x dx v x dx! !=^ ^ ^ ^h h h h7 A# ##


NCEES 499

5. x dx mx

1m

m 1= +

+

# m 1-!_ i

6. u x dv x u x v x v x du x-=^ ^ ^ ^ ^ ^h h h h h h# #

7. lnax bdx

a ax b1+ = +# for a = 1 and b = 0: lnx

dx x=#8.

xdx x2#

9. lna dx aaxx

=#10. sin cosx dx x-=#11. cos sinx dx x=#

12. sin sinx dx x x2 4

22 -=#

13. cos sinx dx x x2 4

22 = +#

14. sin sin cosx x dx x x x-=#

15. cos cos sinx x dx x x x= +#

16. sin cos sinx x dx x22

=#

17. sin coscos cos

ax bx dxa ba b x

a ba b x

2 2- -=

−−

++

__

__

ii

ii# a b2 2!_ i

18. tan ln cos ln secx dx x x-= =#

19. cot ln csc ln sinx dx x x-= =#

20. tan tanx dx x x2 -=#21. cot cotx dx x x2 -= −#22. e dx a e

1ax ax= c m#

23. xe dx ae ax 1axax

2 -= e ^o h#

24. ln lnx dx x x 1= −^ h8 B# x 02^ h25. tan

a xdx

a ax1

2 21

+= −# a 0!_ i

26. tanax cdx

acx ca1

21

+= − c m# ,a c0 02 2_ i


500 NCEES

27a. tanax bx c

dxac b ac b

ax b42

42

2 21

2+ +=

− −+−# ac b4 02 2-_ i

27b. lnax bx c

dxb ac ax b b ac

ax b b ac4

12 42 4

2 2 2

2

-

- -+ +

=− + +

+# b ac4 02 - 2_ i

27c. ax bx c

dxax b2

22 -+ +

= +# b ac4 02 - =_ i

7.4.3.3 Multivariable Calculus

Partial Derivatives

In a function of two independent variables x and y, a derivative with respect to one of the variables may be found if the other variable is assumed to remain constant. If y is kept fixed, the function

,z f x y= _ ibecomes a function of the single variable x, and its derivative (if it exists) can be found. This derivative is called the partial derivative of z with respect to x. The partial derivative with respect to x is denoted as follows:

( , )xz

xf x y

22

22=

Total Derivative

Given f(x,y), then the total derivative df is

df xf dx y

f dyy x2

222= +d en o

Chain Rule

Given ,f x y_ i where x g t= ^ h and y h t= ^ h, then

dtdf

xf

dtdx

yf

dtdy

y x22

22= +d en o

Identities in Partial Derivatives

xx 1z2

2 =c m

zx 0x2

2 =c m

Implicit Differentiation

If f (x,y,z) cannot be converted to an explicit expression in the form of ,z f x y= )_ i, then

xz

zfxf

,

,

y

x y

y z22

22

22

=−

cd

dm

n

n and y

z

zfyf

,

,

x

x y

x z22

22

22

=−

dd

en

n

o


NCEES 501

Rules for changing the constant or the variable on a partial derivative:

Given f (x,y,z) = constant, then

xf

xf

yf

xy

z y x z22

22

22

22= +d d e dn n o n

zf

yf

zy

x x x22

22

22=d e dn o n

7.4.3.4 Differential EquationsA common class of ordinary linear differential equations is

...b dxd y x

b dxdy x

b y x f x1 0n n

n+ + + =

^ ^ ^ ^h h h hwhere bn, ... , bi, ... , b1, b0 are constants.

When the equation is a homogeneous differential equation, f(x) = 0, the solution is

. . .y x C e C e C e C e1 2hr x r x

ir x

nr x1 2 i n= + + + +^ h

where rn is the nth distinct root of the characteristic polynomial P(x) with

P r b r b r b r b11

1 0n

nn= + + +−

−n^ h

If the root r1 = r2, then C e2r x2 is replaced with C xe2

r x1 .

Higher orders of multiplicity imply higher powers of x. The complete solution for the differential equation is

y(x) = yh(x) + yp(x)

where yp(x) is any particular solution with f(x) present. If f(x) has er xn terms, then resonance is manifested. Further-more, specific f(x) forms result in specific yp(x) forms, some of which are

f(x) yp(x)A BAe xa ,Be rx

n!aa

sin cosA x A x1 2~ ~+ sin cosB x B x1 2~ ~+

Common First-Order Differential Equations and Their Solutions

Form Solution Substitution/Conditions

Linear, homogeneous ODE with constant coefficients

y a y 0+ =l

( )y x C e ax= − C is a constant that satisfies the initial condition.

Linear, homogeneous ODE

y p x y 0+ =l ^ h y(x) Ce( p(x)dx)= − # C is a constant that satisfies the initial condition.


502 NCEES

Common First-Order Differential Equations and Their Solutions (cont'd)Form Solution Substitution/Conditions

Linear, inhomogeneous ODE with constant coefficients

( )y y K p tx + =l

( ) ( )y t KA KB KA e1t= + − − x−a k

lntKB yKB KA

x = −−e o ,ttan

( ) ( )

time cons gain

p t B tA t y K A

K00 02

1

x

= =

= =

' 1

Comment: Solution is for a step function.

Implicit ODE, no y term

x f y= l_ i

( )( )

x f py p f p dp C

== +#

Substitution: y p=l

Comment: Elimination of p leads to a solution in parametric form.

Implicit ODE, no x term

y f y= l_ i

( )

( )

x pf p

dp C

y f p

= +

=

#y p=l

Comment: Elimination of p leads to a solution in parametric form.

Separable ODE

y dxdy

g yf x= =l^_hi

g y dy f x dx C= +_ ^i h# #Comment: The variables x and y can be separated into the left and right

sides of the equation.

Similarity ODE

y f xy=l c m

xdx

f u udu C=

−+^ h# #

:Substitution u xy

y u x dxdu

=

= +l

Comment: Check whether it is possible to transform to f xyc m.

Common Second-Order Differential Equations and Their SolutionsForm Solution Substitution

ODE, y and y' terms missing

y f x=m ^ h( )y x C C x f x dx dx1 2= + + ^ h; E##

Comment: Start the calculation with the inner integral.

ODE, y term missing

y p x f y 01+ =m l^ _h if udu p x dx C

y udx C

1 1

2

= − +

= +

^ ^h h# ##

: 'Substitution u y

y dxdu f y f u

=

= =m l_ ^i h

ODE, x term missing

( , )y f y y=m l

u dydu f y,u

xu ydy

C

=

= +_

_

i

i

#

Substitution:

( , )

Then substitute for .

where ( ) and ( )

u y

y dxdu u dy

du f y u

y dxdy

u

u u y y y x

=

= = =

=

= =

l

m

l


NCEES 503

Common Second-Order Differential Equations and Their SolutionsForm Solution Substitution

Linear, homogeneous ODE with constant coefficients

y a y b y 0+ + =m l

Solution depends on the values of a and b. r a a b2

1 42!= − −,1 2 ` j( )y x C e C er x r x

1 21 2= + ( )overdampeda b42 2

( ) ( )y x C C x er x1 21= + ( )critically dampeda b42 =

( )[ ( ) ( )]cos sin

y x eC x C x

a b a21

21 4

x

1 2

2

b b

a b

=+

= − = −

a

( )underdampeda b42 1

7.4.3.5 The Fourier Transform and Its Inverse X f x t e dt

x t X f e df

2

2

j ft

j ft

=

=

3

3

3

3

r

r

−

+ −

−

+^

_

_

^

h

i

i

h##

We say that x(t) and X(f) form a Fourier transform pair:

x t X f*^ _h i

Fourier Transform Pairs

Fourier Transform Pairsx(t) X(f)1 fd_ itd^ h 1

u t^ h fj2

1 1f2d + r_ i

txPc m csin fx x_ i

csin Bt^ h B Bf1

Pd n

txKc m csin f2x x_ i

e u tat- ^ h a j f a21 02r+

te u tat- ^ ha f

a a22 02 2 2r+ _ i

e a t-

a fa a22 02 2 2r+ _ i

e at 2-^ ha e a

f 2r r-c m


504 NCEES

Fourier Transform Pairs (cont'd)x(t) X(f)

cos f t2r i+0` j e f f e f f2

1 j j0 0d d− + +i i−` `j j9 C

sin f t2r i+0` j j e f f e f f2

1 j j0 0d d− − +i i−` `j j9 C

t nTs

n

n

d −3

3

=−

=+

_ i/ f f kf f T1

s s

k

k

ss

d − =3

3

=−

=+

` j/

Fourier Transform Theorems

Fourier Transform Theorems

Linearity ax t by t+^ ^h h aX f bY f+_ _i i

Scale change x at^ h a X af1 c m

Time reversal x t-_ i X f-` j

Duality X t^ h x f-` j

Time shift x t t0-_ j X f e j ft2 0r-_ i

Frequency shift x t e j f t2 0r-^ h X f f0-` j

Modulation cosx t f t2r 0^ h X f f X f f21

21− + +

0 0` `j j

Multiplication x t y t:^ ^h h *X f Y f_ _i iConvolution *x t y t^ ^h h X f Y f:_ _i i

Differentiationdtd x t

n

n ^ h j f X f2 nr_ _i i

Integration ( )x dtm m

3-# j f X f X f2

121 0r d+_ ^ _i h i

7.4.3.6 Laplace TransformsThe unilateral Laplace transform pair:

F s f t e dtst=3 −

0^ ^h h#

f t j F s e ds21 st

j

j

r=

3

3

v

v

−

+^ ^h h# where s = s + jw

represents a powerful tool for the transient and frequency response of linear time invariant systems. Some useful Laplace transform pairs are


NCEES 505

Laplace Transform Pairsf(t) F(s)

d(t), Impulse at t = 0 1

u(t), Step at t = 0 s1

t[u(t)], Ramp at t = 0 s12

e at-s a

1+_ i

te at-s1

2a+_ i

sine tt ba-

s 2 2a b

b

+ +_ i9 C

cose tt ba-

s

s2 2a b

a

+ +

+

__ii

9 C

dtd f t

n

n ^ h 0s F s s dt

d f1

0

1n n m

m

m

m

n− − −

=

−

^ ^h h/

f dtx x

0^ h# s F s

1c ^m h

x t h dt

x x x-0_ ^i h# H s X s^ ^h h

f t u tx x- -_ _i i e F ssx- ^ hitlim

t f t" 3 ^ h itlims sF s0" ^ h

itlimt f t0" ^ h itlim

s sF s" 3 ^ h

The last two transforms represent the Final Value Theorem (F.V.T.) and Initial Value Theorem (I.V.T.), respectively. It is assumed that the limits exist.


506 NCEES

7.4.4 Statistics and Probability

7.4.4.1 Mean, Median, and ModeIf X1, X2, ... , Xn represents the values of a discrete random sample of n items or observations, the arithmetic mean of these items or observations, denoted X , is defined as

...X n X X X n X1 1n i

i

n

1 21

= + + + =−

c _ cm j m/X " n for sufficiently large values of n.

The weighted arithmetic mean is

X ww X

wii i//=

where Xi = the value of the ith observation and wi = the weight applied to Xi.

The variance of the population is the arithmetic mean of the squared deviations from the population mean. If m is the arithmetic mean of a discrete population of size N, the population variance is defined by

i 1=

...N X X X

N X

1

1i

21

22

2 2

2

v n n n

n

= − + − + + −

= −

N

N

c

c _

_

_ `

m

m i

j

i j: D

/

Standard deviation formulas are

spopulation N X1i

2/ n= −c _m j

ssum = ... n2

22 2v v v+ + +1

sseries = nv

smean = nv

sproduct = A Bb a2 2 2 2v v+

The sample variance is s2 = n X X11

ii

n

1−

−=

2_ _i j= G/

The sample standard deviation is = n X X11

ii

n2

1− −

=c _m j/

The sample coefficient of variation is CV = Xs

The sample geometric mean is ...X X X Xnn1 2 3

The sample root-mean-square value is n X1i2/c m

When the discrete data are rearranged in increasing order and n is odd, the median is the value of the n21 th+c m

item.

When n is even, the median is the avarage of the andn n2 2 1th th

+c cm m items.

The mode of a set of data is the value that occurs with greatest frequency.

The sample range R is the largest sample value minus the smallest sample value.


NCEES 507

7.4.4.2 Permutations and CombinationsA permutation is a particular sequence of a given set of objects. A combination is the set itself without reference to order.

The number of different permutations of n distinct objects taken r at a time is:

,!

!P n rn rn=−

_ _i iAn alternative notation for P(n,r) is nPr.

The number of different combinations of n distinct objects taken r at a time is:

, !,

! !!C n r r

P n rr n rn= =−

_ __i i

i8 B

nCr and rnb l are alternative notations for C(n,r).

The number of different permutations of n objects taken n at a time, given that ni are of type i, where i= 1, 2, ..., k and ,n ni/ = is

; , , ..., ! !... !!P n n n n n n nn

kk

1 21 2

=_ i

7.4.4.3 Probabilities

Property 1. General Character of Probability

The probability P(E) of an event E is a real number in the range of 0 to 1. The probability of an impossible event is 0 and that of an event certain to occur is 1.

Property 2. Law of Total Probability

,P A B P A P B P A B+ = + −^ ^ ^ _h h h iwhere P(A+B) = the probability that either A or B occurs alone or that both occur together

P(A) = the probability that A occurs

P(B) = the probability that B occurs

P(A,B) = the probability that both A and B occur simultaneously

Property 3. Law of Compound or Joint Probability

If neither P(A) nor P(B) is zero, then

P(A, B) = P(A) P(B | A) = P(B) P(A | B)

where

P(B | A) = the probability that B occurs given the fact that A has occurred

P(A | B) = the probability that A occurs given the fact that B has occurred

If either P(A) or P(B) is zero, then P(A, B) = 0.


508 NCEES

Bayes' Theorem:

|

|

|P B A

P A B P B

P B P A Bj

i ii

nj j

1

=

=

` `_`_

j jiji/

where P(Aj ) is the probability of event Aj within the population of A

P(Bj ) is the probability of event Bj within the population of B

7.4.4.4 Distributions and Expected ValuesA random variable X has a probability associated with each of its possible values. The probability is termed a discrete probability if X can assume only discrete values, or

, , , ...,X x x x xn1 2 3=

The discrete probability of any single event X = xi occurring is defined as P(xi) while the probability mass function of the random variable X is defined by

, , , ...,f x P X x k n1 2k k= = =_ _i j

Probability Density Function

If X is continuous, the probability density function, f, is defined such that

P a X b f x dxa

b

# # =^ ^h h#

See the table of probability and density functions.

Cumulative Distribution Function

The cumulative distribution function, F, of a discrete random variable, X, that has a probability distribution described by P(xi) is defined as

, , , ...,F x P x P X x m n1 2m k mk

m

1#= = =

=_ _ _i i i/

If X is continous, the cumulative distribution function F is defined by

F x f t dtx

=3−

^ ^h h#

which implies that F(a) is the probability that X a# .

Expected Values

Let X be a discrete random variable having probability mass function:

, , , ...,f x k n1 2k =_ iThe expected value of X is defined as

E X x f xk k

k

n

1

n = ==

^ h6 @ /


NCEES 509

The variance of X is defined as

V X x f xkk

n

k2 2

1

−v n= ==_ _j i6 @ /

Let X be a continuous random variable having a density function f(X) and let Y = g(X) be some general function. The expected value of Y is

E Y E g X g x f x dx= =3

3

−

^ ^ ^h h h6 7@ A #

The mean or expected value of the random variable X is now defined as

E X xf x dxn = =3

3

−

^ h6 @ #

while the variance is

V X E X x f x dx2 2 2− −v n n= = =

3

3

−

_ _ ^i i h6 :@ D #

The standard deviation is V Xv = 6 @ .The coefficient of variation is defined as n

v .

Combinations of Random Variables

...Y a X a X a Xn n1 1 2 2= + + +

The expected value of Y is ...E Y a E X a E X a E Xy n n1 1 2 2n = = + + +^ _ _ _h i i i.If the random variables are statistically independent, then the variance of Y is

......

V Y a V X a V X a V Xa a a

y n n

n n

212

1 22

22

1212

22

22 2 2

v

v v v

= = + + +

= + + +^ _ _ _h i i i

Also, the standard deviation of Y is y y2v v= .

When Y = f(X1,X2,...,Xn) and Xi are independent, the standard deviation of Y is expressed as

...Xf

Xf

Xf

y x xn

x1

2

2

2 2

22

22

22

v v v v= + + + n21e e eo o o

Normal Distribution (Gaussian Distribution)

This is a unimodal distribution, the mode being x = m, with two points of inflection (each located at a distance s to either side of the mode). The averages of n observations tend to become normally distributed as n increases. The variate x is said to be normally distributed if its density function f (x) is given by an expression of the form

f x e21 x

21

2

v r= v

n−−^ dh n

where

m = the population mean

s = the standard deviation of the population

x3 3# #-


510 NCEES

When m = 0 and s2 = s = 1, the distribution is called a standardized or unit normal distribution. Then

f x e21 /x 22

r= −^ h

where x3 3# #-

It is noted that Z x=-vn follows a standardized normal distribution function.

A unit normal distribution table is included at the end of this section. In the table, the following notations are used:

F(x) = the area under the curve from –∞ to x

R(x) = the area under the curve from x to ∞

W(x) = the area under the curve between –x and x

F(-x) = 1 - F(x)

7.4.4.5 Confidence Intervals

Confidence Interval for the Mean n of a Normal Distribution

When standard devation v is known:

X Zn

X Zn/ /2 2- # #

vn

v+a a

When standard deviation v is not known:

X tns X t

ns

/ /2 2- # #n +a a

where t /a 2corresponds to n - 1 degrees of freedom.

Confidence Interval for the Difference Between Two Means m1 and m2

When standard deviations s1 and s2 are known:

X X Z n n X X Z n n/ /1 2 2 1

12

222

1 2 1 2 2 112

222

- - - -# #v v

n nv v+ + +a a

When standard deviations s1 and s2 are not known:

X X t n nn n n s n s

X X t n nn n n s n s

2

1 1 1 2 1

2

1 1 1 2 1

/

/

1 2 21 2

1 21 1

222

1 2

1 2 21 2

1 21 1

222

- - -

- --

-- -

# #n n+

+ +

+ + −

+ +

a

a

c

c

_

_

^

^

m

m

i

i

h

h

8

8

B

B

where t /2a corresponds to n1 + n2 - 2 degrees of freedom.

Confidence Intervals for the Variance 2v of a Normal Distribution

xn s

xn s1 1

/ , / ,n n2 12

22

1 2 12

2- -# #v

a a- - -

^ ^h h

Sample Size

z

n

X -vn= n x

z /22

nv= −a

re o


NCEES 511

The Central Limit Theorem

Let X1, X2,...,Xn be a sequence of independent and identically distributed random variables having mean m and vari-ance s2.Then for a large n, the Central Limit Theorem asserts that the sum

...Y X X Xn1 2= + + + is approximately normal

yn n=r

and the standard deviation is nyvv=

r .

