LABORATORY MANUALstaffweb.wilkes.edu/perwez.kalim/me323/FMlabmanual19.pdf · 4 Discharge from...

FLUID MECHANICS

LABORATORY MANUAL

ME 323

Edited, Compiled, and Authored by

Dr. S. Perwez Kalim Professor of Mechanical engineering

Department of Mechanical Engineering & Engineering Management

Tel: 570-408-4827

Email: [email protected]

Web page: http://staffweb.wilkes.edu/perwez.kalim/

mailto:[email protected]

http://staffweb.wilkes.edu/perwez.kalim/

Fluid Mechanics Lab Manual/P. Kalim/Wilkes University

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FLUID MECHANICS LABORATORY MANUAL

(ME 323)

Seventh Edition

S. PERWEZ KALIM Ph.D.

Professor of Mechanical engineering

College of Science and Engineering

Wilkes University

Wilkes Barre, PA 18766


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THE MANUAL BELONGS TO: _________________________

THIS MANUAL IS DESIGNED AS A REFERENCE

AND GUIDE FOR STUDENTS IN THE

FLUID MECHANICS LABORATORY - ME 323.

IT INCLUDES SOME THEORY AND INFORMATION ON

EXPERIMENTS TO BE PERFORMED IN THE LABORATORY.

Edited - P. Kalim, Professor of Mechanical Engineering,

All rights reserved. No part of this manual may be reproduced, stored in a retrieval system or

transcribed, in any form or by any means - electronic, mechanical, photocopying, recording, or

otherwise - without prior written permission of publishers.

PREFACE Laboratory experiments provide opportunities for hands-on experience of fluid behavior. This lab manual

is an effort to help you in facilitating this experience. Most of the laboratory experiments emphasize

material presented in Fluid Mechanics course. Some of the experiments will also expose materials that are


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not presented in the course. It is your responsibility to interrelate the laboratory and lecture experience.

Use the laboratory experience to augment your understanding of the concepts of fluid mechanics.

1. In this laboratory you will perform experiments related to:

Fluid pressure, static and dynamic forces

Relate pressure with the hydrostatic force in a stationary fluid

The relationship between pressure and velocity in fluid flow

Aerodynamics, lift, drag, lift, drag and pressure coefficients

Boundary layer, its thickness, and Von Karman theory

2. Understand the basic operating principles of the laboratory equipment and learn how to operate the

equipment properly and safely. As a result of performing these experiments you should be able to:

Develop and reinforce skills in documenting observations

Measure quantities with the maximum precision of the instruments provided in the laboratory.

Record proper experimental data to be used later for analysis

Sketching the physical apparatus used in each experiment

Identify actions taken to improve the outcome of the experiment

Identify factors that contributed to undesirable outcomes.

3. As a result of documenting these experiments you should be able to:

Develop writing skills by following the given writing guidelines or any other standard

engineering format.

Write a complete but not lengthy report. Communicate what did you learn in your own words.


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TABLE OF CONTENTS

Title References Page

Preface 4

Table of Contents 5

Safety Practices, Rules and Laboratory policy 7

Lab Report Format 9

Report Grading 10

Regression Analysis [9, 10] 11

Fluid Mechanics – Jargons and Terminology [3. 4, 5, 15] 13

Experiment # Title References Page

1 21

2 Air Flow Measurement using Pitot-Static Tube [2, 4, 5, 6] 22

3 Major Friction Losses in Pipe Lengths [3, 4, 7, 8, 11] 32

4 Discharge from Venturimeter [3, 4, 7, 8, 11] 38

5 Minor Friction Losses in Fittings. [3, 4, 7, 8, 11] 45

6 Discharge Over Weirs [3, 4, 7, 8, 11] 50

7 Pressure Distribution and Boundary layer around a

Circular Cylinder

[2, 4, 5, 6] 57

8 Develop Operational Characteristics of a Variable Speed

Pump

[2, 4, 5, 6] 60

9 Boundary Layer on a Flat Plate [2, 4, 5, 6] 66

10 Pressure Distribution Over an Airfoil [4, 12, 13, 14] 72

11 Tests on 1/72 Scale model F106 Delta Dart Model [2, 4, 5, 6] 79

12 UAV experiment 83

13 Develop Operational Characteristics of a Centrifugal Pump [3, 4, 8, 11, 12] 84

14 Calibration of Yaw Probe [2, 4, 5, 6] 96

15 Viscosity experiment [2, 4, 5, 6] 99

Demo Reynolds Number and Transitional Flow [3, 4, 8, 11, 15] 101

Demo Pelton Wheel Turbine 105


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Appendices

Appendix A Operation of the Wind Tunnel [1, 2, 5] 106

Appendix B Zeroing Angle of Attack, Normal and Axial Forces,

Pitching and Yawing Moments. Calibrating Normal and

Axial Forces, Pitching and Yawing Moments

[1, 2] 107

Appendix C Installing and Removing the Balance [1, 2] 108

Appendix D Use of Manometer [3, 4, 7, 15] 109

Appendix E Hydraulic Bench Operating Instructions [3, 4, 8, 11] 110

Appendix F Conversion Factor [4, 7] 112

References 113

Sample Reports

Appendix G Sample Report 1 – written by student, errors possible

Sample Report 2 – written by student, errors possible

114

122


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SAFETY PRACTICES AND LABORATORY POLICY

Some important safety practices and rules (however not limited to) in the Fluid Mechanics laboratory are

given below. These are important rules that should be followed all the time.

1. Headphone (when wind tunnel is running) is recommended in the laboratory.

2. Long hair (touching the shoulders) must be contained (cap, net, or tied back). The student is

responsible for providing these items.

3. Food or drink is not permissible in the lab at any time.

4. Proper dress attire in the laboratory includes: short sleeves (or long sleeves rolled above the elbow),

shirt tucked in and closed at the neck, slacks, socks, and shoes that cover the feet. Avoid ties, and

scarves.

5. Don't remove any object from a running wind tunnel or hot bath until proper precautions are taken.

6. Keep your hands, tools, objects, and equipment clean.

7. After finishing an experiment it is your responsibility to clean the equipment, tools and other

accessories and store them at proper place.

8. Avoid inhaling fumes or smoke.

9. If you feel faint - sit down, ask someone for help, or move away from the equipment and rest.

Report all injuries to the instructor in charge and to the Student Health Center.

10. Although the word safety has only six letters the following imply powerful meaning.

S = sound thinking concerning safety

A = be alert

F = acquiring facts

E = efficiency in carefully performing the work

T = thoughtfulness for the safety of your group

Y = you and your own protection in the laboratory is of primary importance


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LABORATORY REPORT FORMAT

Prepare a folder where all experiments will be kept in sequence with page numbers. The first few pages will contain the table of contents. The table of contents should exhibit the following header. Remarks column is reserved for the grade (score) obtained in each report. Lab # Expt # Title of Experiment Page # Date Remarks Lab # corresponds to the experiment you are conducting (in sequential order) while Expt # corresponds to the experiments in the manual Weekly Lab Report Writing Guidelines - See website for detailed guidelines and a sample report All lab reports must be written in compliance with the format and guidelines published on the web and

provided here. The IEEE or ASME (ASME) writing guidelines may also be followed to in writing

technical reports. By in-large, the reports should consist of the following sections: Title, Abstract, Short

procedure and data, Theory, Results and Discussions (Tables and Figures included here), Conclusions,

References and acknowledgements if any. How these sections are sequenced is at the discretion of the

author. For labs, each member of the group would be required to submit individual reports.

The general guidelines for technical reports or articles are similar to one found on the ASME website

above, or my website. The reports must be 1.5 lines-spaced and should be created using word processing

(Times or symbol, Font size 11 or 12) and should include only computer generated graphs and tables.

Must use Equation editor to type equations and they must be numbered.

ETHICAL RESPONSIBILITY: Plagiarism is absolutely unethical, illegal, and unacceptable. Any evidence

of this act will automatically result in zero points for that project or lab. Additional penalty may be levied

at the instructor’s discretion.

Grading: Check out the lab report grading rubric provided by the instructor


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ME 323 Fluid Mechanics Laboratory - Report Grading Rubric Avail. pts. The lab reports may be graded out of 100 or 20 points at the discretion of the

instructor Points Earned

5

Title Properly formatted per Report Preparation Guidelines Team Participation:

10

Abstract 5 Principle objective(s) and scope of the experiment defined 5 Principle conclusion(s) and argument(s) presented 5 Summary of results from experiment

15

Theory and Data 5 Data summarized and presented in logical, concise and interpretable manner

5 Graphs, tables, charts and figures generated using Excel or equivalent, Formulas, variables and data properly defined and dimensioned (units)

5 Graphs, tables, figures and charts properly formatted & captioned

5 Properly formatted per Report Preparation Guidelines

30

Results, Discussion and Analysis 10 Sample calculation for each type of information or data point

5 General discussion of how findings validate the scope of the experiment

Strong defense of the data attained v. theoretical results

10

Brief discussion of what the experiment is to prove or disprove

Accuracy, validity and reliability of required measurements discussed

Error analysis - Identification of error and variability inherent in the experiment 5 Addressed all questions/requirements required for each experiment

10

Conclusion 5 Convincingly delivers what has been learned in the lab 5 Strong defense for agreement/disagreement between actual v. expected results 3 Error and root cause analysis resulting in bad data points 2 Recommendations for mitigating variability and improving data integrity

10

Practical Application 5 Research done to identify a practical app relative to experiment scope 5 Is the application realistic/practical; industry or discipline specific

15

Format and Presentation 2 Report complies with requirements set forth in Report Guidelines 2 Citations and references properly documented iaw APA format 1 Report is written in scientific style: clear and concise

5

Overall expectation of the report: the student... 1 Has accurately analyzed the data for validity and relevancy 1 Has successfully applied theory and computation to arrive at results 1 Has successfully defended the data relative to desired results 1 Has successfully recommended solutions to minimize inherent error/variability 1 Has demonstrated an understanding of the principles set forth in the Abstract

100 Points Earned


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REGRESSION Ref: [9,10,16,17]

Why regression? A classic statistical problem is to try to determine the relationship between two random variables X and Y.

For example, we might consider height and weight of a sample of adults. Linear regression attempts to

explain this relationship with a straight line fit to the data. In that case, regression equation can be used to

express the relationship between two (or more) variables algebraically. It indicates the nature of the

relationship between two (or more) variables. In particular, it indicates the extent to which you can predict

some variables by knowing others, or the extent to which some are associated with others.

A linear regression equation is usually written Y = a + bX + e

Where Y is the dependent variable a is the intercept, b is the slope or regression coefficient, X is the

independent variable (or covariate) and e is the error term

The equation will specify the average magnitude of the expected change in Y given a change in X. The

regression equation is often represented on a scatter plot by a regression line. Also a term called as R-

square value is an indicator of how well the model fits the data.

Often in heat transfer experiments; many data points are taken for a dependent variable, for which it is

necessary to find the relationship of those data points with an independent variable

Regression Line A regression line is a line drawn through the points on a scatter plot to summarize the relationship

between the variables being studied. When it slopes down (from top left to bottom right), this indicates a

negative or inverse relationship between the variables; when it slopes up (from bottom right to top left), a

positive or direct relationship is indicated. The regression line often represents the regression equation on

a scatter plot.

Simple Linear Regression Simple linear regression aims to find a linear relationship between a response variable and a possible

predictor variable by the method of least squares.


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Multiple Regression Multiple linear regression aims is to find a linear relationship between a response variable and several

possible predictor variables.

Let Y be the dependent and X1 and X2 be the two independents. Multiple regressions first regresses X1 on

X2 (and other independents, if there were any) and sets aside these residuals, which represent the unique

variance in X1 uncorrelated with other independent variables. The process is repeated for the regression of

X2 on X1, also setting aside these residuals. As a last step, Y is regressed on the sets of residuals for each

of the independents. The resulting b coefficients are the partial regression coefficients which reflect the

unique association of each independent with the Y variable. The interpretation of the intercept c, is the

same in bivariate and multiple regressions whereas note that the b coefficients differ: they are simple

coefficients for bivariate regression but are partial coefficients for multiple regressions.