Probability and Density FunctionsKind of

DistributionProbability Density Function f(x)

Distribution Function F(x)Expected Mean (m),

Mean (x), Variance (s2)Form of the Density

Function

General (continuous)

Comment: General distribution for continuous values( )

( ) ( )

f x

F x f t dtx

=3−#

( )

( )

x x f x dx

x f x dx2 2 2v n

=

= −3

3

3

3

−

−

##

General (discrete)

Comment: General distribution for discrete values: n is the number in a random sample, xi is the discrete value of the random variable, and Pi is the probability.

( )

P

F x Pi

ii x<=/

( )

( )

x x P

x P

i iin

i iin1

2 2 21v n

=

= −=

=

//

Uniform

Comment: Random variable x = 0 only within the interval <a, b>, where each value is of equal probability. Use when only maximum and minimum values are known

but no other information about the distribution in between.

( )

( )

for

for outsidefor

for

for

f x b a a x b

F x

x a

b ax a a x b

b x

1

00

1

3

3

1 1

1 1

# #

# #

= −

=

−

−−

Z

[

\

]]]]]]]]Z

[

\

]]]]]]]]]]]

x a b

b a2

122

2

v

= +

=−_ i

f(x)

b - a

a μo b x

1

Binomial

Comment: If P(k) is the probability that in n random samples exactly k errors will occur, the error probability is p. Lot size is assumed to be .3

k x<

( )

( )

P k kn p p

F x xn p p

1

1

k n k

k n k

= −

= −

−

−

c `

`

m j

j/ ( )x n p

n p p12v

== −

P(k)n = 20

p = 0.1p = 0.2p = 0.5

0 5

0.30.20.1

10 15 k


512 NCEES

Probability and Density Functions (cont'd)Kind of




Function

Normal (Gaussian)

Comment: Often obtained in practice as measured values with a bell-shaped distribution occurring around a mean value. Special case of the binomial

distribution with . .andn p 0 5" 3 =

( )

( )

exp

exp

f x x

F x

t dt

21

21

21

21x

2

2

v r vn

v r vn

= − −

=

− −3−

d

d

n

n

>

>

H

H

#

m

2v

f(x)μ =

= 0.5

0.5=1

–2 –1 0 1 2x

0σ

σ=2σ

Standardized (unit normal)

Comment: Special case of the Normal (Gaussian) distribution. A unit normal table is included below.

( )

( )

exp

exp

f x x

F x t dt

21

2

21

2x

2

2r

r

= −

= −3−

d

d

n

n#012

n

v

==

---

Hypergeometric

Comment: Sample of dichotomous population (population of two types, e.g., defective/ not defective parts) without replacement. N is lot size, pN is number of defective parts

in the lot, P is the probability that in n random samples k will be defective.

k x#

( )

( )

( )

( )

P knN

kpN

n kN p

F xnN

kpN

n kN p

1

1

=−−

=−−

d

d

c

c

n

n

m

m

=

=

G

G/ ( )

x n p

n p NN n p1 1

2v

=

= −− −

0.3

0.4

0.2

0.1

P(k)

n = 20N = 100

p = 0.04

0 k5 10 15

p = 0.1p = 0.2

Poisson

Comment: P(k) is the probability that in n random samples k errors will occur. Used for curves in a random sampling valuation. Conditions: large value of random samples

with a small value for proportion defective.

k x#

( ) !( )

( ) !( )

P k kn p

e

F x kn p

e

kn p

kn p

=

=

$

$

−

−/x n p

n p2v

==

P(k)n.p = 1

n.p = 10

0.3

0.2

0.1

n.p = 5

0 5 10 15 k


NCEES 513





Function

Exponential

Comment: Special case of the Poisson distribution for x = 0 that gives the probability without error. When used for reliability calculations, replace a x$^ h with failure rate r

multiplied by control time t.

( )

( )

f x a eax

F x e

001

a x

a x

2

$

=

= −

−

−

x a

a

1

122v

=

=

a = 2

a = 1

a = 0.5

0.5

0.5

0

2

1

21

f(x)

x

Geometric

Comment: Describes the number of trials needed to get the first success, with p as the success parameter.

n 1=

( , ) ( )

( ) ( )

f x p p p

F x p p

1

1

x

n

1

1

= −

= −

−

−x

/p

pp

1

122

n

v

=

=− ---

Negative Binomial

Comment: Describes the trial number of the kth success, with k as the stopping parameter and p as the success probability.

k x<

( ) ( )

( ) ( )

P k kn p p

F x kn p p

11 1

11 1

k n k

k n k

= −− −

= −− −

−

−x

c

c

m

m/

x k p

kpp

1

122v

=

=−` j ---

Gamma

Comment: Gamma distribution is widely used to model physical quantities that take positive values. The Gamma function is defined as

( ) ,wherek x e dx k x0 0k x10

$ $C =3 − −#

( )( )

( ) ( )

, where

f xb k

x e

F x k

k bx

bk

1

00

>>

/k

k x b1

C

C

C

=

=

− −

c mx b k

b k2 2v

==

---

Weibull

Comment: Note that when k = 1, the Weibull distribution reduces to the exponential distribution with parameter 1.

( )

( )where

f tbk t e

F t et

10 < <

kk b

t

bt

1k

k

3

=

= −

− −

−c

c

m

m x b k

b k

k

1 1

1 2

1 1

2 2

22

v

C

C

C

= +

= + −

+

c

c

c

m

m

m<

G

---


514 NCEES





Function

Triangular

Comment: The triangular distribution is based on a simple geometric shape. The distribution arises naturally when uniformly distributed random variables are

transformed in various ways.

( )( ) ,

( ) ,

( )( ) ,

( )( ) ,

f x px a a x a p

pa x a p x a w

F x px a a x a p

pa x a p x a w

2

2

1

111

2

2

22

22

# #

# #

# #

# #

~~

~~ ~

~~

~~ ~

=− +

+ − + +

=− +

−−

+ − + +

Z

[

\

]]]]]]]]]]]]

Z

[

\

]]]]]]]]]]]]

( )

[ ( )]

x a p

p p

3 1

18 1 122

~

v~

= + +

= − −

Semicircle

Comment: The semicircular distribution is based on the shape of a semicircle with center a (location parameter) and radius r (scale parameter).

( ) ( )

( ) ( )

arcsin

where

f xr

r x a

F xr

x a r x a

rx a

a r x a r

2

21

1

22 2

22 2

# #

r

r

r

= − −

= + − − − +

−

− +

c m

x ar4

22

v

=

=---

U-Power Distribution

Comment: f(x) is symmetric about m.

( )

( )

where

f x ck

cx

F x cx

c x c

22 1

211

k

k

2

2 1

# #

n

n

n n

= + −

= + −

− −

+

d

d

n

n

> Hx

c kk2 32 12 2

n

v

=

= ++

---


NCEES 515

Normal Distribution Tablex f(x) F(x) R(x) 2 R(x) W(x)

0.0 0.3989 0.5000 0.5000 1.0000 0.00000.1 0.3970 0.5398 0.4602 0.9203 0.07970.2 0.3910 0.5793 0.4207 0.8415 0.15850.3 0.3814 0.6179 0.3821 0.7642 0.23580.4 0.3683 0.6554 0.3446 0.6892 0.31080.5 0.3521 0.6915 0.3085 0.6171 0.38290.6 0.3332 0.7257 0.2743 0.5485 0.45150.7 0.3123 0.7580 0.2420 0.4839 0.51610.8 0.2897 0.7881 0.2119 0.4237 0.57630.9 0.2661 0.8159 0.1841 0.3681 0.63191.0 0.2420 0.8413 0.1587 0.3173 0.68271.1 0.2179 0.8643 0.1357 0.2713 0.72871.2 0.1942 0.8849 0.1151 0.2301 0.76991.3 0.1714 0.9032 0.0968 0.1936 0.80641.4 0.1497 0.9192 0.0808 0.1615 0.83851.5 0.1295 0.9332 0.0668 0.1336 0.86641.6 0.1109 0.9452 0.0548 0.1096 0.89041.7 0.0940 0.9554 0.0446 0.0891 0.91091.8 0.0790 0.9641 0.0359 0.0719 0.92811.9 0.0656 0.9713 0.0287 0.0574 0.94262.0 0.0540 0.9772 0.0228 0.0455 0.95452.1 0.0440 0.9821 0.0179 0.0357 0.96432.2 0.0355 0.9861 0.0139 0.0278 0.97222.3 0.0283 0.9893 0.0107 0.0214 0.97862.4 0.0224 0.9918 0.0082 0.0164 0.98362.5 0.0175 0.9938 0.0062 0.0124 0.98762.6 0.0136 0.9953 0.0047 0.0093 0.99072.7 0.0104 0.9965 0.0035 0.0069 0.99312.8 0.0079 0.9974 0.0026 0.0051 0.99492.9 0.0060 0.9981 0.0019 0.0037 0.99633.0 0.0044 0.9987 0.0013 0.0027 0.9973


516 NCEES

Normal Distribution Table (cont'd)x f(x) F(x) R(x) 2 R(x) W(x)

Fractiles1.2816 0.1755 0.9000 0.1000 0.2000 0.80001.6449 0.1031 0.9500 0.0500 0.1000 0.90001.9600 0.0584 0.9750 0.0250 0.0500 0.95002.0537 0.0484 0.9800 0.0200 0.0400 0.96002.3263 0.0267 0.9900 0.0100 0.0200 0.98002.5758 0.0145 0.9950 0.0050 0.0100 0.9900

7.4.4.6 Linear Regression and Goodness of Fit

Least Squares

y a bx= +t t

where

y-intercept = a y bx-=t r t r

slope = b SSxx

xy=t

1S x y n x y

1 1 1xy i i

i

ni

i

n

ii

n= −

= = −c f fm p p/ / /

S x n x1xx i

i

n

ii

n2

1 1

2

= −= =

c fm p/ /

1y n y1i

i

n=

=r c fm p/

1x n x1i

i

n=

=r c fm p/

where

n = sample size

Sxx = sum of squares of x

Syy = sum of squares of y

Sxy = sum of x-y products

Standard Error Estimate 2S e S e S n

S S SMSE2

2xx

xx yy xy2

=−−

=_ iwhere

1S y n y2

1 1

2

yy ii

ni

i

n= −

= =c fm p/ /


NCEES 517

Confidence Interval for Intercept at

a t n S

x MSE1/ ,n

xx2 2

2! +a −t re o

Confidence Interval for Slope bt

b t SMSE

/ ,nxx

2 2! a -t

Sample Correlation Coefficient R and Coefficient of Determination R2

R

S SS

xx yy

xy= R S SSxx yy

xy22

=

7.4.4.7 Test StatisticsThe following definitions apply:

Zn

Xvar

o-vn= t

ns

Xvar

o- n=

where

Zvar = the standard normal Z score

tvar = the sample distribution test statistic

v = known standard deviation

on = population mean

X = hypothesized mean or sample mean

n = sample size

s = computed sample standard deviation

The Z score is applicable when the standard deviations are known. The test statistic is applicable when the standard deviations are computed at time of sampling.

Za corresponds to the appropriate probability under the normal probability curve for a given Zvar.

ta, n-1 corresponds to the appropriate probability under the t distribution with n-1 degrees of freedom for a given tvar.

Values of Za/2

Confidence Interval Za/2

80% 1.281690% 1.644995% 1.960096% 2.053798% 2.326399% 2.5758

PE C

hemical R

eference Handbook

518

NC

EES

7.5 Chemistry and Physical Properties

7.5.1 Periodic Table of the Elem

entsPeriodic Table of Elements

1

H1.0079

He4.0026

3Li

6.941

4Be

9.0122B

10.811

6C

12.011

7N

14.007

8O

15.999

9F

18.998

10Ne

20.179

11Na

22.990

12Mg

24.305Al

26.981

14Si

28.086

15P

30.974

16S

32.066

17Cl

35.453

18Ar

39.948

19K

39.098

20Ca

40.078

21Sc

44.956

22Ti

47.88

23V

50.941

24Cr

51.996

25Mn

54.938

26Fe

55.847

27Co

58.933

28Ni

58.69

29Cu

63.546

30Zn

65.39

31Ga

69.723

32Ge

72.61

33As

74.921

34Se

78.96

35Br

79.904

36Kr

83.80

37Rb

85.468

38Sr

87.62

39Y

88.906

40Zr

91.224

41Nb

92.906

42Mo

95.94

43Tc

(98)

44Ru

101.07

45Rh

102.91

46Pd

106.42

47Ag

107.87

48Cd

112.41

49In

114.82

50Sn

118.71

51Sb

121.75

52Te

127.60

53I

126.90

54Xe

131.29

55Cs

132.91

56Ba

137.33

57*La

138.91

72Hf

178.49

73Ta

180.95

74W

183.85

75Re

186.21

76Os

190.2

77Ir

192.22

78Pt

195.08

79Au

196.97

80Hg

200.59

81Tl

204.38

82Pb

207.2

83Bi

208.98

84Po

(209)

85At

(210)

86Rn

(222)

87Fr

(223)

88Ra

226.02

89**Ac

227.03

104Rf

(261)

105Ha

(262)

*Lanthanide Series 58Ce

140.12

59Pr

140.91

60Nd

144.24

61Pm

(145)

62Sm

150.36

63Eu

151.96

64Gd

157.25

65Tb

158.92

66Dy

162.50

67Ho

164.93

68Er

167.26

69Tm

168.93

70Yb

173.04

71Lu

174.97

**Actinide Series 90 Th

232.04

91Pa

231.04

92U

238.03

93Np

237.05

94Pu

(244)

95Am

(243)

96Cm

(247)

97Bk

(247)

98Cf

(251)

99Es

(252)

100Fm

(257)

101Md

(258)

102No

(259)

103Lr

(260)

2

5

Atomic Number

Symbol

Atomic Weight

I

II

VIII

VIIVIVIVIII

13

Periodic Table of the Elements


NCEES 519

7.5.2 Relative Atomic Mass

Table of Relative Atomic Mass (Atomic Weight)

Name

SymbolAtomic Number

Atomic Mass

Name

Symbol

Atomic Number

Atomic Mass

Actinium Ac 89 ---* Holmium Ho 67 164.930Aluminum Al 13 26.9815 Hydrogen H 1 1.00797Americium Am 95 ---* Indium In 49 114.82Antimony Sb 51 121.75 Iodine I 53 126.9044Argon Ar 18 39.948 Iridium Ir 77 192.2Arsenic As 33 74.9216 Iron Fe 26 55.847Astatine At 85 ---* Krypton Kr 36 83.80Barium Ba 56 137.34 Lanthanum La 57 138.91Berkelium Bk 97 ---* Lead Pb 82 207.19Beryllium Be 4 9.0122 Lithium Li 3 6.939Bismuth Bi 83 208.980 Lutetium Lu 71 174.97Boron B 5 10.811 Magnesium Mg 12 24.312Bromine Br 35 79.904 Manganese Mn 25 54.9380Cadmium Cd 48 112.40 Mendelevium Md 101 ---*Calcium Ca 20 40.08 Mercury Hg 80 200.59Californium Cf 98 ---* Molybdenum Mo 42 95.94Carbon C 6 12.01115 Neodymium Nd 60 144.24Cerium Ce 58 140.12 Neon Ne 10 20.183Cesium Cs 55 132.905 Neptunium Np 93 ---*Chlorine Cl 17 35.453 Nickel Ni 28 58.71Chromium Cr 24 51.996 Niobium Nb 41 92.906Cobalt Co 27 58.9332 Nitrogen N 7 14.0067Copper Cu 29 63.546 Nobelium No 102 ---*Curium Cm 96 ---* Osmium Os 76 190.2Dysprosium Dy 66 162.50 Oxygen O 8 15.9994Einsteinium Es 99 ---* Palladium Pd 46 106.4Erbium Er 68 167.26 Phosphorus P 15 30.9738Europium Eu 63 151.96 Platinum Pt 78 195.09Fermium Fm 100 ---* Plutonium Pu 94 ---*Fluorine F 9 18.9984 Polonium Po 84 ---*Francium Fr 87 ---* Potassium K 19 39.102Gadolinium Gd 64 157.25 Praseodymium Pr 59 140.907Gallium Ga 31 69.72 Promethium Pm 61 ---*Germanium Ge 32 72.59 Protactinium Pa 91 ---*Gold Au 79 196.967 Radium Ra 88 ---*Hafnium Hf 72 178.49 Radon Rn 86 ---*Helium He 2 4.0026 Rhenium Re 75 186.2


520 NCEES

Table of Relative Atomic Mass (Atomic Weight) (cont'd)

Name

SymbolAtomic Number

Atomic Mass

Name

Symbol

Atomic Number

Atomic Mass

Rhodium Rh 45 102.905 Terbium Tb 65 158.924Rubidium Rb 37 85.47 Thallium Tl 81 204.37Ruthenium Ru 44 101.07 Thorium Th 90 232.038Samarium Sm 62 150.35 Thulium Tm 69 168.934Scandium Sc 21 44 .956 Tin Sn 50 118.69Selenium Se 34 78.96 Titanium Ti 22 47.90Silicon Si 14 28.086 Tungsten W 74 183.85Silver Ag 47 107.868 Uranium U 92 238.03Sodium Na 11 22.9898 Vanadium V 23 50.942Strontium Sr 38 87.62 Xenon Xe 54 131.30Sulfur S 16 32.064 Ytterbium Yb 70 173.04Tantalum Ta 73 180.948 Yttrium Y 39 88.905Technetium Tc 43 ---* Zinc Zn 30 65.37Tellurium Te 52 127.60 Zirconium Zr 40 91.22

* Multiple isotopes


NCEES 521

7.5.3 Oxidation Number

Oxidation Number or Charge NumberName Symbol Charge Name Symbol Charge

Acetate C2H3O2 –1 Iron Fe +2, +3Aluminum Al +3 Lead Pb +2, +4Ammonium NH4 +1 Lithium Li +1Barium Ba +2 Magnesium Mg +2Borate BO3 –3 Mercury Hg +1, +2Boron B +3 Nickel Ni +2, +3Bromine Br –1 Nitrate NO3 –1Calcium Ca +2 Nitrite NO2 –1Carbon C +4, –4 Nitrogen N –3, +1, +2,

+3, +4, +5Carbonate CO3 –2 Oxygen O –2Chlorate ClO3 –1 Perchlorate ClO4 –1Chlorine Cl –1 Permanganate MnO4 –1Chlorite ClO2 –1 Phosphate PO4 –3Chromate CrO4 –2 Phosphorus P –3, +3, +5Chromium Cr +2, +3, +6 Potassium K +1Copper Cu +1, +2 Silicon Si +4, –4Cyanide CN –1 Silver Ag +1Dichromate Cr2O7 –2 Sodium Na +1Fluorine F –1 Sulfate SO4 –2Gold Au +1, +3 Sulfite SO3 –2Hydrogen H +1 Sulfur S –2, +4, +6Hydroxide OH –1 Tin Sn +2, +4Hypochlorite ClO –1 Zinc Zn +2