Nonlinear Regression Nonlinear regression aims to describe the relationship between a response variable and one or more

explanatory variables in a non-linear fashion.

Residual Variance and R-square The smaller the variability of the residual values around the regression line relative to the overall

variability, the better is our prediction. For example, if there is no relationship between the X and Y

variables, then the ratio of the residual variability of the Y variable to the original variance is equal to 1.0.

If X and Y are perfectly related then there is no residual variance and the ratio of variance would be 0.0.

In most cases, the ratio would fall somewhere between these extremes, that is, between 0.0 and 1.0. 1.0

minus this ratio is referred to as R-square or the coefficient of determination. This value is immediately

interpretable in the following manner. If we have an R-square of 0.4 then we know that the variability of

the Y values around the regression line is 1-0.4 times the original variance; in other words we have

explained 40% of the original variability, and are left with 60% residual variability. Ideally, we would

like to explain most if not all of the original variability. The R-square value is an indicator of how well

the model fits the data (e.g., an R-square close to 1.0 indicates that we have accounted for almost all of

the variability with the variables specified in the model).

Correlation Coefficient R. A correlation coefficient is a number between -1 and 1, which measures the degree to which two variables

are related. If there is perfect linear relationship with positive slope between the two variables, we have a


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correlation coefficient of 1; if there is positive correlation, whenever one variable has a high (low) value,

so does the other. If there is a perfect linear relationship with negative slope between the two variables,

we have a correlation coefficient of -1; if there is negative correlation, whenever one variable has a high

(low) value, the other has a low (high) value. If the correlation coefficient is 0.0, it means that there is no

relationship between two variables.

Customarily, the degree to which two or more predictors (independent or X variables) are related to the

dependent (Y) variable is expressed in the correlation coefficient R, which is the square root of R-square.

In multiple regressions, R can assume values between 0 and 1. To interpret the direction of the

relationship between variables, one looks at the signs (plus or minus) of the regression or B coefficients.

If a B coefficient is positive, then the relationship of this variable with the dependent variable is positive

(e.g., the greater the IQ the better the grade point average); if the B coefficient is negative then the

relationship is negative (e.g., the lower the class size the better the average test scores). Of course, if the B

coefficient is equal to 0 then there is no relationship between the variables.

There are a number of different correlation coefficients that might be appropriate depending on the kinds

of variables being studied.


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Often data is listed in various tables shown in the manual are just a guide and simply provide an

order of data and do not represent actual data.

Relevant information may also be found at different websites including the one listed here:

http://www.engineeringtoolbox.com/fluid-mechanics-t_21.html http://www.engineersedge.com/

FLUID MECHANICS - JARGONS AND TERMINOLOGY

Volume Flow Rate Q: The volume flow rate is given as Q = flow area * flow Velocity = A*V - m3/sec,

ft3/sec

Mass Flow Rate •m : The mass flow rate is given as

•m = density*flow area*flow Velocity = ρ*A*V

kg/sec, lbm/sec, 1 Slug =32.2 lbm

Specific weight, γ: γliquid= Specific gravity S* γwater

Bernoulli's Equation: The energy at two points in a moving or stagnant ideal fluid is always constant,

so that

(Ideal Fluid Flow) γ1P +

g2V 2

1 + Z1 = γ2P +

g2V 2

2 + Z2 = Constant

Where γ1P ,

g2V 2

1 , and Z1 are energy terms in head (m, ft) units called as pressure

head, kinetic or velocity head and potential or datum head respectively.

Bernoulli's Equation: The energy at two points in real fluid is also constant. But other irreversibilities in

form of friction losses exist. Additionally, pump and turbine head may be present

in real systems.

Real Fluid Flow 1

211 Zg2

VP++

γ+ hp = ht + 2

222 Zg2

VP++

γ + hL

Where ht , hp and hL are turbine head, pump head and head loss in the system.

Click here to calculate energy terms

Reynolds Number: A dimensionless number, which is equivalent to the ratio of inertia forces to

viscous forces. It is the parameter which determines whether flow is laminar or

turbulent. ReL = ρVL/µ (for plate) and ReD = ρVD/µ for other objects, where ρ

1 2 Datum

http://www.engineeringtoolbox.com/fluid-mechanics-t_21.html

http://lmnoeng.com/energy.htm


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is density and µ is the dynamic viscosity and D is the diameter of the object and L

is the length of the plate.

Laminar flow: A viscosity dominant flow, which is uniform, organized (non chaotic), and

streamlined (in layers). Here Re < 5x105 for plate and Re < 2300 for other objects

(cylinders, sphere and non-circular ducts).

Turbulent Flow: Velocity dominant flow that is chaotic and disorganized. Here Re is ≥ 5x105 for

plate and Re ≥ 2300 for other objects such as cylinders, sphere and non-circular

ducts.

Critical Reynolds # The Reynolds number where the flow changes from laminar to turbulent. This

number is dependent upon the properties of the fluid, the flow speed, and the size

of the test object. The critical Reynolds Number is Rec = 5x105 for flow over a

plate and Rec = 2300 for flow over other objects such as sphere, cylinder, pipe, and

ducts.

For non-circular ducts such as channels, air-conditioning duct etc., the only change

is that the diameter is replaced by hydraulic diameter Dh where Dh =wetted

tionsecx

P

A*4−

and Re = ρVDH/µ

Manometer Manometer is used to determine the pressure at any point in the flow system. The

pressure is measured by first determining the height of the liquid level in the

manometer and then multiply the measured height with the specific weight of the

fluid so that P = γ h, where h is the height and g is the specific weight of the fluid

at its ambient temperature.

Streamline object: A slender shape object is called a

streamlined object. An airfoil, the Viper,

and Lamborghini can be considered as Figure 1. Slender body

streamlined objects.


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Blunt object: The objects that are characterized by a well-defined separation point for example,

flat plate normal to the flow.

Boundary layer: The layer of fluid near the surface that undergoes through velocity changes

because of the varying shear stress at the surface. Shear stress in the fluid over a

surface reduces as the height of the layers increase above the stationary surface.

Figure 2. Flow Over a Cylinder and Blunt Object, depicting the

Boundary Layers, Stagnation Point, and Separation Zone

Stagnation Point: The location on the test object where velocity is zero and pressure is a maximum,

called total pressure Pt = (Pstatic + Pdynamic).

Separation: Regions where boundaries turn away from the flow so as to cause the streamlines

to diverge, that is the flow separates from the boundary and a re-circulating pattern

is generated in the region. The separation and back flow are shown in the figures

2. On a slender shape object the flow has little or no separation point as shown in

the figure 3 below. An airfoil (airplane wing) is a streamlined object.

Figure 3. Flow over a Streamlined Object

Mach number: It is the ratio of velocity over the speed of sound. When Mach numbers are less

than 1 it is considered subsonic, when the Mach number is equal to 1 it is

considered sonic, and when it is greater than 1 it is considered supersonic and when

over 5 it is hypersonic.

Separation Zone Wake Region

Stagnation Point

High Pressure

zone

Low Pressure

zone

Boundary Layers

DynamicPressure

Boundary Layers Stagnation

Point

Separation

Separation

Insignificant Separation

Wake Region Boundary

Layers

DynamicPressure

Stagnation Point


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Wind Tunnel: Wind tunnels are used for flows in which an object is immersed in a larger body

of moving fluid. NASA Ames research Laboratory used to operate two wind

tunnels, Ames wind tunnel and 12 foot pressurized wind tunnel. Unfortunately,

both wind tunnels have now been decommissioned. Now Ames has three

relatively newer wind tunnels, 40 x 80 low speed tunnel, the 11 foot transonic

tunnel, and the 9 x 7 foot supersonic wind tunnel. The European Transonic Wind

Tunnel is also another large wind tunnel in the world.

The Wilkes University subsonic wind tunnel as shown in the figure 1a, is an

enclosure that takes air in the test section (also shown in the figure 1b) for the

purposes of studying aerodynamics, forces, and pressures of different objects. It

employs a motorized fan to produce airflow at different velocities. The tunnel

can be used with a sting balance, which measures normal, side, axial forces and

pitching and yawing moments of objects subjected to airflow. There are different

types of wind tunnels. First is open circuit tunnel such as, Eiffel or NPL. The test

section of the Eiffel type has no solid boundaries whereas the NPL has solid

boundaries. The other type of tunnel is the Prandtl (Gottingen), which is a closed

tunnel. It has a continuous path for the air to flow. This type of tunnel can have

either closed or open test section and some can operate with both open and closed

test sections. There are several other types of tunnels such as the V/STOL, which

is used for flight tests, used by NASA and Boeing. There are also special-purpose

tunnels, which are applied to specific areas for example propeller propulsion,

automobiles, and low-turbulence tunnels, etc.

Contraction

Cone: It contracts the airflow from a large volume to a smaller volume to enable the

tunnel to reach greater velocities by decreasing the pressure.

Honeycomb: The honeycomb shown in the figure 2 serves as anti-turbulence screen and is used

to create streamline airflow during intake.

Static Ring: It is a device used to measure the difference between free stream pressure in the

test section and the atmospheric pressure. Often it is treated as dynamic pressure

q.

http://windtunnels.arc.nasa.gov/nfac80120.html

http://windtunnels.arc.nasa.gov/12.html

http://windtunnels.arc.nasa.gov/40ft1.html



http://windtunnels.arc.nasa.gov/9x7ft1.html

http://www.etw.de/home/fr_home.htm

http://www.etw.de/home/fr_home.htm


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Figure 1. (a) Wind Tunnel

Figure 1. (b) Test Section and Balance

Airspeed: It is the velocity at which the air is flowing in the test section. In our wind tunnel

the speed is measured in miles per hour (mph).

Pressure: In the wind tunnel the measured pressure is always with reference to the

atmospheric pressure and measured in inches of water in the wind tunnel.

1 inch of water =

Delta Dart mounted on the balance in the Test Section

Balance mechanism-

measures forces

Contraction Measures Static Ring

Pressure Test Section Diffuser Suction Fan

Control Panel Balance Mechanism

Intake/ Honeycomb

Suction

Static Ring


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Figure 2. Honeycomb Figure 3. Intake fan

Fan: The intake fan shown in the figure 3 allows the airflow to reduce velocity while

the pressure increases. It is used to create the airflow by rotating the blades at

variable speeds to produce different velocities. In the AEROLAB tunnel the fan

has 9 blades.

Control Panel: The control panel shown in the figure 4, displays pressure, air speed, normal force,

axial force, and angle of attack etc.

Controller It is mounted on the wind tunnel legs towards the suction fan side on the backside

of the tunnel. It controls the electrical supply to the fan, which regulates the fan

speed or the intake air speed.

Figure 4. Control Panel

Airfoil: It is a slender shape object that is used to create greater lift compared to

other shape objects. Cumulative effects of pressure and viscous forces, associated

with the shape, cause the lift. The forces acting on the airfoil are shown in the

Control Panel Rotary 22-point switch to

measure pressure at various points


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figure below. Interested in airplanes and flight, click these sites Evergreen

Aviation Museum, Tillamook Air Museum, or Museum of Flight.

Normal force FL: It is the force that is applied on the object in the direction perpendicular to the

flow. The wind tunnel measure this force in lbf.

Axial force FA It is the force that is applied on the object in the direction parallel to the flow.

The wind tunnel measure this force in lbf.

Drag Force: The sum of all the forces in the direction parallel to the flow (axial) including

pressure and skin drag. The wind tunnel measure this force in lbf.

Lift Force: The pressure difference between top and bottom of the object (at a given angle of

attack) combined with thrust causes the object to lift. The wind tunnel measure

this force in lbf.

Side force: It is the force that is applied to the object in the direction horizontal

(perpendicular) to the airflow.

Thrust: It is a force to over come the effects of drag force developed the plane engines.

Pitching moment: It is the moment caused by the normal force on the object in the tunnel.

Yawing moment: It is the moment caused by the side force applied on the object in the tunnel.

Stall: When the angle of attack increases the lift decreases sharply while the drag

increases. At stall condition the plane starts loosing its altitude. In this case Drag

forces become greater than Lift forces.

Drag coefficient CD: A dimensionless number, drag force divided by the dynamic pressure and area

[CD = FD/(q*A)].

Lift coefficient CL: A dimensionless number, lift force divided by the dynamic pressure and area.

[CL =FL/(q*A)].

http://www.sprucegoose.org/

http://www.sprucegoose.org/

http://www.tillamookair.com/

http://www.museumofflight.org/


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Pressure coefficient: It is a ratio of the measured pressure minus a reference pressure (often p∞) to the

dynamic pressure (∆p/q).

Pitching moment

Coefficient: A dimensionless number, pitching moment divided by the dynamic pressure, area

and cord length.

Yawing moment

Coefficient: A dimensionless number yawing moment divided by the dynamic pressure, area

and cord length.

Drag polar plot: It is the plot of coefficient of drag CD, verses coefficient of lift CL.

Tunnel corrections: The conditions under which a model is tested in a wind tunnel are not the same as

those in free air. There is no difference between having the model still and the air

moving or vice versa. The variation of static pressure along the test section

produces a drag force known as "horizontal buoyancy". It is usually small in the

drag direction in closed test sections, and negligible in open jets where, in some

cases it becomes thrust. Although there are many types of correction we will only

deal with wall corrections.

An alteration to the normal curvature of the flow about a wing so that the wing

moment coefficient, wing lift, and angle of attack are increased in a closed wind

tunnel, and decreased in open section. It also affects normal downwash so that

the measured lift and drag are in error. The closed jet makes the lift too large and

the drag too small at a given angle of attack. An open jet has just the opposite

effect. In summary, the corrections are made for the purpose of taking into

account that the streamlines are being forced straight by the flat walls ultimately

limiting the volume of air that the model 'flies' in.

Flow Rate and Velocity Measurements Many techniques available to measure the flow rate and velocity of flowing fluid

are given below:

(1) Venturimeter/orifice plate


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(2) Pitot tubes

(3) Hot wire probes

(4) Rotameter

(5) Laser velocimetery

(6) Ultrasonic velocimetery

(7) Magneto hydrodynamic (MHD) flow meter

(8) Vortex type flow meter

(9) Turbine flow meter

(10) Smoke Injection or Laser Doppler Anemometry

Except for laser velocimeters, all these measurement techniques are commonly

used in industry, including nuclear power plants.

Conversion factors:

1 atm = 2116 Psf = 29.92 in Hg = 33.9 ft of H2O = 101325 Pa = 14.7 Psi

1 Btu = 778 ft-lb = 1055 Joules, 1 HP = 556 ft-lb/sec = 746 watts = 2545 Btu/hr

449 Gal/min = 1 ft3/sec, 1 m3/sec = 35.32 cfs,

1 slug/ft-Sec = 479 Poise = 47.9 cP

Physical Properties:

Density of water ρ = 1000 kg/m3 = 1.94 lbm/ft3

Sp. Weight of water γ = 9810 N/m3 = 62.4 lbf/ft3

Density of Air ρ = 1.22 kg/m3 = 0.00237 slugs/ft3 = 0.0763 lbm/ft3


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EXPERIMENT # 1

PITOT-STATIC TUBE

OBJECTIVE:

To measure flow velocity and determine the sensitivity of a Pitot-static tube to flow misalignment

APPARATUS:

The wind tunnel, Pitot-static tube, a bubble or hand held protractor

The atmosphere is the whole mass of air extending upwards hundreds of miles. It may be compared to a

pile of blankets. The air in the higher altitude, like the top blankets of the pile, is under much less pressure

than the air at the lower altitudes. The air at the earth's surface may be compared to the bottom blankets

because it supports the weight of all the layers above it. The static pressure of the air at any latitude results

from the mass of air supported above that level.

Natural Advisory Committee for Aeronautics (now NASA) adopted the standard atmosphere. This

standard atmosphere is entirely arbitrary, but it provides a reference and standard for comparison

purposes. Atmospheric pressure at sea level under standard condition is 29.92 inches of Mercury (Hg),

101.325 KPa, or 14.67 Psia.

Consider a fluid flowing in a tube as shown in Figure 1, when the hollow rod is inserted into the tube the

fluid rises in the rod to level h, which indicates the hydrostatic pressure

at point 1 While a bent hollow rod B is inserted at the same point 2, the

fluid rises to level H>h. At point l the velocity of the fluid is V1

however the fluid velocity at point 2 is zero, V2=0 (point 2 is the

stagnation point)

Figure 1. Flow in a tube

While the term static means "still", and the term static pressure refers to the pressure exerted by the mass

of stationary air as an object, the dynamic pressure is the pressure associated with moving air (velocity).

The total pressure is the pressure that would be exerted if the moving air were brought to a stop (such as

stagnation point) on a body in the flow. The most appropriate means of visualizing the static and dynamic

pressure is to study the fluid flow within a closed tube.


Page-23

The Pitot tube (named after Henri Pitot in 1732) measures a

fluid velocity by converting the kinetic energy of the flow

into potential energy. The conversion takes place at the

stagnation point, located at the Pitot tube entrance (see the

schematic).

A pressure higher than the free-stream (i.e. dynamic) pressure

results from the kinematic to potential conversion. This

"static" pressure is measured by comparing it to the flow's

dynamic pressure with a differential manometer. Converting

the resulting differential pressure measurement into a fluid

velocity depends on the particular fluid flow regime the Pitot

tube is measuring. Specifically, one must determine whether

the fluid regime is incompressible, subsonic compressible, or supersonic.

Incompressible Flow: A flow can be considered incompressible if its velocity is less than 30% of its sonic

velocity. For such a fluid, the Bernoulli equation describes the relationship between the velocity and

pressure along a streamline.

Assuming specific weight of fluid is γ, at point 1 the static pressure is given by P1 = γ h while the pressure

at point 2 is given by P2 = γ H. The sum of the static pressure and dynamic pressure is called total pressure

Pt=P1+ ½ρV12 . According to Bernoulli's principle we can write,

P1+ Z1 γ + ½ρV12 = P2+ Z2 γ + ½ ρV2

2 (1)

Assuming points 1 and 2 at same elevation and

V2=0 (stagnation point),

⇒ P1+ ½ρV12 = P2

Such that ∆P = P2 - P1=.½ρV12

The term ½ ρV12 is called dynamic pressure q.

Such that the velocity V1=ρ∆P2

But from figure 1, ∆P = P2 - P1= γ (H-h)

Therefore V1=ρ

−γ )hH(2 (2)

A

B

Static

To Wind Tunnel

Total Head Connection Equally spaced Holes ,

Measure Pstatic

Ptotal = Pdynamic + Pstatic Ptotal

C


Page-24

Figure 2 (a) Pitot Tube (b) Pitot Tube in the Test Section

Figure 3 Pitot Tube

Subsonic Compressible Flow: For flow velocities greater than 30%

of the sonic velocity, the fluid must be treated as compressible. In

compressible flow theory, one must work with the Mach number

M, defined as the ratio of the flow velocity v to the sonic velocity

c. When a Pitot tube is exposed to a subsonic compressible flow

(0.3 < M < 1), fluid traveling along the streamline that ends on the

Pitot tube's stagnation point is continuously compressed. If we

assume that the flow decelerated and compressed from the free-

stream state isentropically, the velocity-pressure relationship for

the Pitot tube is, where γ is the ratio of specific heat at constant

pressure to the specific heat at constant volume. If the free-

stream density ρstatic is not available, then one can solve for the

Mach number of the flow instead, where is the speed of sound

(i.e. sonic velocity), R is the gas constant, and T is the free-

stream static temperature.

Pressure Sensing Leads

Equally Spaced

Pressure Sensing hole B,

PB Pressure Sensing hole A,

PA

Threaded Nut which Fits in the

Threaded Fitting in the Test Section Pitot

Tube

Total pressure Ptot = Pstatic + Pdyn

Static Pressure

Pstatic


Page-25

Supersonic Compressible Flow : For supersonic flow (M > 1), the streamline terminating at the Pitot

tube's stagnation point crosses the bow shock in front of the Pitot tube. Fluid traveling along this

streamline is first decelerated non-isentropically (non ideally) to a subsonic speed and then decelerated

isentropically to zero velocity at the stagnation point. The flow velocity is an implicit function of the Pitot

tube pressures,

Note that this formula is valid only for Reynolds numbers R > 400 (using the probe diameter as the

characteristic length). Below that limit, the isentropic assumption breaks down.

The Pitot tube is one of the most widely used instruments (Figures 2 and 3) among the fluid mechanics

measuring instruments. One objective of Pitot tube experiment is to determine unknown velocity of a

flowing fluid. It consists of a tube within a tube that is used to determine the total head and the static

pressure of a fluid. A standard Pitot tube is shown in figure 2. Here the orifice at A reads total head (Po+

½ ρV2) and the orifices at B read static pressure, Po. Therefore, when the pressures from the two orifices

are connected across a pressure transducer, the differential pressure (Po+ ½ρV2-Po) = ½ρV2, known as the

dynamic pressure q, is obtained. From q, the free stream velocity V can be calculated.

The second objective of the experiment is to determine how much the Pitot tube can be pitched before

appreciable errors (more than 2%) in the dynamic pressure result. See Chapter 5 of the text.

PROCEDURE:

(i) Insert the Pitot tube shown in the figure into one of the threaded fittings in the side of the test section

so that the sensing head is in the center of the test section, as shown in figure 2.

(ii) Connect the total pressure lead and the static pressure lead from the Pitot tube to any two connections

(say # 0 and 1) of the 24-input rotary dial pressure system, which is located to the left of the instrument

panel. Refer to Appendix A.

(iii) Turn the fan on and operate the tunnel at the speed recommended by the instructor. Record the static

ring pressure, which is measured at any unconnected input of the rotary dial (note other 22 input from

2 to 23 on the rotary dial are not connected)


Page-26

(iv) Set the Pitot-static tube at 0° and record the corresponding total and static pressure of the Pitot-static

tube using the input rotary dial. Rotate the pitot-static tube at successive 2 degree increments from

0°≤ α ≤10° and 5 degree increments from 10°≤ α ≤20°

(v) Rotate the pitot-static tube at successive -2 degree increments from -10°≤ α ≤ 0° and -5 degree

increments from -20°≤ α ≤ -10°

(vi) Run the wind Tunnel at half the speed and record the static ring pressure, and the corresponding total

and static pressure of the pitot tube at 0° alignment.

RESULTS:

(1) Use the dynamic pressure = ½ρV2 to calculate the experimental free stream velocity in mph and

compare it with the measured wind tunnel speed.

(2) Divide the difference in Pitot tube pressures (measured across two connections) by the static ring

pressure (assumed dynamic pressure q) to obtain a non-dimensional quantity called pressure

coefficient Cp= ∆P/q. Theoretical value of Cp is given by Cp =1- 4 Sin2α, where α is the angle between

the Pitot tube and the air stream. Equation for the pressure coefficient is based on the theory of fluid

mechanics for the flow around a circular cylinder.

(3) Plot both theoretical and experimental curve for Cp versus angle α (as shown in the sample graph,

figure 1.3) and give reasons for dissimilarities in two plots.

(4) Determine the maximum angular misalignment for the Pitot tube to maintain the dynamic pressure

reading within 2% of the value when angular misalignment is zero.

(5) If wind tunnel were run at speeds of V1 = 50 and V2 = 25 mph, theoretically it means that V1/V2 = 2,

verify experimentally whether the ratio[ ][ ]

1

2

2 P /2 P /

∆ ρ

∆ ρ = 2. If this is not the case, perform the error

analysis.


Page-27

Table 1 - Values of Cp (Sample Results)

The following are not necessarily correct data Angle

Degrees (α)

Angle

Radians

Theoretical

Values

Experimental

Values

-10 -0.175 0.879 0.86 -8 -0.140 0.922 0.87 -6 -0.105 0.956 0.88 -4 -0.070 0.980 0.87 -2 -0.035 0.995 0.88 0 0.000 1.000 0.89 2 0.035 0.995 0.88 4 0.070 0.980 0.88 6 0.105 0.956 0.88 8 0.140 0.922 0.89

Figure 4. Variation of Pressure Coefficient (Cp) vs. Pitot Angle

Cp vs Angle

0.840

0.860

0.880

0.900

0.920

0.940

0.960

0.980

1.000

1.020

-15 -10 -5 0 5 10 15

Angle

Cp

Theo.Exp.