522 NCEES

7.5.4 Organic Compounds

Families of Organic Compounds

FAMILY Specific Example IUPAC Name Common

NameGeneral Formula Functional Group

Alkane CH3CH3 Ethane Ethane RH C–H and C–C bonds

Alkene H2C = CH2Ethene or ethylene Ethylene

RCH = CH2 RCH = CHR R2C = CHR R2C = CR2

C C=

Alkyne HC = CH Ethyne or acetylene Acetylene RC = CH

RC = CR C C=– –

Arene Benzene Benzene ArH Aromatic ring

Haloalkane CH3CH2Cl Chloroethane Ethyl chloride RX C X

Alcohol CH3CH2OH Ethanol Ethyl alcohol ROH C OH

Ether CH3OCH3Methoxy-methane

Dimethyl ether ROR C CO

Amine CH3NH2 Methanamine MethylamineRNH2 R2NH R3N

C N

AldehydeCH3CH

=

OEthanal Acetaldehyde

RCH

=

O

=

C HO

KetoneCH3CCH3

=

OAcetone Dimethyl

ketone R1CR2

=

O

=

C

O

Carboxylic Acid CH3COH

=

OEthanoic acid Acetic acid

RCOH

=

O

=

C OHO

EsterCH3COCH3

=

O Methyl ethanoate

Methyl acetate RCOR

=

O

CO

=

C

O


NCEES 523

7.5.5 Industrial Chemicals

Common Names of Industrial ChemicalsCommon Name Chemical Name Molecular Formula

Acetone Acetone (CH3)2COAcetylene Acetylene C2H2Ammonia Ammonia NH3Ammonium Ammonium hydroxide NH4OHAnatase/rutile Titanium dioxide TiO2Aniline Aminobenzene C6H5NH2Baking soda Sodium bicarbonate NaHCO3Battery acid Sulfuric acid H2SO4

Bauxite Aluminum oxide Hydrated aluminum oxide

Al OAl O 2H O

2 3

2 3 2:

Bleach Calcium hypochloride Ca(ClO)2Borane Borane BH3

Borax Sodium tetraborate Na B O 10H O2 4 7 2:

Brine, salt Sodium chloride (solution) NaClCarbide Calcium carbide CaC2Carbolic acid Phenol C6H5OHCarbon dioxide Carbon dioxide CO2Carborundum Silicon carbide SiCCaustic soda/lye Sodium hydroxide NaOHChalk Calcium carbonate CaCO3Chlorite Chlorite ion ClO2

–1

Chlorate Chlorate ion ClO3–1

Cinnabar Mercuric sulfide HgSCumene Isopropyl benzene C6H5CH(CH3)2

Deuterium Deuterium H2

Dichromate Dichromate ion Cr2O7-2

Dolomite Magnesium carbonate MgCO3Epsom salt Magnesium sulfate MgSO4Ether Diethyl ether (C2H3)2OEthylene oxide Ethylene oxide C2H4OEyewash Boric acid (solution) H3BO3Formic acid Methanoic acid HCOOHGlauber's salt Decahydrated sodium sulfate Na SO 10H O2 4 2:

Glycerine Glycerine C3H5(OH)3Grain alcohol Ethanol C2H5OHGraphite Crystalline carbon CGypsum Calcium sulfate CaSO 2H O4 2:


524 NCEES

Common Names of Industrial Chemicals (cont'd)Common Name Chemical Name Molecular Formula

Heavy water Deuterium oxide (H2)2OHydronium Hydronium ion H3O+1

Hydroquinone P-dihydroxybenzene C6H4(OH)2Hypochlorite Hypochlorite ion OCl–1

Iron chloride Ferrous chloride FeCl 4H O2 2:

Laughing gas Nitrous oxide N2OLimestone Calcium carbonate CaCO3Magnesia Magnesium oxide MgOMagnetite Ferrous/ferric oxide Fe3O4Marsh gas Methane CH4Muriate of potash Potassium chloride KClMuriatic acid Hydrochloric acid HClNeopentane 2,2-dimethylpropane CH3C(CH3)2CH3Niter Sodium nitrate NaNO3Niter cake Sodium bisulfate NaHSO4Oleum Fuming sulfuric acid SO3 in H2SO4Ozone Ozone O3Perchlorate Perchlorate ion ClO4

–1

Permanganate Permanganate ion MnO4–1

Phosgene Phosgene COCl2Potash Potassium carbonate K2CO3Prussic acid Hydrogen cyanide HCNPyrite, Fool's Gold Ferrous sulfide FeSPyrolusite Manganese dioxide MnO2Quicklime Calcium oxide CaOQuicksilver Mercury HgSal soda/washing soda Decahydrated sodium carbonate Na CO 10H O3 22 :

Salammoniac Ammonium chloride NH4ClSalt/halite Sodium chloride NaClSalt cake Sodium sulfate (crude) Na2SO4Sand/silica Silicon dioxide SiO2Silane Silane SiH4Slaked lime Calcium hydroxide Ca(OH)2Soda ash Sodium carbonate Na2CO3Styrene Vinyl benzene C6H5CH=CH2Sugar Sucrose C12H22O11

Stannous chloride Stannous chloride SnCl 2H O2 2:

SuperphosphateMonohydrated primary calcium

phosphate Ca H PO H O2 4 2 2:^ h


NCEES 525

Common Names of Industrial Chemicals (cont'd)Common Name Chemical Name Molecular Formula

Toluene Methyl benzene C6H5CH3Trilene Tricholormethylene C2HCl3Tritium Tritium H3

Urea Urea (NH2)2COVinegar (acetic acid) Ethanoic acid CH2COOHVinyl alcohol Vinyl alcohol CH2=CHOHVinyl chloride Vinyl chloride CH2=CHClWood alcohol Methanol CH3OHWolfram Tungsten WXylene Dimethyl benzene C6H4(CH3)2Zinc blende Zinc sulfide ZiS


526 NCEES

527

8 PHYSICAL PROPERTIES


Symbols

Symbol Description Units (U.S.) Units (SI)

cp Heat capacity (at constant pressure) lbm FBtu-c kg K s K

m12

2

: :=

cv Heat capacity (at constant volume) lbm FBtu-c kg K s K

m12

2

: :=

h Specific enthalpy lbmBtu

kgJ

Dhfusion Enthalpy of fusion lbmBtu

kgJ

Dhvap Enthalpy of vaporization lbmBtu

kgJ

k Thermal conductivity hr ft FBtu- -c m K

W:

MW Molar mass (molecular weight) lb molelbm

molg

P Pressureinlbf2 or psi Pa =

m skg

2:

r Ratio of heat capacities = ccv

p dimensionless

s Specific entropy lbm FBtu-c kg K

1:

T Temperature F Rorc c C Korc

v Specific volumelbmft3

kgm3

a Thermal diffusivitysecft2

sm2


528 NCEES


g Surface tension cmdyne

mN

m Dynamic viscosity secftlbm- Pa s m s

kg: :=

u Kinematic viscosity secft2

sm2

r Density ftlbm3 m

kg3

r Electrical resistivity ft-X m:X

8.2 Physical Properties of Metals

8.2.1 U.S. Customary Units

Physical Properties of Metals at 68°F (U.S. Units)

Property:

Mol

ar M

ass

Den

sity

Hea

t C

apac

ity

The

rmal

C

ondu

ctiv

ity

The

rmal

D

iffus

ivity

Ele

ctri

cal

Res

istiv

ity

(0°C

)

Mel

ting

Poin

t

Hea

t of

Fusi

on

U.S. Unit: lb molelbm

ftlbm3 lbm F

Btu-c hr ft F

Btu- -c hr

ft2 ft 10- 8:X− Fc lbm

Btu

Aluminum 26.98 168 0.214 136.35 3.55 8.20 1220 138.2Brass 70%Cu, 30%Zn 532.0 0.091 61.80 1.27 1700 72.2Bronze 75%Cu, 25%Sn 540.0 0.082 15.00 1200Calcium 40.08 95.5 0.152 10.50 1544 83.58Chromium 52.00 449.1 0.097 55.75 41.67 2939 215.4Constantan 557.0 0.098 13.10 0.24 2336Copper 63.54 557.7 0.093 232.84 3.98 5.09 1983 89Gold 196.97 1203.7 0.031 184.31 4.52 6.73 1947 28.8Iron 55.85 491.5 0.109 48.24 0.83 29.20 2804 114.7Iron, cast 455.0 0.100 29.60 0.65 41.4Lead 207.20 708.1 0.031 20.80 0.80 62.99 621 10.62Lithium 6.94 33.3 1.093 49.69 28.05 356 147.4Magnesium 24.31 108.5 0.250 90.71 3.68 12.93 1202Manganese 54.94 466.5 0.120 4.62 452.75 2282 114.6Mercury (liquid) 200.59 845.7 0.034 4.51 308.72 –38 5.08Molybdenum 95.94 638.2 0.065 80.31 16.40 4748 186.3Nickel 58.69 556.1 0.105 54.31 0.87 20.34 2651 132.8Nichrome V 530.0 0.106 7.06 0.12Palladium 106.40 748.8 0.055 41.60 32.81 2829Platinum 195.08 1339.1 0.032 41.60 0.09 32.18 3222 43.3Potassium 39.09 53.8 0.180 60.09 20.01 145 25.0

Chapter 8: Physical Properties

NCEES 529

Physical Properties of Metals at 68°F (U.S. Units) (cont'd)

Property:

Mol

ar M

ass

Den

sity

Hea

t C

apac

ity

The

rmal

C

ondu

ctiv

ity

The

rmal

D

iffus

ivity

Ele

ctri

cal

Res

istiv

ity

(0°C

)

Mel

ting

Poin

t

Hea

t of

Fusi

on

U.S. Unit: lb molelbm

ftlbm3 lbm F

Btu-c hr ft F

Btu- -c hr

ft2 ft 10- 8:X− Fc lbm

Btu

Rhodium 102.91 775.4 0.058 87.24 14.11 3565Silver 107.87 655.5 0.056 247.28 6.42 4.82 1762 45.0Sodium 22.99 60.3 0.295 82.04 13.78 208 37.8Steel, carbonSteel, mild (1%C) 488.0 0.113 24.80 0.45Steel, stainless 488.0 0.110 9.40 0.17Tin 118.69 454.8 0.055 39.29 1.57 37.73 450 25.2Titanium 47.88 281.4 0.126 12.71 127.95 3038 122.6Tungsten 183.85 1202.0 0.034 102.26 2.44 16.08 6129 109.7Uranium 238.03 1189.3 0.028 15.60 0.53 91.86 2075Zinc 65.38 445.4 0.094 67.60 1.55 18.04 786 43.9

8.2.2 SI Units

Physical Properties of Metals at 20°C (SI Units)

Property:

Mol

ar M

ass

Den

sity

Hea

t C

apac

ity

The

rmal

C

ondu

ctiv

ity

The

rmal

D

iffus

ivity

Ele

ctri

cal

Res

istiv

ity

(0°C

)

Mel

ting

Poin

t

Hea

t of

Fusi

on

SI Unit: molg

mkg3 kg K

J: m K

W: s

m2ft 10- 8:X

− Cc kgkJ

Aluminum 26.98 2698 896 236.0 91.61 2.50 660 321.5Brass 70%Cu, 30%Zn 8522 381 107.0 32.77 927 167.9Bronze 75%Cu, 25%Sn 8650 343 26.0 649Calcium 40.08 1530 636 3.20 840 194.4Chromium 52.00 7194 407 96.5 12.70 1615 501.1Constantan 8922 410 22.7 6.19 1280Copper 63.54 8933 389 403.0 102.71 1.55 1084 207.0Gold 196.97 19,281 130 319.0 116.64 2.05 1064 67.0Iron 55.85 7873 456 83.5 21.42 8.90 1540 266.7Iron, cast 7288 419 51.2 16.77 96.3Lead 207.20 11,343 130 36.0 20.64 19.20 327 24.7Lithium 6.94 533 4576 86.0 8.55 180 342.9Magnesium 24.31 1738 1047 157.0 94.97 3.94 650Manganese 54.94 7473 502 8.0 138.00 1250 266.6Mercury (liquid) 200.59 13,547 142 7.8 94.10 –39 11.8


530 NCEES

Physical Properties of Metals at 20°C (SI Units) (cont'd)

Property:

Mol

ar M

ass

Den

sity

Hea

t C

apac

ity

The

rmal

C

ondu

ctiv

ity

The

rmal

D

iffus

ivity

Ele

ctri

cal

Res

istiv

ity

(0°C

)

Mel

ting

Poin

t

Hea

t of

Fusi

on

SI Unit: molg

mkg3 kg K

J: m K

W: s

m2ft 10- 8:X

− Cc kgkJ

Molybdenum 95.94 10,222 272 139.0 5.00 2620 433.3Nickel 58.69 8907 440 94.0 22.45 6.20 1455 308.9Nichrome V 8490 444 12.2 3.10Palladium 106.40 11,995 230 72.0 10.00 1554Platinum 195.08 21,450 134 72.0 2.32 9.81 1772 100.8Potassium 39.09 862 754 104.0 6.10 63 58.1Rhodium 102.91 12,420 243 151.0 4.30 1963Silver 107.87 10,500 235 428.0 165.67 1.47 961 104.7Sodium 22.99 966 1235 142.0 4.20 98 87.9Steel, carbonSteel, mild (1%C) 7817 473 42.9 11.61Steel, stainless 7817 461 16.3 4.39Tin 118.69 7285 230 68.0 40.52 11.50 232 58.6Titanium 47.88 4508 528 22.0 39.00 1670 285.1Tungsten 183.85 19,254 143 177.0 62.97 4.90 3387 255.1Uranium 238.03 19,050 117 27.0 13.68 28.00 1135Zinc 65.38 7135 394 117.0 40.00 5.50 419 102.1

8.3 Physical Properties of Plastics


Physical Properties of Plastics (U.S. Units)Property: Density Heat Capacity Thermal Conductivity

U.S. Unit:ftlbm3 lbm F

Btu-c hr ft F

Btu- -c

ABS 64–75 0.361–0.370 0.092–0.156Nylon 64–71 0.330–0.399 0.098–0.196Polycarbonate 57–78 0.279–0.301 0.110–0.127Polyethylene 57–60 0.499–0.549 0.243–0.283Polyester 69–125 0.320–0.499 0.191–0.526PVC 77–97 0.251 0.081–0.110Polystyrene foam 1.0–2.0 0.017–0.023


NCEES 531

8.3.2 SI Units

Physical Properties of Plastics (SI Units)Property: Density Heat Capacity Thermal Conductivity

SI Unit:mkg3 kg K

1: m K

W:

ABS 1020–1200 1510–1550 0.16–0.27Nylon 1030–1140 1380–1670 0.17–0.34Polycarbonate 910–1250 1170–1260 0.19–0.22Polyethylene 913–968 2090–2300 0.42–0.49Polyester 1100–2010 1340–2090 0.33–0.91PVC 1240–1550 1050 0.14–0.19Polystyrene foam 16–32 0.03–0.04

8.3.3 Chemical Resistance of Plastics

Chemical Resistance of Plastics

Plastic:

Poly

prop

ylen

e,

Poly

ethy

lene

Cel

lulo

se A

ceta

te

But

yrat

e (C

AB

)

Acr

ylon

itrile

B

utad

iene

Sty

rene

Po

lym

er (A

BS)

Poly

viny

l C

hlor

ide,

Typ

e I

(PV

C)

Sara

n

Poly

este

r G

lass

Epo

xy G

lass

Phen

olic

Asb

esto

s

Fluo

roca

rbon

s

Chl

orin

ated

Po

lyet

her

(Pen

ton)

Poly

carb

onat

e

10% H2SO4 Excel. Good Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.50% H2SO4 Excel. Poor Excel. Excel. Excel. Good Good Excel. Excel. Excel. Excel.10% HCl Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.10% HNO3 Excel. Poor Good Excel. Excel. Good Good Fair Excel. Excel. Excel.10% Acetic Excel. Good Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.10% NaOH Excel. Fair Excel. Good Fair Fair Excel. Poor Excel. Excel. Excel.50% NaOH Excel. Poor Excel. Excel. Fair Poor Good Poor Excel. Excel. Excel.NH4OH Excel. Poor Excel. Excel. Poor Fair Excel. Poor Excel. Excel. Excel.NaCl Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.FeCl2 Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.CuSO4 Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.NH4NO3 Excel. Excel. Excel. Excel. Excel. Excel. Excel. Good Excel. Excel. Excel.Wet H2S Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.Wet Cl2 Poor Poor Excel. Good Poor Poor Poor Excel. Excel. Excel.Wet SO2 Excel. Poor Excel. Excel. Good Excel. Excel. Excel. Excel. Excel.Gasoline Poor Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.Benzene Poor Poor Poor Poor Fair Good Excel. Excel. Excel. Fair FairCCl4 Poor Poor Poor Fair Fair Excel. Good Excel. Excel. Fair PoorAcetone Poor Poor Poor Poor Fair Poor Good Poor Excel. Good GoodAlcohol Poor Poor Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.

Source: Perry, R.H., and D. Green, Perry’s Chemical Engineers’ Handbook, 6th ed., New York: McGraw-Hill, 1985, pp. 23–52.


532 NCEES

8.4 Physical Properties of Liquids and Gases—Temperature-Independent Properties


Temperature-Independent Properties of Liquids and Gases (U.S. Units)

Property:

Form

ula

Mol

ar M

ass

Nor

mal

B

oilin

g Po

int

(NB

P)

Trip

le P

oint

Hea

t of

Vapo

riza

tion

at N

BP

Cri

tical

Te

mpe

ratu

re

Cri

tical

Pr

essu

re

Cri

tical

D

ensi

ty

Chemical

$

lb molelbm Fc Fc lbm

Btu Fc psiaftlbm3

Acetaldehyde C2H4O 44.053 69.8 –190.1 253.2 379.1 807.8 17.85Acetic Acid C2H4O2 60.052 244.2 62.0 167.4 605.8 839.2 21.17Acetone C3H6O 58.079 455.1 –138.5 219.3 455.1 681.7 17.34Acetylene C2H2 26.037 –114.7 564.4 270.5 95.4 900.1 13.82Air 28.965 –317.6 –352.1 –221.1 549.1 21.39Ammonia NH3 17.031 –28.0 –107.8 588.8 270.1 1643.7 14.05Argon Ar 39.948 –302.5 –301.7 69.3 –188.4 724.1 33.44Benzene C6H6 78.112 176.1 41.9 169.3 552.0 711.7 19.02n-Butane C4H10 58.122 31.1 –216.9 165.7 305.5 550.6 14.23iso-Butane C4H10 58.122 10.9 –255.0 157.0 274.4 526.3 14.081-Butene C4H8 56.106 20.6 –301.6 167.5 295.4 583.1 14.541-Butanol C4H10O 74.1216 245.8 –128.7 249.6 553.9 640.2 16.951,3-Butadiene C4H6 54.090 23.8 –164.0 178.1 305.5 619.4 15.161,2-Butadiene C4H6 54.090 51.7 –213.2 190.4 362.0 702.9 15.45Carbon dioxide CO2 44.010 –109.2 –69.8 246.5 87.8 1070.0 29.19Carbon monoxide CO 28.010 –312.7 –337.0 92.3 –220.5 506.8 18.97Carbonyl sulfide COS 60.075 –58.3 –217.9 132.8 222.1 923.7 27.78Carbon tetrachloride CCl4 153.823 170.0 –9.1 83.0 541.8 661.4 34.79Chlorine Cl2 70.906 –29.2 –149.7 121.5 290.7 1157.1 34.01Cumene (isopropyl-benzene) C9H12 120.192 306.2 –140.8 131.9 676.4 462.2 17.78

Cyclohexane C6H12 84.160 177.3 44.1 153.2 536.8 591.8 16.94n-Decane C10H22 142.282 345.4 –21.4 118.8 652.2 305.0 14.57Diethyl ether C4H10O 74.122 94.0 –177.3 154.2 380.4 527.9 16.52Ethane C2H6 30.069 –127.4 –297.0 210.4 89.9 706.7 12.87Ethanol C2H6O 46.068 172.9 172.9 365.7 465.5 890.1 17.11Ethyl acetate C4H8O2 88.105 170.7 –118.4 156.9 482.3 562.7 19.23Ethylbenzene C8H10 106.165 277.1 –138.9 144.2 651.2 525.4 18.17Ethylene C2H4 28.053 –154.8 –272.5 207.4 48.6 731.3 13.37


NCEES 533

Temperature-Independent Properties of Liquids and Gases (U.S. Units) (cont'd)

Property:

Form

ula

Mol

ar M

ass

Nor

mal

B

oilin

g Po

int

(NB

P)

Trip

le P

oint

Hea

t of

Vapo

riza

tion

at N

BP

Cri

tical

Te

mpe

ratu

re

Cri

tical

Pr

essu

re

Cri

tical

D

ensi

ty

Chemical

$

lb molelbm Fc Fc lbm

BtuFc psia ft

lbm3

Ethylene glycol C2H6O2 62.000 387.0 7.9 Fluorine F2 37.997 –306.6 –363.4 75.0 –199.7 770.2 37.01Formaldehyde CH2O 30.026 –2.7 –180.4 329.7 296.3 955.8 22.02Helium He 4.003 –781.7 –788.4 8.8 –450.3 33.1 4.34n-Heptane C7H16 100.202 209.1 –131.1 136.2 512.6 396.8 14.48n-Hexane C6H14 86.175 155.7 –139.6 144.0 453.8 436.9 14.56Hydrogen H2 2.016 –423.0 –434.6 192.9 –400.0 188.0 1.95Hydrogen chloride HCl 36.461 –121.0 –173.5 190.7 124.5 1202.1 26.86Hydrogen sulfide H2S 34.081 –76.5 –121.8 234.9 211.9 1305.3 21.68Methane CH4 16.043 –258.7 –296.4 219.6 –116.7 667.1 10.15Methanol CH4O 32.042 148.5 –143.8 473.1 462.8 1172.5 17.09Methyl acetate C3H6O2 74.07854 134.5 –144.4 176.7 452.1 688.9 20.28Methyl amine CH5N 31.057 20.6 –136.2 361.0 314.4 1082.0 12.59Methyl ethyl ketone C4H8O 72.106 175.4 –124.0 188.5 504.2 601.9 16.85Neon Ne 20.180 –410.9 –415.5 36.9 –379.6 398.9 30.09Nitrogen N2 28.013 –320.4 –346.0 85.6 –232.5 492.5 19.56n-Nonane C9H20 128.255 303.4 –64.2 124.1 610.5 330.8 14.49n-Octane C8H18 114.229 258.1 –70.2 129.9 564.2 360.7 14.66iso-Octane (2,2,4- trimethylpentane) C8H18 114.229 210.6 –161.3 115.3 519.5 373.0 15.12

Oxygen O2 31.999 –297.3 –361.8 91.6 –181.4 731.4 27.23n-Pentane C5H12 72.149 96.9 –201.4 153.7 385.8 488.8 14.48Propane C3H8 44.096 –43.8 –305.7 183.0 206.1 616.6 13.761-Propanol C3H8O 60.095 207.0 –195.2 297.5 506.6 749.7 17.13Propylene C3H6 42.080 –53.7 –301.4 188.7 195.9 660.6 14.33Sulfur dioxide SO2 64.064 14.0 –103.8 167.3 315.5 1143.5 32.77Styrene C8H8 104.149 293.5 –23.2 151.2 683.7 563.2 18.24Toluene C7H8 92.138 231.1 –139.3 155.1 605.5 598.5 18.23Water H2O 18.015 212.0 32.0 970.1 705.1 3200.1 20.10p-Xylene C8H10 106.165 281.0 55.9 144.6 649.4 512.2 17.85m-Xylene C8H10 106.165 282.3 –54.1 146.2 650.7 512.7 17.66o-Xylene C8H10 106.165 291.9 –13.3 147.3 674.8 542.1 17.79


534 NCEES

8.4.2 SI Units

Temperature-Independent Properties of Liquids and Gases (SI Units)

Property:

Form

ula

Mol

ar M

ass

Nor

mal

B

oilin

g Po

int

(NB

P)

Trip

le P

oint

Hea

t of

Vapo

riza

tion

at N

BP

Cri

tical

Te

mpe

ratu

re

Cri

tical

Pr

essu

re

Cri

tical

D

ensi

ty

Chemical

$

molg

Cc Cc kgkJ

Cc MPamkg3

Acetaldehyde C2H4O 44.053 21.0 –123.4 588.8 192.9 5.57 286Acetic Acid C2H4O2 60.052 117.9 16.7 389.3 318.8 5.79 339Acetone C3H6O 58.079 235.1 –94.7 510.0 235.1 4.70 278Acetylene C2H2 26.037 –81.5 295.8 629.3 35.2 6.21 221Air 28.965 –194.2 –213.4 –140.6 3.79 343Ammonia NH3 17.031 –33.3 –77.7 1,369.5 132.3 11.33 225Argon Ar 39.948 –185.8 –185.4 161.2 –122.5 4.99 536Benzene C6H6 78.112 80.1 5.5 393.8 288.9 4.91 305n-Butane C4H10 58.122 –0.5 –138.3 385.5 152.0 3.80 228Isobutane C4H10 58.122 –11.7 –159.4 365.2 134.7 3.63 2261-Butene C4H8 56.106 –6.35 –185.35 389.7 146.35 4.02 2331-Butanol C4H10O 74.1216 118.75 –89.3 580.573 289.95 4.414 2721,3-Butadiene C4H6 54.090 –4.6 –108.9 414.3 151.9 4.27 2431,2-Butadiene C4H6 54.090 11.0 –136.2 442.9 183.4 4.85 247Carbon dioxide CO2 44.010 –78.5 –56.6 573.4 31.0 7.38 468Carbon monoxide CO 28.010 –191.5 –205.0 214.7 –140.3 3.49 304Carbonyl sulfide COS 60.075 –50.2 –138.8 308.9 105.6 6.37 445Carbon tetrachloride CCl4 153.823 76.6 –22.82 193.1 283.2 4.56 557Chlorine Cl2 70.906 –34.0 –100.9 282.6 143.7 7.98 545Cumene (isopropyl-benzene) C9H12 120.192 152.3 –96.0 306.8 358.0 3.19 285

Cyclohexane C6H12 84.160 80.7 6.7 356.3 280.5 4.08 271n-Decane C10H22 142.282 174.1 –29.7 276.3 344.6 2.10 233Diethyl ether C4H10O 74.122 34.4 –116.3 358.6 193.6 3.64 265Ethane C2H6 30.069 –88.6 –182.8 489.4 32.2 4.87 206Ethanol C2H6O 46.068 78.3 78.3 850.6 240.9 6.14 274Ethyl acetate C4H8O2 88.105 77.1 –83.6 365.0 250.2 3.88 308Ethylbenzene C8H10 106.165 136.2 –95.0 335.4 344.0 3.62 291Ethylene C2H4 28.053 –103.8 –169.2 482.4 9.2 5.04 214Ethylene glycol C2H6O2 62.000 197.2 –13.4 Fluorine F2 37.997 –188.1 –219.7 174.4 –128.7 5.31 593Formaldehyde CH2O 30.026 –19.3 –118.0 767.0 146.9 6.59 353Helium He 4.003 –452.1 –455.8 20.6 –268.0 0.23 70n-Heptane C7H16 100.202 98.4 –90.6 316.8 267.0 2.74 232n-Hexane C6H14 86.175 68.7 –95.3 334.9 234.3 3.01 233


NCEES 535

Temperature-Independent Properties of Liquids and Gases (SI Units) (cont'd)

Property:

Form

ula

Mol

ar M

ass

Nor

mal

B

oilin

g Po

int

(NB

P)

Trip

le P

oint

Hea

t of

Vapo

riza

tion

at N

BP

Cri

tical

Te

mpe

ratu

re

Cri

tical

Pr

essu

re

Cri

tical

D

ensi

ty

Chemical

$

molg

Cc Cc kgkJ Cc MPa

mkg3

Hydrogen H2 2.016 –252.8 –259.2 448.7 –240.0 1.30 31Hydrogen chloride HCl 36.461 –85.0 –114.1 443.6 51.4 8.29 430Hydrogen sulfide H2S 34.081 –60.3 –85.5 546.4 100.0 9.00 347Methane CH4 16.043 –161.5 –182.5 510.8 –82.6 4.60 163Methanol CH4O 32.042 64.7 –97.7 1100.5 239.4 8.08 274Methyl acetate C3H6O2 74.07854 56.9 –98.0 411.1 233.4 4.75 325Methyl amine CH5N 31.057 –6.3 –93.5 839.8 156.9 7.46 202Methyl ethyl ketone C4H8O 72.106 79.6 –86.7 438.3 262.4 4.15 270Neon Ne 20.180 –246.0 –248.6 85.8 –228.7 2.75 482Nitrogen N2 28.013 –195.8 –210.0 199.2 –147.0 3.40 313n-Nonane C9H20 128.255 150.8 –53.5 288.7 321.4 2.28 232n-Octane C8H18 114.229 125.6 –56.8 302.1 295.7 2.49 235iso-Octane (2,2,4-tri-methylpentane) C8H18 114.229 99.2 –107.4 268.2 270.9 2.57 242

Oxygen O2 31.999 –183.0 –218.8 213.1 –118.6 5.04 436n-Pentane C5H12 72.149 36.1 –129.7 357.5 196.6 3.37 232Propane C3H8 44.096 –42.1 –187.6 425.7 96.7 4.25 2201-Propanol C3H8O 60.095 97.2 –126.2 692.0 263.7 5.17 274Propylene C3H6 42.080 –47.6 –185.2 438.9 91.1 4.55 230Sulfur dioxide SO2 64.064 –10.0 –75.5 389.1 157.5 7.88 525Styrene C8H8 104.149 145.3 –30.7 351.7 362.1 3.88 292Toluene C7H8 92.138 110.6 –95.2 360.8 318.6 4.13 292Water H2O 18.015 100.0 0.0 2256.5 705.1 22.06 322p-Xylene C8H10 106.165 138.3 13.3 336.3 343.0 3.53 286m-Xylene C8H10 106.165 139.1 –47.9 340.1 343.7 3.53 283o-Xylene C8H10 106.165 144.4 –25.2 342.6 357.1 3.74 285

Source for tables in Section 8.4: "Table of Physical Properties for Hydrocarbons and Other Compounds of Interest to the Natural Gas and Natural Gas Liquids Industries," GPS Standard 2145-16, Tulsa, OK:

GPA Midstream Association, 2016, pp. 4–9, and NIST Chemistry Web Book, NIST Standard Reference Database Number 69, P.J. Linstrom and W.G. Mallard, eds.


536 NCEES

8.5 Physical Properties of Liquids and Gases—Temperature-Dependent Properties


Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units)

GasTemperature Density Heat

Capacity (Cp)Thermal

ConductivityThermal

Diffusivity ViscosityPrandtl Number

Fcftlbm3 lb F

Btu-c ft hr F

Btu- -c hr

ft2secft

lbm-

Nitrogen

0 0.0835 0.248 0.0129 0.624 10.6E–6 0.730200 0.0582 0.249 0.0175 1.21 13.9E–6 0.713400 0.0446 0.251 0.0217 1.93 16.8E–6 0.704600 0.0362 0.256 0.0256 2.76 19.5E–6 0.701800 0.0304 0.262 0.0294 3.69 22.0E–6 0.7041000 0.0263 0.269 0.0331 4.68 24.3E–6 0.709

Oxygen

0 0.0955 0.218 0.0133 0.637 12.2E–6 0.722200 0.0664 0.222 0.0184 1.24 16.3E–6 0.710400 0.0510 0.230 0.0231 1.97 19.9E–6 0.714600 0.0414 0.239 0.0276 2.79 23.1E–6 0.721800 0.0348 0.246 0.0318 3.71 26.1E–6 0.7271000 0.0300 0.252 0.0359 4.74 28.8E–6 0.730

Carbon Monoxide

0 0.0835 0.248 0.0126 0.608 10.5E–6 0.745200 0.0581 0.249 0.0172 1.18 13.9E–6 0.727400 0.0446 0.253 0.0213 1.88 16.8E–6 0.719600 0.0362 0.259 0.0251 2.68 19.4E–6 0.721800 0.0304 0.266 0.0286 3.54 21.7E–6 0.7261000 0.0263 0.273 0.0320 4.47 23.9E–6 0.733

Carbon Dioxide

0 0.131 0.190 0.00763 0.307 8.65E–6 0.774200 0.0914 0.219 0.0127 0.632 12.2E–6 0.760400 0.0701 0.239 0.0179 1.07 15.3E–6 0.739600 0.0569 0.255 0.0230 1.59 18.2E–6 0.723800 0.0479 0.268 0.0279 2.18 20.8E–6 0.7161000 0.0413 0.279 0.0325 2.82 23.2E–6 0.715

Sulfur Dioxide

0 0.195* 0.143 0.00443 0.159 7.38E–6 0.856200 0.134 0.158 0.00738 0.349 10.7E–6 0.823400 0.102 0.171 0.0107 0.612 13.8E–6 0.791600 0.0829 0.182 0.0142 0.945 16.6E–6 0.764800 0.0697 0.190 0.0177 1.34 19.3E–6 0.7461000 0.0601 0.196 0.0208 1.76 21.8E–6 0.741

Air

0 0.0864 0.239 0.0132 0.639 11.06E–6 0.716200 0.0601 0.240 0.0178 1.23 14.5E–6 0.705400 0.0461 0.244 0.0220 1.95 17.5E–6 0.698600 0.0374 0.249 0.0259 2.78 20.1E–6 0.697800 0.0315 0.256 0.0297 3.69 22.5E–6 0.6981000 0.0272 0.262 0.0333 4.68 24.7E–6 0.698


NCEES 537

Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) (cont'd)



ConductivityThermal


Fc ftlbm3 lb F

Btu-c ft hr F

Btu- -c hr

ft2secft

lbm-

Hydrogen

0 0.00600 3.37 0.0911 4.50 5.38E–6 0.718200 0.00420 3.45 0.121 8.34 6.89E–6 0.708400 0.00320 3.47 0.148 13.3 8.27E–6 0.697600 0.00260 3.47 0.174 19.3 9.54E–6 0.685800 0.00220 3.48 0.199 25.9 10.7E–6 0.6781000 0.00190 3.51 0.222 33.4 11.9E–6 0.675

Ammonia

0 0.0514 0.484 0.0117 0.471 5.76E–6 0.857200 0.0355 0.529 0.0193 1.03 8.48E–6 0.837400 0.0272 0.581 0.0278 1.76 11.2E–6 0.843600 0.0220 0.630 0.0371 2.67 13.9E–6 0.851800 0.0185 0.677 0.0471 3.76 16.6E–6 0.8601000 0.0160 0.722 0.0577 4.99 19.3E–6 0.869

Helium

0 0.0119 1.24 0.0802 5.43 12.0E–6 0.669200 0.00830 1.24 0.102 9.94 15.4E–6 0.671400 0.00640 1.24 0.123 15.5 18.5E–6 0.672600 0.00520 1.24 0.142 22.0 21.4E–6 0.672800 0.00440 1.24 0.160 29.4 24.2E–6 0.6721000 0.00380 1.24 0.178 37.8 26.8E–6 0.672

Neon

0 0.0601 0.246 0.0253 1.71 19.0E–6 0.664200 0.0419 0.246 0.0325 3.15 24.3E–6 0.662400 0.0321 0.246 0.0390 4.93 29.1E–6 0.660600 0.0261 0.246 0.0449 7.00 33.5E–6 0.660800 0.0219 0.246 0.0505 9.38 37.6E–6 0.6591000 0.0189 0.246 0.0558 12.0 41.5E–6 0.659

Argon

0 0.119 0.124 0.00903 0.609 13.4E–6 0.663200 0.0830 0.124 0.0121 1.17 18.0E–6 0.666400 0.0636 0.124 0.0148 1.87 22.1E–6 0.667600 0.0516 0.124 0.0173 2.69 25.8E–6 0.667800 0.0434 0.124 0.0196 3.63 29.2E–6 0.6671000 0.0375 0.124 0.0217 4.66 32.4E–6 0.667

Fluorine

0 0.113 0.192 0.0127 0.585 13.6E–6 0.740200 0.0789 0.204 0.0179 1.11 18.4E–6 0.758400 0.0605 0.214 0.0229 1.77 22.7E–6 0.763600 0.0491 0.220 0.0279 2.58 26.7E–6 0.759800 0.0413 0.225 0.0328 3.53 30.4E–6 0.7511000 0.0356 0.229 0.0376** 4.62 33.9E–6 0.741


538 NCEES




ConductivityThermal


Fc ftlbm3 lb F

Btu-c ft hr F

Btu- -c hr

ft2secft

lbm-

Chlorine

0 0.215 0.112 0.00429 0.178 7.72E–6 0.724200 0.148 0.118 0.00649 0.372 11.0E–6 0.720400 0.113 0.121 0.00861 0.629 14.1E–6 0.713600 0.0918 0.123 0.0106 0.943 17.0E–6 0.708800 0.0772 0.124 0.0126 1.31 19.8E–6 0.7051000 0.0666 0.125 0.0144 1.73 22.5E–6 0.704

Methane

0 0.0480 0.512 0.0164 0.667 6.57E–6 0.739200 0.0333 0.578 0.0256 1.33 8.93E–6 0.727400 0.0256 0.673 0.0360 2.09 11.0E–6 0.741600 0.0207 0.772 0.0475 2.97 12.9E–6 0.755800 0.0174 0.866 0.0599** 3.97 14.6E–6 0.7621000 0.0150 0.953 0.0731** 5.11 16.3E–6 0.763

Ethane

0 0.0907 0.377 0.00939 0.275 5.43E–6 0.786200 0.0627 0.485 0.0179 0.590 7.59E–6 0.739400 0.0480 0.599 0.0282 0.981 9.56E–6 0.731600 0.0389 0.700 0.0399 1.46 11.4E–6 0.720800 0.0327 0.787 0.0526 2.04 13.1E–6 0.7061000 0.0282 0.863 0.0663 2.72 14.7E–6 0.691

Propane

0 0.135 0.353 0.00777 0.163 4.87E–6 0.797200 0.0923 0.470 0.0151 0.348 6.74E–6 0.757400 0.0705 0.589 0.0242 0.583 8.56E–6 0.750600 0.0571 0.690 0.0348 0.884 10.3E–6 0.738800 0.0480 0.773 0.0467 1.26 12.1E–6 0.7201000 0.0414 0.844 0.0597 1.71 13.8E–6 0.702

Acetylene

0 0.0784 1.60 0.0193 0.0377 9.36E–6 0.774200 0.0542 0.442 0.0171 0.715 8.38E–6 0.778400 0.0415 0.494 0.0241 1.18 10.6E–6 0.786600 0.0337 0.531 0.0309 1.73 12.7E–6 0.787800 0.0283 0.558 0.0375 2.37 14.6E–6** 0.7831000 0.0244 0.581 0.0441 3.11 16.4E–6** 0.777


NCEES 539




ConductivityThermal


Fc ftlbm3 lb F

Btu-c ft hr F

Btu- -c hr

ft2secft

lbm-

Ethylene

0 0.0844 0.332 0.00930 0.332 5.90E–6 0.758200 0.0584 0.424 0.0170 0.685 8.31E–6 0.749400 0.0447 0.515 0.0266 1.16 10.5E–6 0.730600 0.0363 0.595 0.0380 1.76 12.4E–6 0.702800 0.0305 0.665 0.0508** 2.51 14.2E–6 0.6691000 0.0263 0.725 0.0651** 3.41 15.8E–6 0.635

Hydrogen Sulfide

0 0.1027 0.237 0.0065 0.267 7.27E–6 0.956200 0.0711 0.246 0.0108 0.616 10.5E–6 0.862400 0.0544 0.258 0.0144 1.03 13.7E–6 0.884600 0.0441 0.272 0.0184 1.53 16.9E–6** 0.901800 0.0371 0.286 0.0229** 2.16 20.2E–6** 0.9081000 0.0320 0.300 0.0279** 2.90 23.4E–6** 0.908

Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®)

using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor.