Page-28

EXPERIMENT # 3

MAJOR FRICTION LOSSES IN PIPE LENGHTS

OBJECTIVE:

Find the major friction (pressure) loss for the straight pipe sections. Obtain the head loss as a function of

volume flow rate and also obtain the friction factor as a function of Reynolds Number. The error may be

calculated by {(Experimental friction loss measured -Theo. pressure loss calculated)/Expt. loss

measured}*100

APPARATUS:

Friction loss apparatus, the Hydraulic Bench, and the Stop Watch

Figure 1. Friction Loss Apparatus

INTRODUCTION:

One of the most common problems in fluid mechanics is the estimation of pressure loss. By calculating

total loss in a piping system provides the basis to calculate pump power requirement to push the fluid

through the system. The apparatus in the lab consists of two separate hydraulic circuits, one painted dark

blue, one painted light blue, each one containing a number of pipe system components as shown in the

figure 1. Both circuits are supplied with water from the same hydraulic bench. The components in each of

the circuits are shown in the table 1 and 2. Try to physically locate them.

Sudden Contraction

Light Blue Circuit

Dark Blue Circuit Smooth Elbow

Smooth Bend

Miter Elbow

Globe Valve

Gate Valve

Sudden Expansion

Manometers

Similar fittings exist both in the dark blue and

light blue circuits


Page-29

Table 1- Pipe Lengths Data

Dark Blue Circuit

Straight Pipe Length - 0.914 m

Diameter - 13.6 mm

The pressure change across each of the component is measured using the piezometric tubes or manometers.

In the case of valves a mercury manometer measures the pressure difference. The pipes are made up of light

gage copper tubing (British Standard 659). The piezometers are numbered and connected to different units

as shown in the table 2:

Table 2- Piezometric Data

Piezometer # 3-4

Unit Dark Blue StraightPipe

THEORY:

For an incompressible fluid flow, the equations of

Continuity (mass) and Bernoulli (energy) are applicable

There are two kinds of losses, Major and Minor. The

major loss relates to pressure losses due to friction

(viscous resistance) in the straight pipe while, the minor

losses occur in fittings such as valves, expansion,

contraction, orifice, and bends. The overall head loss is

combination of these categories. Because of mutual interference between neighboring components in a

complex circuit the total head loss may differ from that estimated from the losses due to the individual

components considered in isolation. The head loss in a straight pipe is given by Darcy-Weisbach

equation,

hL= g2* D

V L f 2 (1)

Where f depends upon the Reynolds number and the roughness factor of the pipe. See Moody diagram,

Figure 10.8 [4]. Apply Bernoulli's equation between 1 and 2 in figure 2,

Z1 + g

P1ρ

+ g2

V21 = Z2 + g

P2ρ

+ g2

V22 + hL. (2)

Q Z 1

2 P

V

Z

A

2 2

2 P

V 1

1 1

2

Figure 2: Pipe of varying dimension

A 1


Page-30

The first term is potential (energy) head, the second term is the pressure head, and the third is the velocity

or kinetic energy head. All terms have length unit and hL is the head or pressure loss between two points in

a pipe because of friction (surface roughness). Now if the pipe is horizontal and it has uniform area of cross

section then V1=V2, Z1 = Z2, so that

hL = γ− )PP( 21 =

γ∆P = ∆h = difference in manometer height (3)

This is experimental value of the head loss. We have already learned from Darcy-Weisbach equation that

theoretically, hL = g2

VD

L f 2.

If you need to know how much power must be produced by the pump to accommodate for the friction loss

in the pipe of given length then use the equation

Power = γ Q hL Watts (4)

Which can be changed to horsepower by dividing the expression by 746?

FOLLOW INSTRUCTIONS BEFORE CONDUCTING THE ACTUAL EXPERIMENT

1. Connect hydraulic bench supply line to the apparatus inlet and direct outlet hose into hydraulic bench

weighing tank.

2. Close globe valve, open gate valve and admit water to dark blue circuit by starting pump and opening

outlet valve on hydraulic bench.

3. Allow water to flow a couple of minutes.

4. Close the gate valve and manipulate all trapped air into air space in piezometric tubes. Check that the

piezometric tubes all indicate zero pressure difference in the beginning (fluid levels are same in the

piezometers and manometers).


Page-31

5. Open gate valve and by manipulating bleed screws on U-tube fill both limbs with water ensuring that

no air remains.

The apparatus is now set up for measurement to be made on the components in either circuit. Note that the

datum position of the piezometers can be adjusted to any desired position either by pumping air into the

manifold with the bicycle pump supplied, or by gently allowing air to escape through the manifold valve.

Ensure that there is no water locks in these manifolds, as these will tend to suppress the head of water

recorded and so provide incorrect reading.

EXPERIMENTAL PROCEDURE

The following procedure assumes that pressure loss measurements are to be made on all the circuit

components.

(i) Open fully the water control valves on the hydraulic bench. With the globe valve closed, open the

gate valve fully to obtain maximum flow through the dark blue circuit. Record the readings on the

piezometric tubes and the manometer. Collect a sufficient quantity of water in the weighing tank

to ensure that the weighing takes place over a minimum period of 60 seconds. Determine the flow

rate by hanging a total mass of 4 Kg, 6 Kg on the lever (Note that 2 kg of dead weight is already

hanging on the lever in other words hanger itself weighs 2 kg), which is equivalent to 12 and 18

Kg of water respectively.

Time with stopwatch and determine the flow rate= Mass/time=•m (experimental). Take five time

readings for the same flow rate. The mass and volume flow rates are given as(5)

(ii) Volume flow rate Q = AV (6)

Ma ss flow rate •m = ρAV = Q

This gives the velocity of flow V =•m /ρA , from which the Reynolds number Re = ρVD/µ may be

calculated, if Re < 2300, the flow is laminar otherwise turbulent.

(iii) Repeat the above procedure for a total of 5 different flow rates, obtained by closing the gate valve,

equally spaced over the full flow range.

(iv) Record the water temperature in the sump tank of the bench each time a reading is taken.

(v) Before switching off the pump, close both the globe valve and the gate valve. This procedure

prevents the air in gaining access to the system and so saves time in subsequent set up. Switch the

pump off and drain all the water in the system as much as possible.


Page-32

(vi) Record the water temperature in the sump tank of the bench each time a reading is taken.

(vii) Before switching off the pump, close both the globe valve and the gate valve. This procedure

prevents the air in gaining access to the system and so saves time in subsequent set up. Switch the


Table 3 - Experimental Data- Bench with weight hanging mechanism Trial

Number

Hanging mass

Time to collect ‘m’ kg Equivalent to ‘3m’ kg

of water flow

Calculate Mass flow Rate

m

Piezometric readings Between 3 and 4

1. m1 = For example assume m1 = 4 kg

t1 = t2 =

t3 =

t4 =

t5 = tavg =

m

= 3m1/tavg

=

For example If tavg = 24 sec

m

= 12/24 = 0.5

2. m2 =

t1 = t2 =

t3 =

t4 =

t5 = tavg =

3m2/tavg

3. m3 =

t1 = t2 =

t3 =

t4 =

t5 = tavg =

3m3/tavg

4. m4 =

t1 = t2 =

t3 =

t4 =

t5 = tavg =

3m4/tavg

5. m5 =

t1 = t2 =

t3 =

t4 =

t5 = tavg =

3m5/tavg

For flow in the straight pipe (dark blue circuit) Calculate:

• Mass flow rate ( m•

= ρAV) and Volume flow rate (Q = AV), from column 2 of the table 3, Area of

flow, Mean velocity, Reynolds Number


Page-33

• Friction factor (See text book Chapter 10, Figure 10.8)and head loss (hL) using the formula (equation

1, consider this as theoretical value of hL)

• Compare theoretical hL with the experimental values of hL as observed and noted in the column 4 of

table 3.

• Perform error analysis on all parameters, which are determined both experimentally and

theoretically.

• Plot Log hL (experimental data on y-axis) against Log Q (experimental data on x-axis). Determine

relationship of the form hL ∞ Qn . Use EXCEL, MATLAB, or any other curve fitting software to

perform this operation. Determine the value of the exponent ‘n’ from the graph. Note that this value

normally should range from 1.75 to 2.0.

• Plot Reynolds number (on x-axis- experimental values) against the friction factor f (on y-axis,

calculated from the moody diagram and also from the experimental value of hL equation 1).

• Also plot in the same graph the Blasius equation given by f = 0.316/(Re)0.25.


Page-34

EXPERIMENT # 4

VENTURI METER

OBJECTIVE:

Measure the flow rate or discharge of a pipe using a Venturi meter.

APPARATUS:

Friction loss apparatus and the Hydraulic Bench

FOLLOW INSTRUCTIONS BEFORE CONDUCTING ACTUAL EXPERIMENT

1. Connect hydraulic bench supply line to the apparatus inlet and direct outlet hose into hydraulic bench

weighing tank.

2. Open both flow control and bench supply valve such that the difference in the heights between h1 and

ht (h4) is at least 100 mm. Make sure the air purge valve on the manifold is closed tightly. Do not over

tight any valve.

3. The apparatus is now set up for measurement to be made. Allow water to flow a couple of minutes.

4. Close the flow control valve on the right. Air will now be trapped in the manometer upper parts.

Release the air purge valve sufficient to allow water to rise approximately half way up the manometer

scale. Close the purge valve.

5. Adjust all valves to obtain reasonable flow and record the height difference between the venturi inlet

and the venturi throat.

6. All Venturimeter data is provided on the backside of the Venturimeter panel.

INTRODUCTION:

One of the most common problems in fluid mechanics is the determination of flow rate. The venturi is a

device, which has been used over many years for measuring the flow rate through a pipe and is based on

Bernoulli’s theorem. The instrument consists of a short pipe which contracts up to a section called as throat

and then enlarges up to a diameter at outlet as shown in Figure 1. The conical portions joining the inlets

and the throat and the outlet are called as converging cone and diverging cone respectively. The fluid is led

through the contraction section to the throat with much smaller cross-sectional area than the pipe. By

contracting the passage of flow at the throat, the velocity of flow and hence the velocity head is increased.

This increase in the velocity head causes change in pressure head.


Page-35

A differential manometer as depicted in the figure 1 measures the pressure difference. The magnitude of

which depends on the rate of flow, so that by measuring the pressure drop, the volume flow rate or discharge

may be calculated. Beyond the throat the fluid is decelerated in a pipe of slowly diverging section or

diffuser, where pressure increases as the velocity decreases. The meter is shown in the figure 1.

THEORY:

Simplistically, theoretical discharge through Venturimeter can be given as

Qtheo. = k * h (1a)

And Actual discharge through Venturimeter Qact= C Qtheo = C * k * )hh( t1 − (1b) Where, C = Coefficient of discharge of Venturimeter, k = Constant of Venturimeter, and h = Difference of

head in terms of water column between inlet and throat.

Figure 1. (a) Venturimeter (b) Venturimeter

Sketch

To determine the expression for k and C, consider the flow of incompressible fluid through a Venturi meter.

Apply Bernoulli’s equation at inlet and at throat. If friction loss are assumed to be negligible (in particular

if the flow is in a glass pipe) and Z’s are same then Bernoulli’s equation is reduced to,

Throat, Area At

Water Supply from Bench

Flow Control Valve

Water exit to Bench

Manifold

Area A1

Inlet From Supply

Manometer Tubes

Air Valve

Control Valve

To tank Throat

Vena Contracta Location


Page-36

t

2t

1

21 h

g2V

hg2

V+=+ (2)

Q is the volume flow rate or discharge through the pipe and the equation of continuity gives

Q = V1A 1 = Vt At (3)

P/γ = h (4)

From equation 3, V1 = Vt * At/A1

Substituting for V1 into equation 1,

t

2t

1

2

1

t2t h

g2V

hAA

g2V

+=+

(5)

Which gives 2

1

t

t1t

AA1

)hh(g2V

−

−= (6)

So that discharge Qact = At 2

1

t

t1

AA

1

)hh(g2

−

− (7)

= C AA

g2AA2

t2

1

t1

−)hh( t1 − (8)

Qact = C Qtheo

In this experiment, since we know the flow rate, we will determine the value of discharge coefficient C.