These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.

* The vapor pressure of sulfur dioxide at 0˚F is 10.2 psia. Hypothetical vapor density at 0˚F and 14.7 psia is reported in the table.

** Extrapolated values


540 NCEES

8.5.2 SI Units

Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units)



ConductivityThermal


Ccmkg3 kg K

kJ: m K

W: hr

m2Pa s:n

Nitrogen

0 1.23 1.04 0.0237 0.0665 16.6 0.727100 0.903 1.04 0.0307 0.117 21.0 0.712200 0.712 1.05 0.0372 0.179 24.9 0.704300 0.588 1.07 0.0434 0.249 28.5 0.701400 0.500 1.09 0.0494 0.326 31.8 0.703500 0.436 1.12 0.0551 0.408 35.0 0.707

Oxygen

0 1.41 0.914 0.0244 0.0682 19.2 0.718100 1.03 0.933 0.0323 0.121 24.6 0.710200 0.813 0.963 0.0397 0.182 29.4 0.713300 0.671 0.995 0.0466 0.251 33.8 0.720400 0.572 1.02 0.0533 0.328 37.8 0.725500 0.498 1.05 0.0597 0.412 41.5 0.729

Carbon Monoxide

0 1.23 1.04 0.0231 0.0650 16.5 0.741100 0.903 1.04 0.0301 0.115 20.9 0.726200 0.712 1.06 0.0365 0.175 24.8 0.719300 0.588 1.08 0.0425 0.241 28.3 0.720400 0.500 1.11 0.0481 0.313 31.5 0.725500 0.436 1.13 0.0535 0.390 34.5 0.731

Carbon Dioxide

0 1.94 0.816 0.0145 0.0331 13.8 0.772100 1.42 0.924 0.0224 0.0617 18.4 0.758200 1.12 1.00 0.0306 0.0985 22.6 0.740300 0.924 1.06 0.0386 0.142 26.5 0.725400 0.786 1.11 0.0464 0.192 30.0 0.717500 0.685 1.15 0.0536 0.245 33.3 0.715

Sulfur Dioxide

0 2.87 0.609 0.00843 0.0174 11.8 0.851100 2.08 0.664 0.0131 0.0342 16.2 0.821200 1.63 0.714 0.0183 0.0565 20.3 0.792300 1.35 0.756 0.0238 0.0842 24.2 0.767400 1.15 0.788 0.0292 0.117 27.8 0.749500 0.997 0.813 0.0343 0.152 31.2 0.741

Air

0 1.28 1.00 0.0242 0.0681 17.2 0.714100 0.933 1.01 0.0312 0.120 21.8 0.704200 0.736 1.02 0.0377 0.181 25.8 0.698300 0.608 1.04 0.0439 0.250 29.4 0.697400 0.517 1.06 0.0498 0.326 32.7 0.697500 0.450 1.09 0.0556 0.408 35.7 0.698


NCEES 541

Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) (cont'd)



ConductivityThermal


Ccmkg3 kg K

kJ: m K

W: hr

m2Pa s:n

Hydrogen

0 0.0887 14.2 0.166 0.475 8.39 0.716100 0.0649 14.5 0.212 0.814 10.4 0.708200 0.0512 14.5 0.255 1.23 12.2 0.697300 0.0423 14.5 0.295 1.73 13.9 0.687400 0.0360 14.6 0.334 2.29 15.6 0.679500 0.0314 14.6 0.371 2.91 17.1 0.675

Ammonia

0 0.758 2.05 0.0222 0.0516 9.21 0.849100 0.551 2.23 0.0342 0.100 12.9 0.837200 0.434 2.42 0.0475 0.163 16.5 0.843300 0.358 2.61 0.0618 0.238 20.1 0.850400 0.304 2.79 0.0772 0.327 23.7 0.858500 0.265 2.96 0.0934 0.429 27.4 0.866

Helium

0 0.176 5.19 0.145 0.571 18.7 0.669100 0.129 5.19 0.179 0.964 23.2 0.671200 0.102 5.19 0.211 1.44 27.3 0.672300 0.0840 5.19 0.241 1.99 31.3 0.672400 0.0715 5.19 0.270 2.62 35.0 0.672500 0.0623 5.19 0.298 3.32 38.6 0.672

Neon

0 0.888 1.030 0.0459 0.181 29.6 0.663100 0.650 1.030 0.0570 0.306 36.6 0.661200 0.513 1.030 0.0670 0.457 43.0 0.660300 0.423 1.030 0.0764 0.630 48.9 0.660400 0.361 1.030 0.0852 0.826 54.5 0.659500 0.314 1.030 0.0935 1.04 59.8 0.659

Argon

0 1.76 0.520 0.0165 0.0649 21.1 0.663100 1.29 0.520 0.0212 0.114 27.1 0.666200 1.02 0.520 0.0254 0.173 32.6 0.667300 0.838 0.520 0.0293 0.242 37.6 0.667400 0.714 0.520 0.0329 0.319 42.2 0.667500 0.621 0.520 0.0364 0.405 46.6 0.667

Fluorine

0 1.67 0.812 0.0235 0.0622 21.5 0.744100 1.22 0.858 0.0314 0.108 27.8 0.759200 0.966 0.893 0.0393 0.164 33.6 0.763300 0.797 0.919 0.0470 0.231 38.9 0.760400 0.679 0.938 0.0547 0.309 43.9 0.753500 0.591 0.953 0.0623* 0.398 48.7 0.745


542 NCEES




ConductivityThermal


Ccmkg3 kg K

kJ: m K

W: hr

m2Pa s:n

Chlorine

0 3.17 0.473 0.00803 0.0193 12.3 0.724100 2.30 0.494 0.0115 0.0363 16.7 0.720200 1.81 0.506 0.0148 0.0581 20.8 0.714300 1.49 0.514 0.0179 0.0844 24.8 0.709400 1.27 0.519 0.0210 0.115 28.5 0.706500 1.10 0.523 0.0239 0.149 32.1 0.704

Methane

0 0.708 2.17 0.0307 0.0720 10.4 0.733100 0.517 2.44 0.0453 0.129 13.5 0.727200 0.408 2.80 0.0615 0.194 16.3 0.741300 0.337 3.17 0.0793 0.267 18.8 0.754400 0.287 3.53 0.0983 0.350 21.2 0.761500 0.250 3.87 0.119* 0.442 23.4 0.764

Ethane

0 1.34 1.64 0.0184 0.0301 8.62 0.772100 0.973 2.06 0.0320 0.0575 11.5 0.738200 0.765 2.49 0.0481 0.0908 14.1 0.731300 0.631 2.88 0.0661 0.131 16.6 0.722400 0.537 3.21 0.0857 0.179 18.9 0.709500 0.468 3.51 0.107 0.234 21.1 0.696

Propane

0 1.98 1.55 0.0152 0.0178 7.70 0.785100 1.43 2.00 0.0270 0.0339 10.2 0.756200 1.125 2.45 0.0412 0.0539 12.6 0.750300 0.927 2.83 0.0575 0.0788 15.0 0.740400 0.788 3.16 0.0757 0.109 17.4 0.724500 0.686 3.44 0.0955 0.146 19.7 0.708

Acetylene

0 1.16 1.60 0.0193 0.0377 9.36 0.774100 0.842 1.87 0.0304 0.0696 12.7 0.778200 0.663 2.06 0.0412 0.109 15.7 0.786300 0.547 2.20 0.0518 0.155 18.5 0.788400 0.465 2.31 0.0622 0.208 21.1 0.785500 0.405 2.40 0.0724 0.268 23.5* 0.779

Ethylene

0 1.24 1.45 0.0180 0.0359 9.38 0.755100 0.907 1.80 0.0303 0.0668 12.6 0.748200 0.714 2.14 0.0453 0.107 15.5 0.731300 0.589 2.45 0.0628 0.157 18.1 0.706400 0.501 2.72 0.0824* 0.218 20.5 0.677500 0.436 2.95 0.104* 0.290 22.8 0.646


NCEES 543




ConductivityThermal


Ccmkg3 kg K

kJ: m K

W: hr

m2Pa s:n

Hydrogen Sulfide

0 1.51 1.00 0.0126 0.0302 11.6 0.911100 1.10 1.03 0.0190 0.0601 15.9 0.862200 0.868 1.08 0.0247 0.0949 20.2 0.883300 0.716 1.13 0.0308 0.137 24.5* 0.899400 0.609 1.18 0.0376* 0.188 28.9* 0.907500 0.530 1.24 0.0452* 0.248 33.2* 0.909

Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®)

using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor.

These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.

* Extrapolated values

8.6 Physical Properties of Air

8.6.1 Dry Atmospheric Air Composition

Composition of Dry Atmospheric Air

Component Mole FractionMolar Mass

lb molelb

molg

ord nNitrogen 0.780848 28.0134Oxygen 0.209390 31.9988Argon 0.009332 39.948Carbon dioxide 0.000400 44.0095Neon 18.2 × 10–6 20.1797Helium 5.2 × 10–6 4.0026Methane 1.5 × 10–6 16.0325Krypton 1.1 × 10–6 83.798Hydrogen 0.5 × 10–6 2.01588Nitrous oxide 0.3 × 10–6 44.0128Carbon monoxide 0.2 × 10–6 28.0101Xenon 0.1 × 10–6 131.294Total 1.0 28.96546


544 NCEES

8.6.2 Dry Atmospheric Air Properties

Properties of Dry Atmospheric AirProperty U.S. Units* SI Units**

Molar mass 28.965 lb molelb 28.965 mol

g

NBP temperature –317.64 °F 78.903 KTriple point temperature –352.12 °F 59.75 KCritical temperature –221.12 °F 132.53 KCritical pressure 549.11 psia 3.7860 MPa

Critical density 21.393 ftlbm3 342.68

mkg3

Density of liquid at NBP54.637

ftlbm3

7.3039 gallbm 875.21

mkg3

Volume of liquid at NBP 0.13691 lbmgal

0.0011426 kgm3

Density of ideal gas 0.07633 ftlbm3 1.2250

mkg3

Volume of ideal gas 13.101 lbmft3 0.81631 kg

m3

Speed of sound in air p = 14.696 psia, T = 32°F p = 0.1 MPa, T = 0°C

1090 secft 330 s

m

Speed of sound in air p = 14.696 psia , T = 68°F p = 0.1 MPa, T = 20°C

1130 secft 343 s

m

* U.S. unit values are given at 60°F and 14.696 psia, except where noted otherwise. ** SI unit values are given at 15°C and 0.101325 MPa, except where noted otherwise.


NCEES 545

8.6.3 Temperature-Dependent Properties of Air (U.S. Customary Units)

Temperature-Dependent Properties of Air at 14.7 psia (U.S. Units)

Tem

pera

ture

Den

sity

Hea

t Cap

acity

(c

p)

Hea

t Cap

acity

R

atio

Vis

cosi

ty

The

rmal

C

ondu

ctiv

ity

Pran

dtl

Num

ber

The

rmal

D

iffus

ivity

°Fftlbm3 lbm F

Btu-c secft

lbm- hr ft F

Btu- -c hr

ft2

–50 0.094 0.2400 1.40 9.98E–06 0.0120 0.719 0.5300 0.086 0.2400 1.40 1.09E–05 0.0132 0.714 0.642

32 0.081 0.2400 1.40 1.15E–05 0.0140 0.710 0.726100 0.071 0.2400 1.40 1.28E–05 0.0156 0.708 0.917200 0.060 0.2401 1.40 1.44E–05 0.0179 0.701 1.233300 0.052 0.2424 1.39 1.60E–05 0.0202 0.692 1.599400 0.046 0.2452 1.39 1.74E–05 0.0225 0.685 1.989500 0.041 0.2476 1.38 1.89E–05 0.0247 0.681 2.415600 0.0374 0.2507 1.38 2.01E–05 0.0268 0.678 2.857700 0.034 0.2533 1.37 2.14E–05 0.0288 0.677 3.323800 0.0286 0.2567 1.37 2.25E–05 0.0307 0.679 4.173


546 NCEES

8.6.4 Temperature-Dependent Properties of Air (SI Units)

Temperature-Dependent Properties of Air at 0.1 MPa (SI Units)Te

mpe

ratu

re

Den

sity

Hea

t Cap

acity

(c

p)

Hea

t Cap

acity

R

atio

Vis

cosi

ty

The

rmal

C

ondu

ctiv

ity

Pran

dtl

Num

ber

The

rmal

D

iffus

ivity

°Cmkg3 kg K

kJ: Pa s:n m K

W: s

m2

–50 1.534 1.005 1.40 14.6 0.0204 0.722 1.32E–050 1.293 1.005 1.40 17.2 0.0243 0.711 1.87E–05

20 1.205 1.005 1.40 18.2 0.0257 0.712 2.12E–0540 1.127 1.005 1.40 19.1 0.0271 0.709 2.39E–0560 1.067 1.009 1.40 20.2 0.0285 0.714 2.65E–0580 1.000 1.009 1.40 20.9 0.0299 0.707 2.96E–05

100 0.946 1.009 1.40 21.8 0.0314 0.701 3.29E–05120 0.898 1.013 1.40 22.7 0.0328 0.700 3.61E–05140 0.854 1.013 1.40 23.5 0.0343 0.695 3.96E–05160 0.815 1.017 1.39 24.3 0.0358 0.691 4.32E–05180 0.779 1.022 1.39 25.2 0.0372 0.691 4.67E–05200 0.746 1.026 1.39 25.8 0.0386 0.687 5.04E–05250 0.675 1.034 1.38 27.8 0.0421 0.683 6.03E–05300 0.616 1.047 1.38 29.5 0.0454 0.680 7.04E–05350 0.566 1.055 1.37 31.2 0.0485 0.678 8.12E–05400 0.524 1.068 1.37 32.8 0.0515 0.679 9.20E–05

C

hapter 8: Physical Properties

NC

EES

547

8.6.5 Psychrometric Chart (U.S. Customary Units)

∆∆

∞∞

∞

Source: American Society of Heating, Refrigeration, and Air Conditioning Engineers, 1992.

PE C

hemical R

eference Handbook

548

NC

EES

8.6.6 Psychrometric Chart (SI Units)

∆∆

∞

∞∞

Source: American Society of Heating, Refrigeration, and Air Conditioning Engineers, 1992.


NCEES 549

8.7 Physical Properties of Water


Physical Properties of Liquid Water (U.S. Units)Te

mpe

ratu

re

Vapo

r Pr

essu

re

Den

sity

Hea

t C

apac

ity

Vis

cosi

ty

The

rmal

C

ondu

ctiv

ity

Pran

dtl

Num

ber

Surf

ace

Tens

ion

°F psiaftlbm3 lbm F

Btu-c secft

lbm- - -hr ft F

Btuc cm

dyne

32.02 0.08872 62.415 1.0086 1.204E–03 0.3244 13.47 75.6540 0.12173 62.423 1.0055 1.038E–03 0.3293 11.42 75.0250 0.17814 62.406 1.0028 8.776E–04 0.3353 9.45 74.2260 0.2564 62.364 1.0010 7.533E–04 0.3413 7.95 73.4070 0.36336 62.299 0.9999 6.552E–04 0.3471 6.79 72.5780 0.50747 62.213 0.9993 5.761E–04 0.3527 5.88 71.7190 0.69904 62.110 0.9990 5.114E–04 0.3579 5.14 70.84

100 0.95051 61.991 0.9989 4.577E–04 0.3628 4.54 69.96110 1.2767 61.857 0.9991 4.127E–04 0.3672 4.04 69.05120 1.695 61.710 0.9993 3.744E–04 0.3713 3.63 68.13130 2.2259 61.549 0.9998 3.417E–04 0.3750 3.28 67.19140 2.893 61.377 1.0003 3.134E–04 0.3783 2.98 66.24150 3.7232 61.193 1.0009 2.888E–04 0.3813 2.73 65.27160 4.7472 60.998 1.0016 2.673E–04 0.3839 2.51 64.28170 5.9998 60.793 1.0025 2.484E–04 0.3862 2.32 63.28180 7.5195 60.578 1.0035 2.316E–04 0.3881 2.16 62.26190 9.3496 60.354 1.0046 2.168E–04 0.3898 2.01 61.23200 11.538 60.120 1.0059 2.035E–04 0.3912 1.88 60.19210 14.136 59.877 1.0073 1.916E–04 0.3924 1.77 59.13220 17.201 59.626 1.0088 1.808E–04 0.3934 1.67 58.05230 20.795 59.366 1.0106 1.712E–04 0.3941 1.58 56.96240 24.986 59.097 1.0125 1.624E–04 0.3947 1.50 55.86250 29.844 58.820 1.0147 1.544E–04 0.3951 1.43 54.74260 35.447 58.535 1.0170 1.471E–04 0.3953 1.36 53.62270 41.878 58.241 1.0196 1.405E–04 0.3953 1.30 52.47280 49.222 57.940 1.0224 1.344E–04 0.3952 1.25 51.32290 57.574 57.630 1.0254 1.288E–04 0.3949 1.20 50.16300 67.029 57.312 1.0287 1.236E–04 0.3944 1.16 48.98320 89.667 56.650 1.0362 1.144E–04 0.3931 1.09 46.59340 118.02 55.955 1.0449 1.065E–04 0.3912 1.02 44.16


550 NCEES

Physical Properties of Liquid Water (U.S. Units) (cont'd)Te

mpe

ratu

re

Vapo

r Pr

essu

re

Den

sity

Hea

t C

apac

ity

Vis

cosi

ty

The

rmal

C

ondu

ctiv

ity

Pran

dtl

Num

ber

Surf

ace

Tens

ion

°F psiaftlbm3 lbm F

Btu-c secft

lbm- - -hr ft F

Btuc cm

dyne

360 153.03 55.225 1.0550 9.958E–05 0.3888 0.97 41.69380 195.74 54.458 1.0666 9.354E–05 0.3857 0.93 39.19400 247.26 53.652 1.0802 8.820E–05 0.3819 0.90 36.66420 308.76 52.804 1.0959 8.343E–05 0.3776 0.87 34.10440 381.48 51.912 1.1143 7.913E–05 0.3725 0.85 31.52460 466.75 50.971 1.1358 7.523E–05 0.3666 0.84 28.92480 565.95 49.976 1.1612 7.165E–05 0.3599 0.83 26.30500 680.55 48.920 1.1916 6.833E–05 0.3522 0.83 23.69520 812.10 47.795 1.2285 6.521E–05 0.3436 0.84 21.08540 962.24 46.590 1.2740 6.225E–05 0.3340 0.85 18.47560 1132.7 45.290 1.3317 5.940E–05 0.3233 0.88 15.89580 1325.5 43.876 1.4072 5.661E–05 0.3118 0.92 13.35600 1542.5 42.318 1.5100 5.382E–05 0.2995 0.98 10.846620 1786.2 40.572 1.6588 5.097E–05 0.2867 1.06 8.415640 2059.2 38.566 1.8958 4.796E–05 0.2735 1.20 6.078660 2364.9 36.152 2.3480 4.463E–05 0.2600 1.45 3.876680 2707.3 32.936 3.5861 4.054E–05 0.2461 2.13 1.877700 3093.0 27.283 15.5790 3.399E–05 0.2547 7.48 0.2565702 3134.5 26.085 28.2960 3.268E–05 0.2765 12.04 0.1375704 3176.6 24.196 97.4060 3.180E–05 0.3584 31.11 0.0375705.1 3200.1 20.102 3.333E–05


NCEES 551

8.7.2 SI Units

Physical Properties of Liquid Water (SI Units)

Tem

pera

ture

Vapo

r Pr

essu

re

Den

sity

Hea

t C

apac

ity

Vis

cosi

ty

The

rmal

C

ondu

ctiv

ity

Pran

dtl

Num

ber

Surf

ace

Tens

ion

°C MPamkg3 kg s

kJ: Pa s: m K

W: m

N 10 3:−

0.01 0.000612 999.79 4.2199 1.791E–03 0.5610 13.47 75.655 0.000873 999.92 4.2055 1.518E–03 0.5705 11.19 74.94

10 0.001228 999.65 4.1955 1.306E–03 0.5800 9.45 74.2215 0.001706 999.06 4.1888 1.138E–03 0.5893 8.09 73.4920 0.002339 998.16 4.1844 1.002E–03 0.5984 8.09 72.7425 0.00317 997.00 4.1816 8.901E–04 0.6072 6.13 71.9730 0.004247 995.61 4.1801 7.974E–04 0.6155 5.42 71.1935 0.005629 993.99 4.1795 7.193E–04 0.6233 4.82 70.4040 0.007385 992.18 4.1796 6.530E–04 0.6306 4.33 69.6045 0.009595 990.17 4.1804 5.961E–04 0.6373 3.91 68.7850 0.012352 988.00 4.1815 5.468E–04 0.6436 3.55 67.9455 0.015762 985.66 4.1831 5.040E–04 0.6492 3.25 67.1060 0.019946 983.16 4.1851 4.664E–04 0.6544 2.98 66.2465 0.025042 980.52 4.1875 4.332E–04 0.6590 2.75 65.3770 0.031201 977.73 4.1902 4.039E–04 0.6631 2.55 64.4875 0.038595 974.81 4.1933 3.777E–04 0.6668 2.38 63.5880 0.047414 971.77 4.1969 3.543E–04 0.6700 2.22 62.6785 0.057867 968.59 4.2008 3.333E–04 0.6728 2.08 61.7590 0.070182 965.30 4.2053 3.144E–04 0.6753 1.96 60.8295 0.084608 961.88 4.2102 2.973E–04 0.6773 1.85 59.87

100 0.10142 958.35 4.2157 2.817E–04 0.6791 1.75 58.91110 0.14338 950.95 4.2283 2.547E–04 0.6817 1.58 56.96120 0.19867 943.11 4.2435 2.321E–04 0.6832 1.44 54.97130 0.27028 934.83 4.2615 2.129E–04 0.6837 1.33 52.93140 0.36154 926.13 4.2826 1.965E–04 0.6833 1.23 50.86150 0.47616 917.01 4.3071 1.825E–04 0.6820 1.15 48.74160 0.61823 907.45 4.3354 1.702E–04 0.6800 1.09 46.59170 0.79219 897.45 4.3678 1.596E–04 0.6771 1.03 44.41180 1.0028 887.00 4.4050 1.501E–04 0.6733 0.98 42.19190 1.2552 876.08 4.4474 1.418E–04 0.6688 0.94 39.95


552 NCEES

Physical Properties of Liquid Water (SI Units) (cont'd)Te

mpe

ratu

re

Vapo

r Pr

essu

re

Den

sity

Hea

t C

apac

ity

Vis

cosi

ty

The

rmal

C

ondu

ctiv

ity

Pran

dtl

Num

ber

Surf

ace

Tens

ion

°C MPamkg3 kg s

kJ: Pa s: m K

W: m

N 10 3:−

200 1.5549 864.66 4.4958 1.343E–04 0.6633 0.91 37.68210 1.9077 852.72 4.5512 1.276E–04 0.6570 0.88 35.38220 2.3196 840.22 4.6146 1.215E–04 0.6497 0.86 33.07230 2.7971 827.12 4.6876 1.160E–04 0.6413 0.85 30.74240 3.3469 813.37 4.7719 1.109E–04 0.6319 0.84 28.39250 3.9762 798.89 4.8701 1.061E–04 0.6212 0.83 26.04260 4.6923 783.63 4.9856 1.017E–04 0.6092 0.83 23.69270 5.503 767.46 5.1230 9.750E–05 0.5959 0.84 21.34280 6.4166 750.28 5.2889 9.351E–05 0.5812 0.85 18.99290 7.4418 731.91 5.4931 8.966E–05 0.5650 0.87 16.66300 8.5879 712.14 5.7504 8.590E–05 0.5474 0.90 14.36310 9.8651 690.67 6.0848 8.217E–05 0.5288 0.95 12.09320 11.284 667.09 6.5373 7.841E–05 0.5092 1.01 9.864330 12.858 640.77 7.1863 7.454E–05 0.4891 1.10 7.703340 14.601 610.67 8.2080 7.043E–05 0.4685 1.23 5.626350 16.529 574.71 10.1160 6.588E–05 0.4474 1.49 3.665360 18.666 527.59 15.0040 6.033E–05 0.4257 2.13 1.877370 21.044 451.43 45.1550 5.207E–05 0.4250 5.53 0.388371 21.297 438.64 62.3510 5.075E–05 0.4384 7.22 0.269372 21.554 422.26 102.1500 4.908E–05 0.4674 10.72 0.160373 21.814 398.68 243.7800 4.781E–05 0.5479 21.27 0.065373.94 22.064 322.00 4.854E–05


NCEES 553

8.7.3 Properties of Water

Properties of WaterProperty U.S. Units SI Units

Molar mass 18.01528 lb molelb 18.01528 mol

g

Boiling temperature 212°F 373.15 KTriple point temperature 32°F 273.15 KTriple point pressure 0.0887 psia 611.657 PaCritical temperature 705.1°F 647.09 KCritical pressure 3200.1 psia 22.06 MPa

Critical density 20.102 ftlbm3 322.00

mkg3

Maximum density of liquid (4°C = 39°F)

62.426 ftlbm3

8.3455 gallbm 1000

mkg3

Minimum volume of liquid (4°C = 39°F) 0.11983 lbm

gal0.001 kg

m3

Heat of vaporization (100°C = 212°F)

970.17 lbmBtu 2257 kg

kJ

Density of ice (0°C = 32°F)

57.227 ftlbm3 916.7

mkg3

Latent heat of fusion (0°C = 32°F) 143.38 lbm

Btu 333.55 kgkJ

Dielectric constant (0°C = 32°F) 87.88 87.88

Dielectric constant (100°C = 212°F) 55.51 55.51

Refractive index 1.3325 1.3325


554 NCEES

8.8 Steam TablesSource for all tables in Section 8.8: GPSA Engineering Data Book, 13th ed., Vol. 2,

Tulsa, OK: GPSA, 2012, Figures 24-30 and 24-31 on pp. 24-35 through 24-38.

8.8.1 Properties of Saturated Steam (U.S. Customary Units)

Saturated Steam (U.S. Units)—Temperature Table

Temperature Pressure Specific Volume, v Specific Enthalpy, h Specific Entropy, s

Fc psia Liquid Vapor Liquid Vapor Liquid Vapor

32.018 0.08865 0.016022 3302.4 0.000 1075.5 0.0000 2.187235 0.09991 0.016020 2948.1 3.002 1076.8 0.0061 2.176740 0.12163 0.016019 2445.8 8.027 1079.0 0.0162 2.159445 0.14744 0.016020 2037.8 13.044 1081.2 0.0262 2.142650 0.17796 0.016023 1704.8 18.054 1083.4 0.0361 2.126255 0.21392 0.016027 1432.0 23.059 1085.6 0.0458 2.110260 0.25611 0.016033 1207.6 28.060 1087.7 0.0555 2.094665 0.30545 0.016041 1022.1 33.057 1089.9 0.0651 2.079470 0.36292 0.016050 868.4 38.052 1092.1 0.0745 2.064575 0.42964 0.016060 740.3 43.045 1094.3 0.0839 2.050080 0.50683 0.016072 633.3 48.037 1096.4 0.0932 2.035985 0.59583 0.016085 543.6 53.027 1098.6 0.1024 2.022190 0.69813 0.016099 468.1 58.018 1100.8 0.1115 2.008695 0.81534 0.016114 404.4 63.008 1102.9 0.1206 1.9954

100 0.94294 0.016130 350.4 67.999 1105.1 0.1295 1.9825110 1.2750 0.016165 265.39 77.98 1109.3 0.1472 1.9577120 1.6927 0.016204 203.26 87.97 1113.6 0.1646 1.9339130 2.2230 0.016247 157.33 97.96 1117.8 0.1817 1.9112140 2.8892 0.016293 122.98 123.00 1122.0 0.1985 1.8895150 3.7184 0.016343 97.07 117.95 1126.1 0.2150 1.8686160 4.7414 0.016395 77.27 127.96 1130.2 0.2313 1.8487170 5.9926 0.016451 62.08 137.97 1134.2 0.2473 1.8295180 7.5110 0.016510 50.225 148.00 1138.2 0.2631 1.8111190 9.3400 0.016572 40.957 158.04 1142.1 0.2787 1.7934200 11.5260 0.016637 33.639 168.09 1146.0 0.2940 1.7764210 14.1230 0.016705 27.816 178.15 1149.7 0.3091 1.7600212 14.6960 0.016719 26.799 180.17 1150.5 0.3121 1.7568220 17.1860 0.016775 23.148 188.23 1153.4 0.3241 1.7442230 20.7790 0.016849 19.381 198.33 1157.1 0.3388 1.7290240 24.9680 0.016926 16.321 208.45 1160.6 0.3533 1.7142


NCEES 555

Saturated Steam (U.S. Units)—Temperature Table (cont'd)


Fc psia Liquid Vapor Liquid Vapor Liquid Vapor

250 29.8250 0.017066 13.819 218.59 1164.0 0.3677 1.7000260 35.4270 0.017089 11.762 228.76 1167.4 0.3819 1.6862270 41.8560 0.017175 10.060 238.95 1170.6 0.3960 1.6729280 49.2000 0.017264 8.644 249.17 1173.8 0.4098 1.6599290 57.5500 0.01736 7.4603 259.4 1167.8 0.4236 1.6473300 67.0050 0.01745 6.4658 269.7 1179.7 0.4372 1.6351320 89.6430 0.01766 4.9138 290.4 1185.2 0.4640 1.6116340 117.9920 0.01787 3.7878 311.3 1190.1 0.4902 1.5892360 153.01 0.01811 2.9573 332.3 1194.4 0.5161 1.5678380 195.73 0.01836 2.3353 353.6 1198.0 0.5416 1.5473400 247.26 0.01864 1.8630 375.1 1201.0 0.5667 1.5274420 308.78 0.01894 1.4997 396.9 1203.1 0.5915 1.5080440 381.54 0.01926 1.2169 419.0 1204.4 0.6161 1.4890460 466.87 0.01961 0.99424 441.5 1204.8 0.6405 1.4704480 566.15 0.02000 0.81717 464.5 1204.1 0.6648 1.4518500 680.86 0.02043 0.67492 487.9 1202.2 0.6890 1.4333520 812.53 0.02091 0.55956 512.0 1199.0 0.7133 1.4146540 962.79 0.02146 0.46513 536.8 1194.3 0.7378 1.3954560 1133.38 0.02207 0.38714 562.4 1187.7 0.7625 1.3757580 1326.17 0.02279 0.32216 589.1 1179.0 0.7876 1.3550600 1543.2 0.02364 0.26747 617.1 1167.7 0.8134 1.3330620 1786.9 0.02466 0.22081 646.9 1153.2 0.8403 1.3092640 2059.9 0.02595 0.18021 679.1 1133.7 0.8686 1.2821660 2065.7 0.02768 0.14431 714.9 1107.0 0.8995 1.2498680 2708.6 0.03037 0.11117 758.5 1068.5 0.9365 1.2086700 3094.3 0.03662 0.07519 825.2 991.7 0.9924 1.1359702 3135.5 0.03824 0.06997 835.0 979.7 1.0006 1.1210704 3177.2 0.04108 0.06300 854.2 956.2 1.0169 1.1046705.47 3208.2 0.05078 0.05078 906.0 906.0 1.0612 1.0612


556 NCEES

Saturated Steam (U.S. Units)—Pressure Table

Pressure Temperature Specific Volume, v Specific Enthalpy, h Specific Entropy, s

psia Fc Liquid Vapor Liquid Vapor Liquid Vapor

0.1 35.02 0.016020 2,945.5 3.03 1076.8 0.0061 2.17660.2 53.16 0.016025 1,526.3 21.22 1084.7 0.0422 2.10600.3 64.48 0.016040 1,039.7 32.54 1089.7 0.0641 2.08090.4 72.87 0.016056 792.1 40.92 1093.3 0.0799 2.05620.6 85.22 0.016085 540.1 53.25 1098.7 0.1028 2.02150.8 94.38 0.016112 411.69 62.39 1102.6 0.1195 1.99701 101.74 0.016136 333.60 69.73 1105.8 0.1326 1.97812 126.07 0.016230 173.76 94.03 1116.2 0.1750 1.92003 141.47 0.016300 118.73 109.42 1122.6 0.2009 1.88644 152.96 0.016358 90.64 120.92 1127.3 0.2199 1.56266 170.05 0.016451 61.98 138.03 1134.2 0.2174 1.82948 182.80 0.016527 47.35 150.87 1139.3 0.2676 1.8060

10 193.21 0.016592 38.42 161.26 1143.3 0.2836 1.787920 227.96 0.016834 20.087 196.27 1156.3 0.3358 1.732030 250.34 0.017009 13.744 218.9 1164.1 0.3682 1.699540 267.25 0.017151 10.4965 236.1 1169.8 0.3921 1.676550 281.02 0.017274 8.5140 250.2 1174.1 0.4112 1.658660 292.71 0.017383 7.1736 262.2 1177.6 0.4273 1.644070 302.93 0.017482 6.2050 272.7 1180.6 0.4411 1.631680 312.04 0.017573 5.4711 282.1 1183.1 0.4534 1.620890 320.28 0.017659 4.8953 290.7 1185.3 0.4643 1.6113

100 327.82 0.01774 4.4310 298.5 1187.2 0.4743 1.6027150 358.43 0.01809 3.0139 330.6 1194.1 0.5141 1.5695200 381.80 0.01839 2.2873 355.5 1198.3 0.5438 1.5454250 400.97 0.01865 1.84317 376.1 1201.1 0.5679 1.5264300 417.35 0.01889 1.54274 394.0 1202.9 0.5882 1.5105350 431.73 0.01912 1.32554 409.8 1204.0 0.6059 1.4968400 444.60 0.01934 1.16095 424.2 1204.6 0.6217 1.4847450 456.28 0.01954 1.03179 437.3 1204.8 0.6360 1.4738500 467.01 0.01975 0.92762 449.5 1204.7 0.6490 1.4639600 486.20 0.02013 0.76975 471.7 1203.7 0.6723 1.4461700 503.08 0.02050 0.65556 491.6 1201.8 0.6928 1.4304800 518.21 0.02087 0.56896 509.8 1199.4 0.7111 1.4163900 531.95 0.02123 0.50091 526.7 1196.4 0.7279 1.4032

1000 544.58 0.02159 0.44596 542.6 1192.9 0.7434 1.39101200 567.19 0.02232 0.36245 571.9 1184.8 0.7714 1.36831400 587.07 0.02307 0.30178 598.8 1175.8 0.7966 1.34741600 604.87 0.02387 0.25545 624.2 1164.5 0.8199 1.32741800 621.02 0.02472 0.21861 648.5 1152.3 0.8417 1.3079


NCEES 557

Saturated Steam (U.S. Units )—Pressure Table (cont'd)


psia Fc Liquid Vapor Liquid Vapor Liquid Vapor

2000 635.80 0.02565 0.18831 672.1 1138.3 0.8625 1.28812200 649.45 0.02669 0.16272 695.5 1122.2 0.8828 1.26762400 662.11 0.02790 0.14076 719.0 1103.7 0.9031 1.24602600 673.91 0.02938 0.1211 744.5 1082.0 0.9247 1.22252800 684.96 0.03134 0.10305 770.7 1055.5 0.9468 1.19583000 695.33 0.03428 0.08500 801.8 1020.3 0.9728 1.16193100 700.28 0.03681 0.07452 824.0 993.3 0.9914 1.13733200 705.08 0.04472 0.05663 875.5 931.6 1.0351 1.08323208.2 705.47 0.05078 0.05078 906.0 906.0 1.0612 1.0612

8.8.2 Saturated Steam (SI Units)

Saturated Steam (SI Units)—Temperature Table


Cc kPa Liquid Vapor Liquid Vapor Liquid Vapor

0.01 0.6113 0.001000 206.14 0.01 2501.4 0 9.15625 0.8721 0.001000 147.12 20.98 2510.6 0.0761 9.0257

10 1.2276 0.001000 106.38 42.01 2519.8 0.151 8.900815 1.7051 0.001001 77.93 62.99 2528.9 0.2245 8.781420 2.339 0.001002 57.79 83.96 2538.1 0.2966 8.667225 3.169 0.001003 43.36 104.89 2547.2 0.3674 8.558030 4.246 0.001004 32.89 125.79 2556.3 0.4369 8.453335 5.628 0.001006 25.22 146.68 2565.3 0.5053 8.353140 7.384 0.001008 19.52 167.37 2574.3 0.5725 8.257045 9.593 0.001010 15.26 188.45 2583.2 0.6387 8.164850 12.349 0.001012 12.03 209.33 2592.1 0.7038 8.076355 15.758 0.001015 9.568 230.23 2600.9 0.7679 7.991360 19.94 0.001017 7.671 251.13 2609.6 0.8312 7.909665 25.03 0.001020 6.197 272.06 2618.3 0.8935 7.831070 31.19 0.001023 5.042 292.98 2626.8 0.9549 7.755375 38.58 0.001026 4.131 313.93 2635.3 1.0155 7.682480 47.39 0.001029 3.407 334.91 2643.7 1.0753 7.612285 57.83 0.001033 2.828 355.90 2651.9 1.1343 7.544590 70.14 0.001036 2.361 376.92 2660.1 1.1925 7.479195 84.55 0.001040 1.982 397.96 2668.1 1.2500 7.4159