Note that, the coefficient of discharge C is never unity and it is determined experimentally. So that from

equation 7 we find that C .= smaller

l arg er

Q Q

(∴C < 1). Where C is the discharge coefficient of the

venturimeter. It usually ranges between 0.92 to 0.99. The variation of discharge coefficient (C) for

various metal venturimeters are shown in figure 2 [19] below. You can compare the experimental value of

C with the value obtained from figure 2.

Comparing equation 7 with the equation 1, it can be found that the venturimeter constant k can be written as

k = AA

g2AA2

t2

1

t1

− (8)

Where, A1 = Area of inlet which can be found out from inlet diameter d1 and At = Area of throat which can

be found out from throat diameter dt.


Page-37

Figure 2. Discharge Coefficient of Venturimeter [19]

The above formula in equation 7 can also be written in the form

Qact = α 1 t(h h )β− (9)

Log Qact = β Log 1 t(h h )− + Log α

Log Qact = β Log h∆ + Log α (10)

Plot a graph of logQact (y-axis) vs. log(h1 - ht) (x-axis) and fit a straight line through the data points.

Fitting a straight line into your plot will yield straight line equation y = m x + c so that your graph will

give

Slope (m) = β, and Intercept (c) = logα Hence the constants α and β can be found out by the slope and intercept.Compare graphical values with

the theoretical values of α and β given by

α ≅ 0.98*k and β ≅ 0.5 (10) EXPERIMENTAL PROCEDURE


components.

(i) Open all water control valves one third full. Take the pressure measurements for one flow rate.


Page-38

(ii) Repeat the above procedure for a total of five different flow rates. Change the flow rate by opening

or closing the bench control valve.

(iii) Record the water temperature in the sump tank of the bench.

(iv) Switch the pump off and drain all the water in the system as much as possible.

(v) Calculate the value of C, the discharge coefficient. Determine the error in the values of

experimentally determined C and theoretical value of C = 0.98.

(vi) Calculate the venturimeter constant ‘k’ using equation 8.

(vii) Search for the Venturi-meter codes and standards on the web and report your findings. Provide the

references.

Table 1- Experimental Data (READINGS TO BE TAKEN)

No. Manometer Readings Qtheo=

k * h∆ m3/s

Actual discharge h1

mm ht

mm ∆h m

Time sec m

g

Kg/sec

Qact m3/s

1

t1 = m/tavg

t2 = t3 = t4 = t5 = tavg=

2

t1 =

t2 = t3 = t4 = t5 = tavg=

3

t1 =

t2 = t3 = t4 = t5 = tavg=

4

t1 =

t2 = t3 = t4 = t5 = tavg=

5

t1 =

t2 = t3 = t4 = t5 = tavg=


Page-39

Results and Discussion

C = Q

Q

theo

act log10 Qa log10 h

Average C = …. GRAPHS TO BE PLOTTED: 1. Plot graph of log10Qact vs log10h to determine α and β. Changing Q and h in cm units will produce

better results. Also you may have to eliminate one or two data points to reduce error blips in the data. Plot Calibration curve: Plot Qact Vs h

2. Plot graph of C vs. Re at throat. {Re is the Reynolds number Re = throat

VDρµ

Your data plot should exhibit a plot similar to graphs shown in the figures 2 and 3.

Figure 2. Actual Discharge vs. Differential Head


Page-40

Figure 3. Log10Qact Vs. Log10 h

RESULTS:

1. Error Analysis between Qact and Qtheo

2. The discharge coefficient of the Venturimeter is k =______ from calculation (eqn. 8).

k =______ from graph (eqn. 10).

3. The law of the Venturimeter is Qact = α hβ cm3/s.= _____ m3/s. From Graphical data The value of α = _____ The value of β = ____ 4. Practical utility of calibration curve: For ………cm pressure head difference across the

Venturimeter, the discharge through the Venturimeter is …………cm3/s.


Page-41

EXPERIMENT # 5

MINOR FRICTION LOSSES IN PIPE FITTINGS

OBJECTIVE:

Find the minor losses in the fittings. The error may be calculated by {(Experimental loss measured -

Theoretical loss calculated)/Experimental loss measured}*100

APPARATUS:

Friction loss apparatus and the Hydraulic Bench

INTRODUCTION:

One of the most common problems in fluid mechanics is the estimation of pressure loss. By calculating

total loss in a piping system provides the basis to calculate pump power requirement to push the fluid

through the system. The apparatus in the lab consists of two separate hydraulic circuits, one painted dark

blue, one painted light blue, each one containing a number of pipe system components. Both circuits are

supplied with water from the same hydraulic bench. The components in each of the circuits are as shown

in the table 1. Try to physically locate them.

Figure 1. Friction Loss Apparatus (repeat)

Sudden Contraction

Light Blue Circuit

Dark Blue Circuit Smooth 90o Bend

Smooth Bend

Miter Elbow

Globe Valve

Gate Valve

Sudden Expansion

Manometers


Page-42

Table 1- Pipe System Data (Figure 1)

Dark Blue Circuit Light Blue Circuit

Proprietary 90o Elbow Sudden Enlargement –

13.7 mm to 26.4 mm

90o Sharp Bend (Miter) Sudden Contraction –

26.4 mm to 13.7 mm

Proprietary 90o Elbow Smooth 90o bend 50.8 mm radius

Gate Valve Standard Elbow Bend

Smooth 90o bend 101.6 mm radius Smooth 90o bend 152.4 mm radius

Globe Valve

In all cases including the gate and globe valves a pair of pressurized piezometric tubes measures the pressure

change across each of the components. In the case of two valves a mercury manometer measures the

pressure difference. The pipes are made up of light gage copper tubing (British Standard 659). The

piezometers are numbered and connected to different units as follows:

Table 2- Fitting Data in Different Water Flow Circuits

Piezometer

# 1-2 5-6 7-8 9-10 11-12 13-14 15-16

Unit Elbow Miter

Bend

Sudden

Expansion

Sudden

Contraction

152.4

Bend

101.6

Bend

50.8

Bend

Note that the Piezometer readings (experimental for example, 5-6) represent the loss in the fitting as well

as the loss in the pipe lengths associated with that fitting. To determine the head loss in the fittings only,

the head loss in the associated pipe lengths must be subtracted. Therefore, for each fitting measure and

record the pipe length associated with that fitting.

THEORY:

For an incompressible fluid flow, the equations of Continuity and Bernoulli are applicable. The minor losses

occur in fittings such as valves, expansion, contraction, orifice, and bends. Because of mutual interference

between neighboring components in a complex circuit the total head loss may differ from that estimated

from the losses due to the individual components considered in isolation.


Page-43

The head loss in any fitting is calculated by hL= g2VK 2

L , where KL is loss coefficient, a dimensionless

parameter. For sudden expansion, loss coefficient KL = 21 2(V V )

2g− .

For sudden contraction and different valves, the values of KL are given in the table 3 and figure 2. The loss

coefficients for the gate and globe valves are given in Table 4. Note that the loss in the Valves is given by

KL*V2/2g, where V is the valve inlet velocity. For bends, KB depends upon the bend radius/pipe diameter

ratio and the angle of the bend. Typical values of KB for 90o bend are given by the graph shown in the

figure 2. Refer chapter 10 of the text book [4] for further details.

Table 3 –Contractions

A2/A1 0 0.1 0.2 0.3 0.4 0.6 0.8 1.0

K 0.5 0.46 0.41 0.36 0.3 0.18 0.06 0

Figure 2. 90o Smooth Bend Data- for different angle bends there are different K values If other data are needed, refer to the Chapter 10 [4].

Table 4 – Valves Loss Coefficient

KL

Globe valve, fully open 10.0

Gate valve, fully open 0.2

Gate valve, half open 5.6

00.10.20.30.40.50.60.70.80.9

11.11.21.3

0r/D

2 4 6 8 10 12

KB


Page-44

PERFORM THE FOLLOWING BEFORE CONDUCTING THE ACTUAL EXPERIMENT

1. Collect a sufficient quantity of water in the weighing tank to ensure that the weighing takes place over

a minimum period of 60 seconds. Connect hydraulic bench supply line to the apparatus inlet and direct

outlet hose into hydraulic bench weighing tank. Allow water to flow a couple of minutes.

2. Close globe valve, open gate valve and admit water to dark blue circuit by starting pump. Close the

gate valve and open the globe valve and let the water run through light blue circuit.

3. Manipulate bleed screws on U-tube and fill both limbs with water (if necessary) to ensure that no air

remains in piezometric tubes. Check that all piezometric tubes all indicate zero pressure difference in

the beginning.

The apparatus is now set up for measurement to be made on the components in either circuit. Note that

the datum position of the piezometers can be adjusted to any desired position either by pumping air into

the manifold with the bicycle pump supplied, or by gently allowing air to escape through the manifold

valve. Ensure that there is no water locks in these manifolds, as these will tend to suppress the head of

water recorded and so provide incorrect reading.



components.

(i) Open fully the water control valves on the hydraulic bench. With the globe valve closed, open the

gate valve fully to obtain maximum flow through the dark blue circuit. Record the readings on the

piezometric tubes and the manometer. Determine the flow rate by hanging say 4 Kg on the bench

(which is equivalent to 12 Kg of water respectively). Record the flow time with stopwatch. Repeat

this procedure five times to get avg. time to flow 12 kg of water from the bench to the pipe system as

shown in the table 5.

(ii) Record the data in a tabular form shown in the table 5.

(iii) Open gate valve. Take the readings for all the fittings in dark blue circuit.

(iv) Open globe valve and close the gate valve, and repeat the above procedure for the light blue circuit

for the same flow.

(v) Repeat the above procedure for a total of 5 different flow rates, equally spaced over the full flow

range.

(vi) Record the water temperature in the sump tank of the bench each time a reading is taken.


Page-45

(vii) Before switching off the pump, close both the globe valve and the gate valve. This procedure

prevents air from gaining access to the system and so saves time in subsequent set up. Switch the


Table 5 - Typical Experimental Data: Trial

Number

Hanging mass

Time to collect ‘m’ kg

Equivalent to ‘3m’ kg of water flow

Calculate Mass

flow Rate

U-tube mm – Hg

Gate Valve

U-tube mm – Hg

Globe Valve

Piezom. readings Between

5-6 Miter Bend


7-8 Expansion


9-10 Contraction


11-12 Bend

1.

m1

t1 = t2 =

t3 =

t4 =

t5 = tavg =

3m1/tavg

Repeat for five different

flows

Note: to calculate the change in the head (energy) from one point to another for varying cross-section pipe

with no datum changes such as in sudden contraction, use the formula (h2 - h1) = g2VV 2

22

1 − - hL. where hL.

is the head loss in the pipe lengths only. RESULTS 1. Determine the flow rate

•m gives V =

•m /ρA, and Re =ρVD/µ. (obtain at least five time readings as

shown in the Major loss experiment) If Re < 2300, the flow is laminar otherwise turbulent. Determine

the losses in the pipe lengths associated with several fittings using the Darcy’s formula and Moody

diagram. Subtract the head loss in the pipe length from the total head loss measured for that fitting. This

will yield the head loss in the fitting only.

2. Compare the measured head rise or loss from manometer with the calculated (theoretical) head rise or

loss for miter bend, globe valve, sudden Expansion, contraction and other fittings installed in the

system and perform the error analysis. 3. Plot the measured head rise or loss from manometer (as y-axis) against the calculated (theoretical)

head rise or loss for miter bend, globe valve, sudden expansion, contraction and other fittings

installed in the system.


Page-46

EXPERIMENT # 6

DISCHARGE OVER WEIRS

OBJECTIVE:

The purpose of this experiment to derive relationships between head on the weir and discharge for both

rectangular and V-shaped notches and calculate the discharge coefficient. Compare it wit ASME codes.

APPARATUS:

Weirs and the Hydraulic Bench

INTRODUCTION:

In hydraulic engineering, weirs are commonly used to regulate flow in rivers

and other open channels. In some cases the relationship between the water Figure 1. Weir- Sketch

level upstream of the weir and the discharge over it is known, so that the discharge at any time may be

found by observing the upstream water level. Figures 1 and 2 show a V-shaped notch weir. Similarly,

rectangular notches can also be prepared. Such notches usually have sharp edges so that the water springs

clear of the plate as it passes through the notch. Two V-shaped notches are supplied with angles θ of 15o

and 45o respectively.

Figure 2. Weir Experimental setup

V-notched Weir

Water Supply From the Bench

Enlarged End of the Weir Tank

Contraction Section

Exit Tank

Depth Gage

Connect Water supply here

Location M Location N

M

Flow over a weir

N


Page-47

DESCRIPTION OF APPARATUS

Figure 2 shows the arrangement in which water from the bench supply valve is led through a flexible hose

to a pipe, which serves to distribute the water fairly evenly in the enlarged end of the tank. A contraction

section leads the water to a short channel, into which either the rectangular or V-notched weir plates may

be fitted.

Water flow over the notch is collected in the exit tank; the outlet leads via a drain port to the weigh tank of

the Hydraulic Bench.

The water level in the short approach channel may be measured with the height or depth gauge placed in

the recesses on the top edge of the tank. Loosening the nut on the top of the gauge rack may zero the gauge.

INSTALLATION AND PREPARATION

Skip this step in case the weir is installed

(a) Check for damage and thoroughly clean all traces of unwanted material.

(b) Assemble the plastic inlet pipe assembly and the pad of rubber sponge into the tank as shown.

(The sponge pad acts as a 'water settler').

(c) Place depth gauge in recesses on top flanges of the tank.

(d) Place the apparatus onto the Hydraulic Bench top with the widest (inlet) end to the rear of the bench

and the discharge over the bench weigh tank.

(e) Connect the Hydraulic Bench supply hose to the apparatus.

(f) Apply silicon compound (supplied) to the sides, lower corners and bottom edges of the plate to be fitted

into the channel. Fit the plate into the groove, ensure it is properly seated and smear the silicon

compound around the join, adding more if necessary, to give a full seal. Remove any excess.

(h) After use, the apparatus should be drained of all water and dried with a lint free cloth. The glass fiber

tank has a white-pigmented interior and can easily be cleaned with any good quality car body cleaner

and polished.

THEORY:

Consider the motion of a particle of fluid from a position M some distance up-stream of the weir to its

subsequent position N in the plane of the vertical weir plate. If there is no energy loss, the Bernoulli's

equation gives:


Page-48

g2

V2M +

γMP + zM = g2

V2N +

γNP + zN (1)

Now provided that the approach channel has a much larger cross-sectional area than the notch, the fluid in

the vertical plane containing M will be comparatively at rest, so that it is in almost a hydro-static condition

for which the total head of all points has the same value H relative to the datum shown. Making the further

assumption (justifiable) that pressure PN = 0, i.e. the static pressure is atmospheric at N, equation 1

simplifies to:

g2

V2N + zN = H (2)

Now H - zN = h (3)

It may be seen from the figure that

g2

V2N = h ⇒ VN = gh2 (4)

This velocity is the same as that which would be attained by a particle falling freely from the level of the

upstream surface to the position of N. The discharge over each weir may now be found by integration. For

the rectangular weir of width b, the area of an element having height dh is b*dh, so that the flow rate dQ

through the weir is

dQ = VN b dh = gh2 b dh (5) The total flow rate Q is obtained by integrating between zero and H. This result neglects the lowering of

the surface level in the plane of the rectangular weir:

Q = ∫H

0bdhgh2 = g2

32 b H3/2 (6)

For the V notch of angle 2θ the width of an element is 2(H - h) tanθ, so that the area of the element having

height dh is 2(H - h) tanθ dh. The flow rate through it is:

dQ = VN 2(H - h) tanθ dh = gh2 2(H - h) tanθ dh (7)

So that, integration gives, Q = ∫ θ−Η

0dh tan )hH(2gh2


Page-49

or Q = g2158 tanθ H5/2 , for the V notch. (8)

There is in fact, a considerable contraction of the stream as it passes through the notch. This can be seen to

take place both in the vertical plane, where the upper surface slopes downwards over the notch and the

lower surface springs from the crest of the notch in an upward direction, and in the horizontal plane, where

the water leaves the edges of the weir in a curve which reduces the width of the stream. This contraction is

similar to that previously observed at a sharp-edged orifice and has the same effect of reducing the

discharge. It is therefore customary to re-write the equations in the form:

Q = Cd g2

32 b H3/2 , for the rectangular notch (9)

and Q = Cd g2158 tanθ H5/2 , for the V notch (10)

Where, Cd is a coefficient of discharge of the notch, which is not necessarily independent of H and may be

determined by experiment. A convenient way of finding Cd, and the exponent of H, in either of these

expressions is as follows. Either of equations 9 or 10 may be written in the form:

Q = k Hn (11) or log Q = log k + n log H (12)

If experimental results are plotted on a graph having logH as abscissa and logQ as ordinate, then, provided

that k and n are constant over the range of the results, they will lie on a straight line having slope n and

intercept log k on the axis of log Q.


The apparatus is first leveled and the depth gauge zeroed. To do this, water is admitted from the bench

supply to the apparatus until the level is approximately correct, and then carefully baled out or in, using a

small beaker, until the crest of the weir lies just in the surface. For the rectangular notch, this can be checked

as illustrated in figure 1(a) by placing a steel rule on the crest. For the V notch, the reflection of the V in

the surface serves to indicate whether the level is correct or not as illustrated in fig 5(b). When the correct

level has been obtained the gauge should be set to coincide with the free water surface and the dial set to

read zero. The following procedure relates to use of the height gauge:

i. Set scale to whole number on Vernier depth gage

ii. Lock Vernier gage

iii. Loosen nut and slide down depth pointer to touch water - lock nut.


Page-50

iv. Set dial on depth gauge to zero.

v. Datum is now set at whole number on Vernier gauge.

A series of five measurements of discharge and head on the weir are then taken, the flow being regulated

at the bench supply valve. It is recommended that the first reading is taken at maximum discharge, and

subsequent readings with approximately equal decrements in head. Readings should be discontinued when

the level has fallen to a point at which the stream ceases to spring clear of the notch plate; this is likely to

occur when the head has been reduced to about 10 mm for a rectangular notch and about 20 mm for a V

notch.

Table 1 – Flow Rate Results with Rectangular Notch (not necessarily accurate data)

H - mm 104*Q m3/sec LogQ LogH 5 4.50 -4.3 -1.3 4 3.20 -3.3686 -1.4074 6 1.78 -4.1051 -1.8817

Table 2 - Flow Rate Results with V Notch (15o) (not necessarily accurate data)

H - mm 104*Q m3/sec LogQ LogH H

mm

104*Q

m3/sec LogQ LogH

5 4.50 -4.3 -1.3

4 3.20 -3.1273 -1.0760

6 1.78 -4.0799 -1.4729

About 5 different discharges for each notch should be sufficient. The width of the rectangular notch and the

angle of the V notches (best found by measuring the depth and width of the V) should be recorded. For

each flow rate data take at least 5 time readings and use the average of the five time readings to determine

the average flow rate.

RESULTS AND CALCULATIONS

Results given in this section are although obtainable; there may be slight problems. Tables 1 and 2 show

the results. From these results a graph of discharge rate logQ (y-axis) against head logH (x-axis) should be

plotted. Figs 3 shows the form of the graph expected. The slope n and intercept k on the axis of the logQ


Page-51

scale should be determined and used to derive the relationship between Q, the discharge rate, and H, the

head. See above for the related theory.

Table 3- Not Relevant Data Column C Column D 1 Log H Log Q 2 2 3 3 5 4 4 9 6 5 12 8 6 14 9

From Sample Graph

Log K = 1.6790

n = 0.5144

Note: The value of n should be 5/2, and value

of k should be 8 2g15

tanθ Figure 3- Plot of Log Q Vs Log H

QUESTIONS FOR FURTHER DISCUSSION

How would you interpret results, which, when plotted logarithmically such as Variations of Discharge

with Head for Rectangular and V Notches and variations of LogQ vs LogH for Rectangular and V

Notches, fall on a line which is not straight, but slightly curved?

To what extent does the experiment confirm the theoretical treatment? Has the dependence on b (for the

rectangular notch) or (for the V notch) been established? A suggested project is to plan a series of tests to

explore the dependence on b, using a set of notches or by partially covering the width of the one supplied

with a sharp-edged metal strip. What range of b should be chosen? What is the best way to present the

results? Is there a recognized modification to the form of equation 9, which allows for the effect of the

contractions at the side?

What suggestions you may provide for improving the experiment? Reference Information [19] V-notch weir equations have become somewhat standardized. ISO (1980), ASTM (1993), and

USBR (1997) all suggest using the Kindsvater-Shen equation, which is presented below from

USBR (1997) for Q in cfs and heights in ft units. All of the references show similar curves for C

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12 14 16

Log

Q

Log H

Log Q Vs Log H Log Q

Linear (Log Q)

Intercept = 1.6790123Slope = 0.5144033

INTERCEPT(D2:D6,C2:C6) =SLOPE(D2:D6,C2:C6) =


Page-52

and k vs. angle, but none of them provide equations for the curves. To produce automated

calculations, LMNO Engineering used a curve fitting program to obtain the equations which best

fit the C and k curves. Our equations are shown below. The graph shown in figure 4 is from our

fits. If you compare it to the graphs shown in the references, it looks nearly identical which

implies that our fits are very good.

Figure 4- Theoretical Weir Discharge Coefficient


Page-53

EXPERIMENT # 7

PRESSURE DISTRIBUTION OVER A CIRCULAR CYLINDER

OBJECTIVE:

Calculate the pressure distribution resulting from the flow of an ideal fluid about a circular cylinder and

compare with the data obtained from real fluid flow about the circular cylinder in the wind tunnel.

APPARATUS:

Wind tunnel and a circular cylinder

INTRODUCTION:

In this experiment, the pressure coefficient from the flow of air about a cylinder will be calculated and

compared with theory. From ideal flow theory, the pressure coefficient, Cp, of an ideal fluid at any angular

position θ on the surface of a circular cylinder is

Cp = 1 - 4 sin2θ (1)

From the wind tunnel measurements the pressure coefficient, Cp, of a real fluid at any angular position θ,

is

Cp = 2o

V

pp

21 ρ

− (2)

Note that there are sensing holes at 15-degree intervals about the cylinder being zero at the horizontal.

These sensing holes indicate total pressure, P = Po+ ½ ρV2. However, the pressure indicated on the LED

display [front panel of the wind tunnel], is the difference between the total pressure p, and the static pressure

Po. In other words it displays ∆p = P- Po. The dynamic pressure q = ½ ρV2, can be calculated using free

stream velocity and density of the fluid at that temperature are known. The pressure coefficient, Cp, could

then be calculated for both the real and ideal flow case.

Wake A

B C

D

Stagnation Point, A

Low Pressure zone

High Pressure zone

A B P < P along the surface of the cylinder P < P along the surface of the cylinder C B ,

Figure 1 Flow Separation about a cylinder

Separation


Page-54

The flow about the cylinder is shown in the figure 3.1. A is the stagnation point while C and D are separation

points. If the velocity is increased, then it is possible to further move the separation towards downstream.

It may be noted here that the positions of the separation points as depicted in the figure 3.1, are determining

factors in the flow patterns. Therefore it is suggested that the care must be taken in determining these flow

reversal points.

PROCEDURE:

(i) Very carefully remove the balance. (For help, refer to appendix-C before you proceed)

(ii) Record the diameter of the circular cylinder. Fasten tufts near the equatorial diameter of the circular

cylinder to determine approximately where separation occurs. The tuft may be a piece of thread or

wool, which can be taped on the cylinder. Remove the top panel of the test section.