100 101.35 0.001044 1.6729 419.04 2676.1 1.3069 7.3549105 120.82 0.001048 1.4194 440.15 2683.8 1.3630 7.2958110 143.27 0.001052 1.2102 461.30 2691.5 1.4185 7.2387


558 NCEES

Saturated Steam (SI Units)—Temperature Table (cont'd)



115 169.06 0.001056 1.0366 482.48 2699.0 1.4734 7.1833120 198.53 0.001060 0.8919 503.71 2706.3 1.5276 7.1296125 232.1 0.001065 0.7706 524.99 2713.5 1.5813 7.0775130 270.1 0.001070 0.6685 546.31 2720.5 1.6344 7.0269135 313.0 0.001075 0.5822 567.69 2727.3 1.6870 6.9777140 361.3 0.001080 0.5089 589.13 2733.9 1.7391 6.9299145 415.4 0.001085 0.4463 610.63 2740.3 1.7907 6.8833150 475.8 0.001091 0.3928 632.20 2746.5 1.8418 6.8379155 543.1 0.001096 0.3468 653.84 2752.4 1.8925 6.7935160 617.8 0.001102 0.3071 675.55 2758.1 1.9427 6.7502165 700.5 0.001108 0.2727 697.34 2763.5 1.9925 6.7078170 791.7 0.001114 0.2428 719.21 2768.7 2.0419 6.6663175 892.0 0.001121 0.2168 741.17 2773.6 2.0909 6.6256180 1002.1 0.001127 0.194005 763.22 2778.2 2.1396 6.5857185 1122.7 0.001134 0.174009 785.37 2782.4 2.1879 6.5465190 1254.4 0.001141 0.156054 807.62 2786.4 2.2359 6.5079195 1397.8 0.001149 0.141005 829.98 2790.0 2.2835 6.4698200 1553.8 0.001157 0.127036 852.45 2793.2 2.3309 6.4323205 1723.0 0.001164 0.115021 875.04 2796.0 2.3780 6.3952210 1906.2 0.001173 0.104041 897.76 2798.5 2.4248 6.3585215 2104 0.001181 0.094079 920.62 2800.5 2.4714 6.3221220 2318 0.001190 0.086019 943.62 2802.1 2.5178 6.2861225 2518 0.001199 0.078049 966.78 2803.3 2.5639 6.2503230 2795 0.001209 0.071058 990.12 2804.0 2.6099 6.2146235 3060 0.001219 0.065037 1013.62 2804.2 2.6558 6.1791240 3344 0.001229 0.059076 1037.32 2803.8 2.7015 6.1437245 3618 0.001240 0.054071 1061.23 2803.0 2.7472 6.1083250 3973 0.001251 0.050130 1085.36 2801.5 2.7927 6.0730255 4319 0.001263 0.045098 1109.73 2799.5 2.8383 6.0375260 4688 0.001276 0.042021 1134.37 2796.9 2.8838 6.0019265 5081 0.001289 0.038077 1159.28 2793.6 2.9294 5.9662270 5499 0.001302 0.035064 1184.51 2789.7 2.9751 5.9301275 5942 0.001317 0.032079 1210.07 2785.0 3.0208 5.8938280 6412 0.001332 0.030017 1235.99 2779.6 3.0668 5.8571285 6909 0.001348 0.027077 1262.31 2773.3 3.1130 5.8199290 7436 0.001366 0.025057 1289.07 2766.2 3.1594 5.7821295 7993 0.001384 0.023054 1316.3 2758.1 3.2062 5.7437300 8581 0.001404 0.021067 1344.0 2749.0 3.2534 5.7045305 9202 0.001425 0.019948 1372.4 2738.7 3.3010 5.6643


NCEES 559

Saturated Steam (SI Units)—Temperature Table (cont'd)



310 9856 0.001447 0.018350 1401.3 2727.3 3.3493 5.6230315 10,547 0.001472 0.016867 1431.0 2714.5 3.3982 5.5804320 11,274 0.001499 0.015488 1461.5 2700.1 3.4480 5.5362330 12,845 0.001561 0.012996 1525.3 2665.9 3.5507 5.4417340 14,586 0.001638 0.010797 1594.2 2622.0 3.6594 5.3357350 16,513 0.001740 0.008813 1670.6 2563.9 3.7777 5.2112360 18,651 0.001893 0.006945 1760.5 2481.0 3.9147 5.0526370 21,030 0.002213 0.004925 1890.5 2332.1 4.1106 4.7971374.14 22,090 0.003155 0.003155 2099.3 2099.3 4.4298 4.4298

Saturated Steam (SI Units)—Pressure Table


kPa Cc Liquid Vapor Liquid Vapor Liquid Vapor

0.6113 0.01 0.001000 206.14 1 2501.4 0 9.15621 6.98 0.001000 129.21 29.3 2514.2 0.1059 8.97561.5 13.03 0.001001 87.98 54.71 2525.3 0.1957 8.82792 17.50 0.001001 67 73.48 2533.5 0.2607 8.72372.5 21.08 0.001002 54.25 88.49 2540.0 0.3120 8.64323 24.08 0.001003 45.67 101.05 2545.5 0.3545 8.57764 28.96 0.001004 34.8 121.46 2554.4 0.4226 8.47465 32.88 0.001005 28.19 137.82 2561.5 0.4764 8.39517.5 40.29 0.001008 19.24 168.79 2574.8 0.5764 8.2515

10 45.81 0.001010 14.67 191.83 2584.7 0.6493 8.150215 53.97 0.001014 10.02 225.94 2599.1 0.7549 8.008520 60.05 0.001017 7.649 251.4 2609.7 0.8320 7.908525 64.97 0.001020 6.204 271.93 2618.2 0.8931 7.831430 69.10 0.001022 5.229 289.23 2625.3 0.9439 7.768640 75.87 0.001027 3.993 317.58 2636.8 1.0259 7.670050 81.33 0.001030 3.24 340.49 2645.9 1.0910 7.593975 91.78 0.001037 2.217 384.39 2663.0 1.2130 7.4564

100 99.63 0.001043 1.694 417.46 2675.5 1.3026 7.3594125 105.99 0.001048 1.3749 444.32 2685.4 1.3740 7.2844150 111.37 0.001053 1.1593 467.11 2693.6 1.4336 7.2233175 116.06 0.001057 1.0036 486.99 2700.6 1.4849 7.1717200 120.23 0.001061 0.8857 504.7 2706.7 1.5301 7.1271225 124.00 0.001064 0.7933 520.72 2712.1 1.5706 7.0878250 127.44 0.001067 0.7187 535.37 2716.9 1.6072 7.0527


560 NCEES

Saturated Steam (SI Units)—Pressure Table (cont'd)Pressure Temperature

Specific Volume, v Specific Enthalpy, h Specific Entropy, s


275 130.60 0.001070 0.6573 548.89 2721.3 1.6408 7.0209300 133.55 0.001073 0.6058 561.47 2725.3 1.6718 6.9919325 136.30 0.001076 0.5620 573.25 2729.0 1.7006 6.9652350 138.88 0.001079 0.5243 584.33 2732.4 1.7275 6.9405375 141.32 0.001081 0.4914 594.81 2735.6 1.7528 6.9175400 143.63 0.001084 0.4625 604.74 2738.6 1.7766 6.8959450 147.93 0.001088 0.4140 623.25 2743.9 1.8207 6.8565500 151.86 0.001093 0.3749 640.23 2748.7 1.8607 6.8213550 155.48 0.001097 0.3427 655.93 2753.0 1.8973 6.7893700 164.97 0.001108 0.2729 697.22 2763.5 1.9922 6.7080750 167.78 0.001112 0.2556 709.47 2766.4 2.0200 6.6847800 170.43 0.001115 0.2404 721.11 2769.1 2.0462 6.6628850 172.96 0.001118 0.2270 732.22 2771.6 2.0710 6.6421900 175.38 0.001121 0.2150 742.83 2773.9 2.0946 6.6226950 177.69 0.001124 0.2042 753.02 2776.1 2.1172 6.6041

1000 179.91 0.001127 0.194044 762.81 2778.1 2.1387 6.58651100 184.09 0.001133 0.177053 781.34 2781.7 2.1792 6.55361200 187.99 0.001139 0.163033 798.65 2784.8 2.2166 6.52331300 191.64 0.001144 0.151025 814.93 2787.6 2.2515 6.49531400 195.07 0.001149 0.140084 830.30 2790.0 2.2842 6.46931500 198.32 0.001154 0.131077 844.89 2792.2 2.3150 6.44481750 205.76 0.001166 0.113049 878.50 2796.4 2.3851 6.38962000 212.42 0.001177 0.099063 908.79 2799.5 2.4474 6.34092250 218.45 0.001187 0.088075 936.49 2801.7 2.5035 6.29722500 223.99 0.001197 0.079098 962.11 2803.1 2.5547 6.25753000 233.90 0.001217 0.066068 1008.42 2804.2 2.6457 6.18693500 242.60 0.001235 0.057007 1049.75 2804.2 2.7253 6.12534000 250.40 0.001252 0.049078 1087.31 2801.4 2.7964 6.07015000 263.99 0.001286 0.039044 1154.23 2794.3 3.9202 5.97346000 275.64 0.001319 0.032044 1213.35 2784.3 3.0267 5.88927000 285.88 0.001351 0.027037 1267.00 2772.1 3.1211 5.81338000 295.06 0.001384 0.023052 1316.64 2758.0 3.2068 5.74329000 303.40 0.001418 0.020048 1363.26 2742.1 3.2858 5.6772

10,000 311.06 0.001452 0.018026 1407.56 2724.7 3.3596 5.614111,000 318.15 0.001489 0.015987 1450.1 2705.6 3.4295 5.552712,000 324.75 0.001527 0.014263 1491.3 2684.9 3.4962 5.492413,000 330.93 0.001567 0.01278 1531.5 2662.2 3.5606 5.432314,000 336.75 0.001611 0.011485 1571.1 2637.6 3.6232 5.371715,000 342.24 0.001658 0.010337 1610.5 2610.5 3.6848 5.3098


NCEES 561

Saturated Steam (SI Units)—Pressure Table (cont'd)Pressure Temperature

Specific Volume, v Specific Enthalpy, h Specific Entropy, s


16,000 347.44 0.001711 0.009306 1650.1 2580.6 3.7461 5.245517,000 352.37 0.001770 0.008364 1690.3 2547.2 3.8079 5.177718,000 357.06 0.001840 0.007489 1732.0 2509.1 3.8715 5.104419,000 361.54 0.001924 0.006657 1776.5 2464.5 3.9388 5.022820,000 365.81 0.002036 0.005834 1826.3 2409.7 4.0139 4.926921,000 369.89 0.002207 0.004952 1888.4 2334.6 4.1075 4.801322,000 373.80 0.002742 0.003568 2022.2 2165.6 4.3110 5.532722,090 374.14 0.003155 0.003155 2099.3 2099.3 4.4298 4.4298

PE C

hemical R

eference Handbook

562

NC

EES

8.8.3 Superheated Steam (U.S. Customary Units)

Superheated Steam (U.S. Units)Pressure (psia)

Saturated Temp. (°F)Temperature (°F)

200 300 400 500 600 700 800 900 1000 1200 1400 1600

1 (101.74)

v 392.6 452.3 512.0 571.6 631.2 690.8 750.4 809.9 869.5 988.7 1107.8 1227.0h 1150.4 1195.8 1241.7 1288.3 1335.7 1383.8 1432.8 1482.7 1533.5 1637.7 1745.7 1857.5s 2.0512 2.1153 2.1720 2.2233 2.2702 2.3137 2.3542 2.3923 2.4283 2.4952 2.5566 2.6137

5 (162.24)

v 78.16 90.25 102.26 114.22 126.16 138.10 150.03 161.95 173.87 197.71 221.60 245.40h 1148.8 1195.0 1241.2 1288.0 1335.4 1383.6 1432.7 1482.6 1533.4 1637.7 1745.7 1857.4s 1.8718 1.9370 1.9942 2.0456 2.0927 2.1361 2.1767 2.2148 2.2509 2.3178 2.3792 2.4363

10 (193.21)

v 38.85 45.00 51.04 57.05 63.03 69.01 74.98 80.95 86.92 98.84 110.77 122.69h 1146.6 1193.9 1240.6 1287.5 1335.1 1383.4 1432.5 1482.4 1533.2 1637.6 1745.6 1857.3s 1.7927 1.8595 1.9172 1.9689 2.0160 2.0596 2.1002 2.1383 2.1744 2.2413 2.3028 2.3598

14.696 (212)

v 30.53 34.68 38.78 42.86 46.94 51.00 55.07 59.13 67.25 75.37 83.48h 1192.8 1239.9 1287.1 1334.8 1383.2 1432.3 1482.3 1533.1 1637.5 1745.5 1857.3s 1.8160 1.8743 1.9261 1.9734 2.0170 2.0576 2.0958 2.1319 2.1989 2.2603 2.3174

20 (227.96)

v 22.36 25.43 28.46 31.47 34.47 37.46 40.45 43.44 49.41 55.37 61.34h 1191.6 1239.2 1286.6 1334.4 1382.9 1432.1 1482.1 1533.0 1637.4 1745.4 1857.2s 1.7808 1.8396 1.8918 1.9392 1.9829 2.0235 2.0618 2.0978 2.1648 2.2263 2.2834

40 (267.25)

v 11.04 12.628 14.168 15.688 17.198 18.702 20.20 21.70 24.69 27.68 30.66h 1186.8 1236.5 1284.8 1333.1 1381.9 1431.3 1481.4 1532.4 1637.0 1745.1 1857.0s 1.6994 1.7608 1.8140 1.8619 1.9058 1.9467 1.9850 2.0212 2.0883 2.1498 2.2069

60 (292.71)

v 7.259 8.357 9.403 10.427 11.441 12.449 13.452 14.454 16.451 18.446 20.440h 1181.6 1233.6 1283.0 1331.8 1380.9 1430.5 1480.8 1531.9 1636.6 1744.8 1856.7s 1.6492 1.7135 1.7678 1.8162 1.8605 1.9015 1.9400 1.9762 2.0434 2.1049 2.1621

80 (312.03)

v 6.220 7.020 7.797 8.562 9.322 10.077 10.830 12.332 13.830 15.325h 1230.7 1281.1 1330.5 1379.9 1429.7 1480.1 1531.3 1636.2 1744.5 1856.5s 1.6791 1.7346 1.7836 1.8281 1.8694 1.9079 1.9442 2.0115 2.0731 2.1303

100 (327.81)

v 4.937 5.589 6.218 6.835 7.446 8.052 8.656 9.860 11.060 12.258h 1227.6 1279.1 1329.1 1378.9 1428.9 1479.5 1530.8 1635.7 1744.2 1856.2s 1.6518 1.7085 1.7581 1.8029 1.8443 1.8829 1.9193 1.9867 2.0484 2.1056

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Superheated Steam (U.S. Units) (cont'd)Pressure (psia)


200 300 400 500 600 700 800 900 1000 1200 1400 1600

120 (341.25)

v 4.081 4.636 5.165 5.683 6.195 6.702 7.207 8.212 9.214 10.213h 1224.4 1277.2 1327.7 1377.8 1428.1 1478.8 1530.2 1635.3 1743.9 1856.0s 1.6287 1.6869 1.7370 1.7822 1.8237 1.8625 1.8990 1.9664 2.0281 2.0854

140 (353.02)

v 3.468 3.954 4.413 4.861 5.301 5.738 6.172 7.035 7.895 8.752h 1221.1 1275.2 1326.4 1376.8 1427.3 1478.2 1529.7 1634.9 1743.5 1855.7s 1.6087 1.6683 1.7190 1.7645 1.8063 1.8451 1.8817 1.9493 2.0110 2.0683

160 (363.53)

v 3.008 3.443 3.849 4.244 4.631 5.015 5.396 6.152 6.906 7.656h 1217.6 1273.1 1325.0 1375.7 1426.4 1477.5 1529.1 1634.5 1743.2 1855.5s 1.5908 1.6519 1.7033 1.7491 1.7911 1.8301 1.8667 1.9344 1.9962 2.0535

180 (373.06)

v 2.649 3.044 3.411 3.764 4.110 4.452 4.792 5.466 6.136 6.804h 1214.0 1271.0 1323.5 1374.7 1425.6 1476.8 1528.6 1634.1 1742.9 1855.2s 1.5745 1.6373 1.6894 1.7355 1.7776 1.8167 1.8534 1.9212 1.9831 2.0404

200 (381.79)

v 2.361 2.726 3.060 3.380 3.693 4.002 4.309 4.917 5.521 6.123h 1210.3 1268.9 1322.1 1373.6 1424.8 1476.2 1528.0 1633.7 1742.6 1855.0s 1.5594 1.6240 1.6767 1.7232 1.7655 1.8048 1.8415 1.9094 1.9713 2.0287

220 (389.86)

v 2.125 2.465 2.772 3.066 3.352 3.634 3.913 4.467 5.017 5.565h 1206.5 1266.7 1320.7 1372.6 1424.0 1475.5 1527.5 1633.3 1742.3 1854.7s 1.5453 1.6117 1.6652 1.7120 1.7545 1.7939 1.8308 1.8987 1.9607 2.0181

240 (397.37)

v 1.9276 2.247 2.533 2.804 3.068 3.327 3.584 4.093 4.597 5.100h 1202.5 1264.5 1319.2 1371.5 1423.2 1474.8 1526.9 1632.9 1742.0 1854.5s 1.5319 1.6003 1.6546 1.7017 1.7444 1.7839 1.8209 1.8889 1.9510 2.0084

260 (404.42)

v 2.063 2.330 2.582 2.827 3.067 3.305 3.776 4.242 4.707h 1262.3 1317.7 1370.4 1422.3 1474.2 1526.3 1632.5 1741.7 1854.2s 1.5897 1.6447 1.6922 1.7352 1.7748 1.8118 1.8799 1.9420 1.9995

280 (411.05)

v 1.9047 2.156 2.392 2.621 2.845 3.066 3.504 3.938 4.37h 1260.0 1316.2 1369.4 1421.5 1473.5 1525.8 1632.1 1741.4 1854.0s 1.5796 1.6354 1.6834 1.7265 1.7662 1.8033 1.8716 1.9337 1.9912

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200 300 400 500 600 700 800 900 1000 1200 1400 1600

300 (417.33)

v 1.7675 2.005 2.227 2.442 2.652 2.859 3.269 3.674 4.078h 1257.6 1314.7 1368.3 1420.6 1472.8 1525.2 1631.7 1741.0 1853.7s 1.5701 1.6268 1.6751 1.7184 1.7582 1.7954 1.8638 1.9260 1.9835

350 (431.72)

v 1.4923 1.7036 1.898 2.084 2.266 2.445 2.798 3.147 3.493h 1251.5 1310.9 1365.5 1418.5 1471.1 1523.8 1630.7 1740.3 1853.1s 1.5481 1.6070 1.6563 1.7002 1.7403 1.7777 1.8463 1.9086 1.9663