(iii) Carefully insert the sensing hole leads through the rubber seal in the floor of the test section and insert

the circular cylinder with the 0 indicator facing the honeycomb into the test section.

(iv) Connect the numbered leads from the sensing holes to the 24-input rotary dial.

(v) Turn the Fan on and operate the tunnel at 40 mph. (For help refer to appendix A)

Caution: Do not increase the air speed above 75 mph., since the large size and drag of the model

limits the speed at which this particular wind tunnel can properly operate and function.

(vi) Record the differential pressure from each of the sensing holes and the static ring pressure.

(vii) Indicate approximately where separation occurs by noting at what angular position the tufts resemble

vortices.

(viii) Record the room temperature. It will be used in calculation of ρ and µ for air. Also record the diameter

of the cylinder.

RESULTS:

1. Calculate the pressure coefficient, Cp, for the real flow case using equation 2.

2. Calculate the pressure coefficient, Cp, for the ideal case using equation 1.

3. Plot the pressure coefficient versus angular position for the ideal flow case and the real flow case.

Locate the approximate position of separation on the curves as depicted in sample curves.

4. Calculate the Reynolds number for real case, Recall Re = ρVD/µ.


Page-55

Figure 2- Variation of Coefficient of Pressure on Various Points of the Cylinder in the Flow

Cp = ∆P/q


Page-56

EXPERIMENT # - 8

VARIABLE SPEED PUMP

This experiment set up has been changed. Modify the procedure according to new set up.

OBJECTIVE:

The objective of this experiment is to measure the efficiency of a variable speed pump over a wide range

of conditions and determine how well the pump affinity laws hold for variable speed pumps and in the

process develop the operational characteristics of a variable speed pump

APPARATUS:

Variable speeds pump setup

INTRODUCTION:

A flowing fluid exerts both pressure and viscous forces o

Figure 1. Pump Theoretical Setup

The pump used here is a Grundfros model CHIE-2-10, .5 HP, 115/230 Volt, 60 Hz, 1 phase TEFC motor

with built-in variable speed control shown in the figure 1 and 2. It has a nominal flow of 10 gal/min and a

nominal head of 20 ft. The rate and amount of flow through a pipe depends upon the head added by the

pumping device. This imbalance is called the pressure difference. For this to happen the pressure at the

pumping device needs to be greater then the pressure in the rest of the system, otherwise the fluid will not

flow. [4, 12, 13]

• The rate of flow in a system is directly proportional to the impeller rotational speed (rpm).


Page-57

322

2311

1

DNQ

DNQ

= (1)

• The head of the pump will vary, as the square of the change in impeller rotational speed (rpm).

22

22

21

21

1

DN

H

DNH 2= (2)

• The horsepower is proportional to the change in impeller rotational speed (rpm).

52

32

251

31

1

DNP

DNP

= (3)

Where Q = Flow, H = Head, P = Power, N = Speed (rpm), D = Impeller Diameter

In our case the impeller diameter is constant, these equations can therefore be simplified as shown in

equations 4-6. Therefore the rate of flow in a system is directly proportional to the impeller rotational speed

2

2

1

1NQ

NQ

= (4)

Similarly the pump head will vary, as the square of the change in impeller rotational speed

22

21

1

N

H

NH 2= (5)

And the power is proportional to impeller rotational speed cubed

32

231

1

NP

NP

= (6)

Pump performance curves are an essential for sizing a pump [13]. The pump performance curve is a vital

tool when considering how the pump will react to changes in the system. It determines what working point

the pump will run at if anything changes. The pump working point is where the pump will work efficiently.

By inspecting figure 2 it is shown that the pump’s efficiency curve intersects the system curve at just under

600-gpm and around an efficiency of 59%. The system curve describes the capacity and head needed for

the various operating conditions of the pump and is made by plotting the capacity (gpm) against the head

needed (ft). By changing the pumps impeller rotational speed the pumps efficiency will be altered and

therefore the working point will move.


Page-58

For example, in figure 3 below, if the impeller speed of the pump were to be slowed it would make the

system more efficient as the working point moved left along the efficiency line, although be reducing the

speed to much the efficiency begin to reduce again; whereas if the speed were increased it would result in

a less efficient working point.

Figure 2. Pump Physical Setup

The size of the pump is another factor that will affect the pump curves. The pump must be able to overcome

the pressure head throughout the system. To find this size the pump curve must be examined to find the

Storage Tank

Rotometer

Suction Side Gage

Discharge Side Gage

Pump Drain

Valve

Tachometer

Graduated Sacle- Water Height - Z1

Water Supply


Page-59

point where it meets the requirements. By having the wrong size pump the system will not be capable of

reaching its maximum efficiency [4, 12, 15]

So when designing a system it is important to take into considerations the differences between the 68oF

airless water and the type of fluid for the particular system in question. The specific gravity of the fluid

will change the amount of horsepower the pump needs to supply the system. This is found using the brake

horsepower equation:

p

p

Q h SGBHP

3 960 ,=

η (7)

Where: BHP = Break Horse Power- hp, Q = Flow - gpm, hp = Pump Head ft, SG = Specific Gravity, and

ηp= Pump Efficiency at Duty or Working Point. Since the experiment is using water the specific gravity is

equal to unity. To determine the pump head, apply Bernoulli’s equation such that

hp = (p2 - p1) / γ + (V22 - V1

2)/ 2*g + (Z2 - Z1) + hL (8)

Find Z1 from the water column on the right side, find

Figure 3: Working Point


Page-60

Figure 4: Energy Cost vs. Efficiency

Figure 5: Efficiency of Various Pumps Vs. Flow Rate

How the efficiency affects the cost can be seen below in figure 4 in which a pump running at 800-gpm was

compared with the cost of running it at various efficiencies. It is obvious by Figure 4 that the efficiency can

greatly affect the cost of running the system, for example running it at 40% efficiency would have a cost of

approximately $9,000 whereas running the same system at 70% efficiency would reduce this cost to around

$5,000; almost half the cost [13, 15]. Figure 5 exhibits how the efficiency of variable speed pumps varies

with the changes in flow. As shown here, the variable speed pump is more efficient than the constant speed

pump at lower and mid-level flow rates. However as the flow rate approaches a maximum the difference

between the constant and variable speed efficiencies reduces until they are the same.

\

CONCLUSIONS:

4,0006,0008,000

10,00012,00014,00016,00018,00020,000

20 30 40 50 60 70 80

Pres

ent W

orth

Efficiency

800 gpm, Const., Qp/Qa=4

30

35

40

45

50

55

60

65

70

75

80

0 50 100 150 200 250 300 350 400

Effic

ienc

y, %

Flow, gpm

For Constant Head - 120 ft

Variable Speed

Cosntant Speed


Page-61

The experiment would include collecting data, including measuring the flow, pressure head, and power

draw. The flow will be measured in using different methods for high and low flows. A rotameter at higher

flow and a graduated cylinder and stopwatch at lower flow rates. The pressure will be measured at two

locations, one before the pump and one after, both at the same elevation. The power draw will be measured

using an amp-meter, which will be attached to the power cord.

1. Measure the pump head, speed, and power required for the pump running at full speed.

2. Use affinity laws, to predict the head and flow rate and Power at various pump speeds and compare

with the experimental values.

3. Calculate efficiency at various speeds.

4. Draw some pump characteristics curves.

• The following is a sample of the approximate results. For instance if the pump was running at 1560

rpm, and we resolve a flow of 15 gpm with a head of 20 ft and an amperage of 0.21 amp, the water

horsepower would be calculated as:

hp076.010058.4ftlb4.62ft20gpm15WHP 6

3 =××××=

• Electric horsepower would then be calculated as:

hp115.0whp00134.39.0volts220EHP =××=

• Then the efficiency would be calculated as follows:

%6666.0115.0076.0

===η


Page-62

EXPERIMENT # 9

BOUNDARY LAYER ON A FLAT PLATE

OBJECTIVE:

To measure the velocity profile in the boundary layer on flat plate and estimate the location of the transition.

APPARATUS:

The wind tunnel, Flat plate

INTRODUCTION:

“The boundary layer is the fluid layer near the surface of an object that has undergone a change in velocity

because of the shear stress at the surface. The general area of study of the flow pattern in the boundary

layer as well as the of the associated shear stress at the boundary, is called boundary layer theory” see

section 9.1, P 351 and figure 9.5 [5] Outside the boundary layer the velocity is the same as that of an ideal

fluid flowing past the object and the pressure is the free stream pressure. However, within the boundary

layer, the velocity and pressure differs from the free stream. The velocity at the plate is zero and the velocity

outside the boundary layer is the free stream velocity. Therefore, a velocity gradient develops on the flow

surface in the boundary layer. Also, because of viscous dissipation the total pressure pt, varies within the

boundary layer, while the static pressure, is approximately equal to the free stream pressure p∞. The

dynamic pressure q, is equal to p - p∞. At each location you are actually measuring the dynamic pressure,

q, from which the velocity of each station can be calculated. Hence, defining fully developed flow as a

point in the flow where the velocity is 99% of the free stream velocity, the point of transition from laminar

flow to turbulent flow can be found. It is therefore possible to determine this point of transition, by

comparing the velocity of a station with the free stream velocity. The boundary layer thickness at any point

is the height of that point from the surface.

Figure 1a. Boundary Layer Mouse, Front View – Sketch

The boundary layer mouse is often used to locate the point of transition between laminar and turbulent flow

in a boundary layer. It consists of a bank of several flat total head tubes arranged to read the total head at


Page-63

various heights from a surface. In this experiment the boundary later mouse is used to measure the total

head at the various heights. The static ring pressure corresponding to any wind speed is also recorded. Using

these data, the velocity profile and the point of transition could be found. Development of a laminar

boundary layer on any surface is depicted in the figure 2.

Figure 1b. Physical -Boundary Layer Mouse, Front View

Figure 1c. Boundary Layer Plate, Top View PROCEDURE:

Pressure Taps

Boundary Layer

Thickness

Air Flow

Bolted in the test section

Pressure Leads Pressure Taps

Plexiglass Flat Plate


Page-64

(i) Refer to appendix C to remove the balance, if it is mounted in the test section. Remove the top plate

of the test section.

(iii) Carefully insert the sensing hole leads through the rubber seal in the floor of the test section and then

insert the flat plate with the boundary layer mouse into the test section with the sensing holes facing

the honeycomb. Note that sensing holes of the mouse act as total pressure (pt) measuring probes.

Figure 2. Boundary Layer development on a surface

Figure 3. Boundary Layer thickness on a flat surface

(iv) The mouse has 10 sensing holes at heights, 0.018, 0.025, 0.030, 0.040, 0.060, 0.080, 0.100, 0.120,

0.160, and 0.200 inches from the plate. These are distance (y’s) from the plate surface.

(v) Connect the sensing holes of the mouse to the 24-input rotary dial. Record the distance from the

leading edge of the plate to the boundary layer mouse.

(vi) Check that the static pressure ring lead is connected to the transducer reference pressure center

connection.

(vii) Operate the tunnel at 10, 12, & 15 mph. Higher velocities will result in turbulent boundary layers

therefore sensing hole readings will be erroneous.

(viii) Record the pressures at each sensing hole.

(ix) Record the static ring pressure and the temperature of the air in the test section.

Separation Back flow near the WallAttached Boundary Layer

Separated flow

Large deflection of outer flow

Boundary Layer Thickness δ at different heights

Fully Developed

Flow

Free Stream Velocity V∞

Stagnation Point

Laminar Flow

Transition Flow

TurbulentFlow

Laminar Sublayer

Velocity V at any location

Distance from the leading edge ‘x’


Page-65

(x) Record the length of the plate from leading edge to the mouse. This is the value of “x” in equations 1

and 2 below.

RESULTS:

(1) Calculate the velocity of flow for each sensing location in the boundary layer (BL) mouse. This will

be calculated by the dynamic pressure recorded at each sensing hole.

(2) Then plot the velocity (V = ρ/q2 ) versus height and determine the boundary layer thickness,

δ, where the velocity reaches 99% of the free stream velocity V∞ shown in figure 3 and 5.