400 (444.59)

v 1.2851 1.477 1.6508 1.8161 1.9767 2.134 2.445 2.751 3.055h 1245.1 1306.9 1362.7 1416.4 1469.4 1522.4 1629.6 1739.5 1852.5s 1.5281 1.5894 1.6398 1.6842 1.7247 1.7623 1.8311 1.8936 1.9513

450 (456.28)

v 1.1231 1.3005 1.4584 1.6074 1.7516 1.8928 2.1700 2.4430 2.7140h 1238.4 1302.8 1359.9 1414.3 1467.7 1521.0 1628.6 1738.7 1851.9s 1.5095 1.5735 1.6250 1.6699 1.7108 1.7486 1.8177 1.8803 1.9381

500 (467.01)

v 0.9927 1.1591 1.3044 1.4405 1.5715 1.6996 1.9504 2.1970 2.4420h 1231.3 1298.6 1357.0 1412.1 1466.0 1519.6 1627.6 1737.9 1851.3s 1.4919 1.5588 1.6115 1.6571 1.6982 1.7363 1.8056 1.8683 1.9262

550 (476.94)

v 0.8852 1.0431 1.1783 1.3038 1.4241 1.5414 1.7706 1.9957 2.2190h 1223.7 1294.3 1354.0 1409.9 1464.3 1518.2 1626.6 1737.1 1850.6s 1.4751 1.5451 1.5991 1.6452 1.6868 1.7250 1.7946 1.8575 1.9155

600 (486.21)

v 0.7947 0.9463 1.0732 1.1899 1.3013 1.4096 1.6208 1.8279 2.0330h 1215.7 1289.9 1351.1 1407.7 1462.5 1516.7 1625.5 1736.3 1850.0s 1.4586 1.5323 1.5875 1.6343 1.6762 1.7147 1.7846 1.8476 1.9056

700 (503.1)

v 0.7934 0.9077 1.0108 1.1082 1.2024 1.3853 1.5641 1.7405h 1280.6 1345.0 1403.2 1459.0 1513.9 1623.5 1734.8 1848.8s 1.5084 1.5665 1.6147 1.6573 1.6963 1.7666 1.8299 1.8881

800 (518.23)

v 0.6779 0.7833 0.8763 0.9633 1.0470 1.2088 1.3662 1.5214h 1270.7 1338.6 1398.6 1455.4 1511.0 1621.4 1733.2 1847.5s 1.4863 1.5476 1.5972 1.6407 1.6801 1.7510 1.8146 1.8729

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200 300 400 500 600 700 800 900 1000 1200 1400 1600

900 (531.98)

v 0.5873 0.6863 0.7716 0.8506 0.9262 1.0714 1.2124 1.3509h 1260.1 1332.1 1393.9 1451.8 1508.1 1619.3 1731.6 1846.3s 1.4653 1.5303 1.5814 1.6257 1.6656 1.7371 1.8009 1.8595

1000 (544.61)

v 0.5140 0.6084 0.6878 0.7604 0.8294 0.9615 1.0893 1.2146h 1248.8 1325.3 1389.2 1448.2 1505.1 1617.3 1730.0 1845.0s 1.4450 1.5141 1.5670 1.6121 1.6525 1.7245 1.7886 1.8474

1100 (556.31)

v 0.4532 0.5445 0.6191 0.6866 0.7503 0.8716 0.9885 1.1031h 1236.7 1318.3 1384.3 1444.5 1502.2 1615.2 1728.4 1843.8s 1.4251 1.4989 1.5535 1.5995 1.6405 1.7130 1.7775 1.8363

1200 (567.22)

v 0.4016 0.4909 0.5617 0.6250 0.6843 0.7967 0.9046 1.0101h 1223.5 1311.0 1379.3 1440.7 1499.2 1613.1 1726.9 1842.5s 1.4052 1.4843 1.5409 1.5879 1.6293 1.7025 1.7672 1.8263

1400 (587.1)

v 0.3174 0.4062 0.4714 0.5281 0.5805 0.6789 0.7727 0.8640h 1193.0 1295.5 1369.1 1433.1 1493.2 1608.9 1723.7 1840.0s 1.3639 1.4567 1.5177 1.5666 1.6093 1.6836 1.7489 1.8083

1600 (604.9)

v 0.3417 0.4034 0.4553 0.5027 0.5906 0.6738 0.7545h 1278.7 1358.4 1425.3 1487.0 1604.6 1720.5 1837.5s 1.4303 1.4964 1.5476 1.5914 1.6669 1.7328 1.7926

1800 (621.03)

v 0.2907 0.3502 0.3986 0.4421 0.5218 0.5968 0.6693h 1260.3 1347.2 1417.4 1480.8 1600.4 1717.3 1835.0s 1.4044 1.4765 1.5301 1.5752 1.6520 1.7185 1.7786

2000 (635.82)

v 0.2489 0.3074 0.3532 0.3935 0.4668 0.5352 0.6011h 1240.0 1335.5 1409.2 1474.5 1596.1 1714.1 1832.5s 1.3783 1.4576 1.5139 1.5603 1.6384 1.7055 1.7660

2500 (668.13)

v 0.1686 0.2294 0.2710 0.3061 0.3678 0.4244 0.4784h 1176.8 1303.6 1387.8 1458.4 1585.3 1706.1 1826.2s 1.3073 1.4127 1.4772 1.5273 1.6088 1.6775 1.7389

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200 300 400 500 600 700 800 900 1000 1200 1400 1600

3000 (695.36)

v 0.0984 0.1760 0.2159 0.2476 0.3018 0.3505 0.3966h 1060.7 1267.2 1365.0 1441.8 1574.3 1698.0 1819.9s 1.1966 1.3690 1.4439 1.4984 1.5837 1.6540 1.7163

3206.2 (705.4)

v 0.1583 0.1981 0.2288 0.2806 0.3267 0.3703h 1250.5 1355.2 1434.7 1569.8 1694.6 1817.2s 1.3508 1.4309 1.4874 1.5742 1.6452 1.7080

3500v 0.0306 0.1364 0.1762 0.2058 0.2546 0.2977 0.3381h 780.5 1224.9 1340.7 1424.5 1563.3 1689.8 1813.6s 0.9515 1.3241 1.4127 1.4723 1.5615 1.6336 1.6968

4000v 0.0287 0.1052 0.1462 0.1743 0.2192 0.2581 0.2943h 763.8 1174.8 1314.4 1406.8 1552.1 1681.7 1807.2s 0.9347 1.2757 1.3827 1.4482 1.5417 1.6154 1.6795

4500v 0.0276 0.0798 0.1226 0.1500 0.1917 0.2273 0.2602h 753.5 1113.9 1286.5 1388.4 1540.8 1673.5 1800.9s 0.9235 1.2204 1.3529 1.4253 1.5235 1.5990 1.6640

5000v 0.0268 0.0593 0.1036 0.1303 0.1696 0.2027 0.2329h 746.4 1047.1 1256.5 1369.5 1529.5 1665.3 1794.5s 0.9152 1.1622 1.3231 1.4034 1.5066 1.5839 1.6499

5500v 0.0262 0.0463 0.0880 0.1143 0.1516 0.1825 0.2106h 741.3 985.0 1224.1 1349.3 1518.2 1657.0 1788.1s 0.9090 1.1093 1.2930 1.3821 1.4908 1.5699 1.6369

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8.8.4 Superheated Steam (SI Units)

Superheated Steam (SI Units)Pressure (MPa)

Saturated Temp. (°C)Temperature (°C)

50 100 150 200 250 300 400 500 600 700 800 9000.01

(45.81)v 14.8690 17.1960 19.5120 21.8250 24.1360 26.4450 31.0630 35.6790 40.2950 44.9110 49.5260 54.1410h 2592.6 2687.5 2783.0 2879.5 2977.3 3076.5 3279.6 3489.1 3705.4 3928.7 4159.0 4396.4s 8.1749 8.4479 8.6882 8.9038 9.1002 9.2813 9.6077 9.8978 10.1608 10.4028 10.6281 10.8396

0.05 (81.33)

v 3.41800 3.88900 4.35600 4.82000 5.28400 6.20900 7.13400 8.05700 8.98100 9.90400 10.8280h 2682.5 2780.1 2877.7 2976.0 3075.5 3278.9 3488.7 3705.1 3928.5 4158.9 4396.3s 7.6958 7.9401 8.1580 8.3556 8.5373 8.8642 9.1546 9.4178 9.6599 9.8852 10.0967

0.1 (99.63)

v 1.69580 1.93640 2.17200 2.40600 2.63900 3.10300 3.56500 4.02800 4.49000 4.95200 5.41400h 2676.2 2776.4 2875.3 2974.3 3074.3 3278.2 3488.1 3704.7 3928.2 4158.6 4396.1s 7.3614 7.6134 7.8343 8.0333 8.2158 8.5435 8.8342 9.0976 9.3398 9.5652 9.7767

0.2 (120.23)

v 0.95960 1.08030 1.19880 1.31620 1.54930 1.78140 2.01300 2.24400 2.47500 2.70600h 2768.8 2870.5 2971.0 3071.8 3276.6 3487.1 3704.0 3927.6 4158.2 4395.8s 7.2795 7.5066 7.7086 7.8926 8.2218 8.5133 8.7770 9.0194 9.2449 9.4566

0.3 (133.55)

v 0.63390 0.71630 0.79640 0.87530 1.03150 1.18670 1.34140 1.49570 1.64990 1.80410h 2761.0 2865.6 2967.6 3069.3 3275.0 3486.0 3703.2 3927.1 4157.8 4395.4s 7.0778 7.3115 7.5166 7.7022 8.0330 8.3251 8.5892 8.8319 9.0576 9.2692

0.4 (143.63)

v 0.47080 0.53420 0.59510 0.65480 0.77260 0.88930 1.00550 1.12150 1.23720 1.35290h 2752.8 2860.5 2964.2 3066.8 3273.4 3484.9 3702.4 3926.5 4157.3 4395.1s 6.9299 7.1706 7.3789 7.5662 7.8985 8.1913 8.4558 8.6987 8.9244 9.1362

0.5 (151.86)

v 0.42490 0.47440 0.52260 0.61730 0.71090 0.80410 0.89690 0.98960 1.08220h 2855.4 2960.7 3064.2 3271.9 3483.9 3701.7 3925.9 4156.9 4394.7s 7.0592 7.2709 7.4599 7.7938 8.0873 7.3522 8.5952 8.8211 9.0329

0.6 (158.85)

v 0.35200 0.39380 0.43440 0.51370 0.59200 0.66970 0.74720 0.82450 0.90170h 2850.1 2957.2 3061.6 3270.3 3482.8 3700.9 3925.3 4156.5 4394.4s 6.9665 7.1816 7.3724 7.7079 8.0021 8.2674 8.5107 8.7367 8.9486

0.8 (170.43)

v 0.26080 0.29310 0.32410 0.38430 0.44330 0.50180 0.56010 0.61810 0.67610h 2839.3 2950.0 3056.5 3267.1 3480.6 3699.4 3924.2 4155.6 4393.7s 6.8158 7.0384 7.2328 7.5716 7.8673 8.1333 8.3770 8.6033 8.8153

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Superheated Steam (SI Units) (cont'd)

Pressure (MPa)Saturated Temp. (°C)

Temperature (°C)

50 100 150 200 250 300 400 500 600 700 800 900

1.0 (179.91)

v 0.20600 0.23270 0.25790 0.30660 0.35410 0.40110 0.44780 0.49430 0.54070h 2827.9 2942.6 3051.2 3263.9 3478.5 3697.9 3923.1 4154.7 4392.9s 6.6940 6.9247 7.1229 7.4651 7.7622 8.0290 8.2731 8.4996 8.7118

1.2 (187.99)

v 0.16930 0.19234 0.21380 0.25480 0.29460 0.33390 0.37290 0.41180 0.45050h 2815.9 2935.0 3045.8 3260.7 3476.3 3696.3 3922.0 4153.8 4392.2s 6.5898 6.8294 7.0317 7.3774 7.6959 7.9435 8.1881 8.4148 8.6272

1.4 (195.07)

v 0.14302 0.16350 0.18228 0.21780 0.25210 0.28600 0.31950 0.35280 0.38610h 2803.3 2927.2 3040.4 3257.5 3474.1 3694.8 3920.8 4153.0 4391.5s 6.4975 6.7467 6.9534 7.3026 7.6027 7.8710 8.1160 8.3431 8.5556

1.6 (201.41)

v 0.14184 0.15862 0.19005 0.22030 0.25000 0.27940 0.30860 0.33770h 2919.2 3034.8 3254.2 3472.0 3693.2 3919.7 4152.1 4390.8s 6.6732 6.8844 7.2374 7.5390 7.8080 8.0535 8.2808 8.4935

1.8 (207.15)

v 0.12497 0.14021 0.16847 0.19550 0.22200 0.24820 0.27420 0.30010h 2911.0 3029.2 3250.9 3469.8 3691.7 3918.5 4151.2 4390.1s 6.6066 6.8226 7.1794 7.4825 7.7523 7.9983 8.2258 8.4386

2.0 (212.42)

v 0.11144 0.12547 0.15120 0.17568 0.19960 0.22320 0.24670 0.27000h 2902.5 3023.5 3247.6 3467.6 3690.1 3917.4 4150.3 4389.4s 6.5453 6.7664 7.1271 7.4317 7.7024 7.9487 8.1765 8.3895

2.5 (223.99°C)

v 0.08700 0.09890 0.12010 0.13998 0.15930 0.17832 0.19716 0.21590h 2880.1 3008.8 3239.3 3462.1 3686.3 3914.5 4148.2 4387.6s 6.4085 6.6438 7.0148 7.3234 7.5960 7.8435 8.0720 8.2853

3.0 (233.90)

v 0.07058 0.08114 0.09936 0.11619 0.13243 0.14838 0.16414 0.17980h 2855.8 2993.5 3230.9 3456.5 3682.3 3911.7 4145.9 4385.9s 6.2872 6.5390 6.9212 7.2338 7.5085 7.7511 7.9862 8.1999

3.5 (242.60)

v 0.05872 0.06842 0.08453 0.09918 0.11324 0.12699 0.14056 0.15402h 2829.2 2977.5 3222.3 3450.9 3678.4 3908.8 4143.7 4384.1s 6.1749 6.4461 6.8405 7.1572 7.4339 7.6837 7.9134 8.1276

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Temperature (°C)

50 100 150 200 250 300 400 500 600 700 800 900

4.0 (250.40)

v 0.05884 0.07341 0.08643 0.09885 0.11095 0.12287 0.13469h 2960.7 3213.6 3445.3 3674.4 3905.9 4141.5 4382.3s 6.3615 6.7690 7.0901 7.3688 7.6198 7.8502 8.0647

4.5 (257.49)

v 0.05135 0.06475 0.07651 0.08765 0.09847 0.10911 0.11965h 2943.1 3204.7 3439.6 3670.5 3903.0 4139.3 4380.6s 6.2828 6.7047 7.0301 7.3110 7.5631 7.7942 8.0091

5.0 (263.99

v 0.04532 0.05781 0.06857 0.07869 0.08849 0.09811 0.10762h 2924.5 3195.7 3433.8 3665.5 3900.1 4137.1 4378.8s 6.2084 6.6459 6.9759 7.2589 7.5122 7.7440 7.9593

6.0 (275.64)

v 0.03616 0.04739 0.05665 0.06525 0.07352 0.08160 0.08958h 2884.2 3177.2 3422.2 3658.4 3894.2 4132.7 4375.3s 6.0674 6.5408 6.8803 7.1677 7.4234 7.6566 7.8727

7.0 (285.88)

v 0.02947 0.03993 0.04814 0.05565 0.06283 0.06981 0.07669h 2838.4 3158.1 3410.3 3650.3 3888.3 4128.2 4371.8s 5.9305 6.4478 6.7975 7.0894 7.3476 7.5822 7.7991

8.0 (295.06)

v 0.02426 0.03432 0.04175 0.04845 0.05481 0.06097 0.06702h 2785.0 3138.3 3398.3 3642.0 3882.4 4123.8 4368.3s 5.7906 6.3634 6.7240 7.0206 7.2812 7.5173 7.7351

9.0 (303.40)

v 0.02993 0.03677 0.04285 0.04857 0.05409 0.05950h 3117.8 3386.1 3633.7 3876.5 4119.3 4364.8s 6.2854 6.6576 6.9589 7.2221 7.4596 7.6783

10.0 (311.06)

v 0.02641 0.03279 0.03837 0.04358 0.04859 0.05349h 3096.5 3373.7 3625.3 3870.5 4114.8 4361.2s 6.2120 6.5966 6.9029 7.1687 7.4077 7.6272

12.5 (327.89)

v 0.02000 0.02560 0.03029 0.03460 0.03869 0.04267h 3039.3 3341.8 3604.0 3855.3 4103.6 4352.5s 6.0417 6.4618 6.7810 7.0536 7.2965 7.5182

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Temperature (°C)

50 100 150 200 250 300 400 500 600 700 800 900

15.0 (342.24)

v 0.01565 0.02080 0.02491 0.02861 0.03210 0.03546h 2975.5 3308.6 3582.3 3840.1 4092.4 4343.8s 5.8811 6.3443 6.6776 6.9572 7.2040 7.4279

17.5 (354.75)

v 0.01245 0.01736 0.02106 0.02434 0.02738 0.03031h 2902.9 3274.1 3560.1 3824.6 4081.1 4335.1s 5.7213 6.2383 6.5866 6.8736 7.1244 7.3507

20.0 (365.81)

v 0.00994 0.01477 0.01818 0.02113 0.02385 0.02645h 2818.1 3238.2 3537.6 3809.0 4069.7 4326.4s 5.5540 6.1401 6.5048 6.7993 7.0544 7.2830

25.0 v 0.00604 0.01112 0.01414 0.01665 0.01891 0.02145h 2580.2 3162.4 3491.4 3777.5 4047.1 4309.1s 5.1418 5.9592 6.3602 6.6707 6.9345 7.1680

30.0 v 0.00279 0.00868 0.01145 0.01366 0.01562 0.01745h 2151.1 3081.1 3443.9 3745.6 4024.2 4291.9s 4.4728 5.7905 6.2331 6.5605 6.8332 7.0718

35.0 v 0.00210 0.00693 0.00953 0.01153 0.01328 0.01488h 1987.6 2994.4 3395.5 3713.5 4001.5 4274.9s 4.2126 5.6282 6.1179 6.4631 6.7450 6.9886

40.0 v 0.00191 0.00562 0.00894 0.00994 0.01152 0.01296h 1930.9 2903.3 3346.4 3681.2 3978.7 4257.9s 4.1135 5.4700 6.0114 6.3750 6.6662 6.9150


NCEES 571

8.9 Diagrams for Water and Steam

Pressure-Enthalpy (p-H) Diagram (U.S. Customary Units)

Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.


572 NCEES

Temperature-Entropy (T-S) Diagram (U.S. Customary Units)



NCEES 573

Pressure-Enthalpy (p-H) Diagram (SI Units)

,

,

,

,

,

,

,

,

,

,



574 NCEES

Temperature-Entropy (T-S) Diagram (SI Units)


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