(3) The free stream velocity is calculated using static ring pressure q, which is equal to ½ ρV∞2

(4) Calculate the Local Reynolds Number Rex at each station (Rex = ρVx/µ), Determine the boundary

layer thickness at that point using BL theory given by

2/1xRex5

=δ for laminar flow (1)

and 7/1xRe

x16.0=δ , for turbulent flow (2)

Where x is distance from the leading edge of the plate.


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Figure 4- Von Karman Plot

Figure 5. Plot of Hole Height Vs Velocity of Flow

(5) Compare the experimental BL thickness with theoretical predictions. The results may not compare

well with the (y =δ) data supplied above in the procedure section item (iv) given in

(6) Estimate the point of transition and the corresponding Reynolds number

(7) Plot the velocity (in dimensionless form V/V∞) versus the height y as shown in the figures 3 and 5.

Using Excel fit curves to plotted data points and verify if they produce graph similar to the Von-

Karman plots shown in the figure 4. Assuming zero pressure gradient along the plate and uniform

external velocity, the shearing stress τo is given by the Von-Karman integral of the momentum

equation:

(8) Determine boundary layer thickness δ at 99 % of the free stream velocity above the surface, and

where the boundary is developed and flow is termed as fully developed flow.

το ≈ ∫ −ρ ∞

d

0dy))uu(u(

dxd

Approximate the derivative by taking the value of the integral (determined graphically) at

successive stations and dividing by the distance between the stations (check units). There is real

integration would be needed as the velocities are not given as functions but are constants. u and u∞

both are constants. Do this for the forward two stations and the last two stations. You can also plot

the data as shown in the figure 6; it will provide the boundary layer thickness at different locations.

Hole height

V(20mph)

Velocity


Page-67

Figure 6. Variation of Air Velocity vs. Hole Height


Page-68

EXPERIMENT # - 10

PRESSURE DISTRIBUTION OVER AN AIRFOIL

OBJECTIVE:

Measure the pressure distribution over a Clark Y-14 Airfoil at different angles of attack. From the

pressure distribution determine the Coefficient of Pressure (CP) Normal Force (lift), Axial force (pressure

drag), the lift and drag coefficients CL and CD.

APPARATUS:

The wind tunnel, Clark Y-14 Airfoil

INTRODUCTION:

Consider the forces acting on an airfoil as any fluid flows over it. The vector normal to the surface of the

airfoil is the normal force. It can be calculated by multiplying the measured pressure and the area of airfoil.

When the flow approaches the upper side of the airfoil, it is accelerated which decreases the pressure.

Consequently the velocity increases from stagnation to a velocity that may be greater than the free stream

velocity (in case of suction pressure). Therefore, the pressure over the top of the airfoil is negative, or less

than the free stream pressure. This follows from application of the Bernoulli equation. As the flow

approaches the lower side of the airfoil, it is decelerated; therefore, its velocity is less that the free stream

velocity. Thus, by applying Bernoulli’s equation it can be found that the pressure over the bottom of the

airfoil is greater than the free stream pressure. The positive pressure on the bottom and the negative pressure

on the top of the airfoil contribute to creation of lift. It is schematically shown in the figure 1.

Figure 1. Pressure and shear forces acting on the airfoil


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Figure 2. Airfoil Openings

The vectors parallel to the surface of the airfoil are shear stresses. These forces essentially are parallel to

the free stream direction. Thus, the shear stresses contribute to the drag on airfoil.

The pressure coefficient in the wind tunnel, Cp, may be defined as the ratio of pressure at any opening in

the airflow (∆p), divided by the dynamic pressure q of the air-stream. It is dimensionless pressure, defined

as ratio of pressure forces and inertia or momentum forces. In this case, the static ring pressure can be

considered as dynamic pressure q.

Cp= ∆pq =

p − p∞q

= pat any location of airfoil

psr

The Clark Y-14 airfoil model is equipped with 18 pressure-measuring openings. These openings are located

at 0, 7.5, 10, 20, 30, 40, 50, 60, and 70 % chord (airfoil length) on both the upper and lower surfaces. There

is also another opening at 80 % chord on the upper surface shown in the figure 2.

PROCEDURE:

(i) If needed remove the balance (refer appendix C for removing procedures).

(ii) Remove the top panel of the test section.

(iii) Trace the outline of the airfoil on a separate sheet on paper (if using alternate method).

(iv) Carefully insert the sensing hole leads through the rubber seal in the floor of the test section and then

mount the airfoil vertically in the test section using the mounting bolts. Do not over tight the bolts.

The mounting bolts are provided in the bottom as shown in the figure 3.

0 % Chord length

7.5 % 10 %

20 %

40 % 50 %

30 %

70 % 60 %

Airfoil Openings

80 %


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(v) The figure 4 depicts the airfoil dimensions and ∆x and ∆y are calculated using (the excel formula

sheet is provided on the web and can be downloaded).

Figure 3. Pressure and Shear Forces Acting on the Airfoil

Figure 4. Airfoil Dimensions See formula sheet on the web

(vi) Connect the sensing openings in sequence, to the 24-input rotary dial.

(vii) Check that the static pressure ring lead is connected to the transducer reference pressure connection

(normally it is connected).

(vii) Operate the tunnel at 60 mph. Record the pressures indicated at the 18 pressure openings at angles

of attacks of -3, 0, 3, and 5 degrees (for help, refer to appendix A)

(viii) Record the dynamic pressure q, of the air-stream from any unconnected input references (which is

Psr). The unconnected input nipples will register the difference between atmospheric and the test

section pressure, which can be taken as the dynamic pressure of the air-stream.

RESULTS:

Pressure Sensing Leads Connecting

to Rotary Gage

Numbered

Mounting Bolts

Airfoil Openings

Airfoil


Page-71

(1) Use the method suggested in the Handout to determine the Normal Force (lift), Axial force (pressure

drag), and coefficient of pressure. Plot the variation of Cp with X and Y-axis. Remember there are

many forms of drag such as skin or friction and form or pressure drag etc.)

(2) Determine the lift and drag coefficients. Discuss their significance. See text Chapter 11 for further

insight and info.

(3) Alternate method: Plot the pressure coefficient along a chord line and normal line according to the

sample graphs shown in the figure 5. The plot along the chord line is the plot against the percentage

of chord given in the manual. The normal line plot is plotting against the wing thickness. Use the

traced drawing of the airfoil and the bottom edge of the airfoil as the chord line to determine the

percentage of maximum height along the normal line where the wing thickness is the largest. Find

the normal and axial forces from the normal and chord line graphs. Use quadruple paper or any

approximate integral method such as Simpson's Rule.

Figure 5. Variation of Pressure Coefficient with Chord Length

0 1 2 3 4 5 6

7 8 9

10 11 12 13 14 15 16 17 3 1/2" Chord

Figure 6. Airfoil Crosssection

Test Section Air Speed ________

-0.80-0.60-0.40-0.200.000.200.400.600.801.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Cp vs x Series1

Series2


Page-72

Static Ring

Pressure___________

Length of Airfoil = 11.375"

1 inch of water = 0.03612 Psi

1. Plot Cp ∝ X and Cp ∝ Y

2. Determine Normal (Lift), and Axial (Pressure Drag) forces

3. Determine the coefficients of Lift (CL) and Drag (CD).

4. Determine the angle for stall. Note that the stall is a specific condition where CL decreases with the

increase in the angle of attack.

Station

No.

Percentage

of Chord

α1 =

Pressure

α2 =

Data

α3 =

α4 =

0 0

1 5

2 10

3 20

4 30

5 40

6 50

7 60

8 70

9 80

10 5

11 10

12 20

13 30

14 40

15 50

16 60

17 70


Page-73

Data on the Air foil Sample calculation of lift and drag forces and coefficients of lift, drag and pressure at zero angle of attack

1" of Water = 0.036 Psi Static Ring Pr ., Psr = 1.31 Length of the Air foil, L = 11.375 in. Wind Tunnel Speed = 80 Mph

Top of the

Air foil Station % of

Chord x in

∆x in

y in ∆y

Pressure in inch of H2O P

α1 = 0 α2 = 3 α3 =−3

Atop (in2) Locations

0 to 9

Top Forces

Abottom

Locations 10 to 17

Bottom Forces

Afront

Locations 0-5&10-13

Front Forces

Aback

Locations 5-9&13-

17

Back Forces

Cp = P/Psr

0 0 0.00 0.09 0.00 0.09 1.13 1.00 0.0406 1.07 0.0435 0.86

1 5 0.18 0.18 0.19 0.22 -0.19 1.99 -0.0137 2.49 -0.0171 -0.15

2 10 0.35 0.26 0.25 0.09 -0.53 2.99 -0.0572 1.07 -0.0205 -0.40

3 20 0.70 0.35 0.31 0.09 -0.79 3.98 -0.1136 1.07 -0.0305 -0.60

4 30 1.05 0.35 0.38 0.05 -0.64 3.98 -0.0920 0.53 -0.0122 -0.49

5 40 1.40 0.35 0.34 -0.04 -0.49 3.98 -0.0705 -0.49 0.0088 -0.37

6 50 1.75 0.35 0.32 -0.04 -0.45 3.98 -0.0647 -0.46 0.0075 -0.34

7 60 2.10 0.35 0.29 -0.06 -0.39 3.98 -0.0561 -0.69 0.0098 -0.30

8 70 2.45 0.35 0.23 -0.08 -0.31 3.98 -0.0446 ∆y * L -0.90 0.0101 -0.24

9 80 2.80 0.35 0.19 -0.04 0.00 3.98 0.0000 -0.43 0.0000 0.00

Bottom of the Air foil

10 5 0.18 0.09 -0.14 -0.07 -0.51 ∆x * L 1.00 -0.0183 0.78 -0.0145 -0.39

11 10 0.35 0.18 -0.13 0.01 -0.31 1.99 -0.0223 0.11 -0.0013 ∆y * L -0.24

12 20 0.70 0.35 -0.13 0.01 0.00 3.98 0.0000 0.07 0.0000 0.00

13 30 1.05 0.35 -0.13 0.00 0.09 3.98 0.0129 0.00 0.0000 0.07

14 40 1.40 0.35 -0.13 0.02 0.11 3.98 0.0158 0.18 0.0007 0.08

15 50 1.75 0.35 -0.09 0.05 0.13 3.98 0.0187 0.53 0.0025 0.10

16 60 2.10 0.35 -0.06 0.03 0.17 3.98 0.0244 0.36 0.0022 0.13

17 70 2.45 0.35 -0.06 0.03 0.21 3.98 0.0302 0.36 0.0027 0.16

ΣPtop* Atop

∆x * L

ΣPbot* Abot

ΣPfront* Afront

ΣPback* Aback

33.841 -0.472 26.873 0.061 6.694 -0.044 -1.064 0.035 Gives total Normal Force Gives total Axial Force

↑ ↑ ↑ ↑


Page-74

Aspect ratio of the airfoil =11.375/3.5 = 3.25

Ap = C*L = 3.5*11.375 = 39.81 in2 = Airfoil projected area Normal = ΣPbot*Abot - ΣPtop*Atop = 0.533 Lift for 0o attack angle Axial = ΣPfront*Afront - ΣPback*Aback = -0.079 Drag for 0o attack angle Clift = Lift/Psr*Apf = 0.282 * see figure 11.24 text Cdrag= Drag/Psr*Apf = -0.042 Bottom Top y Cp Cp x Cp -0.14 -0.3893

0.863 0.00 0.863 -0.13 -0.2366

-0.39 0.18 -0.145 -0.13 0 α =angle of attack -0.24 0.35 -0.405 -0.13 0.0687 0 0.70 -0.603 -0.13 0.08397 0.069 1.05 -0.489 -0.09 0.09924 0.084 1.40 -0.374 -0.06 0.12977 0.099 1.75 -0.344 -0.06 0.16031 0.13 2.10 -0.298 0.00 0.8626

0.16 2.45 -0.237 0.19 -0.145

2.80 0.000 0.19 0 0.23 -0.2366 0.25 -0.4046 0.29 -0.2977 0.31 -0.6031 0.32 -0.3435 0.34 -0.374 0.38 -0.4885 If Lift force < Drag force, this condition is called Stall and the object will crash, if such condition prevails during takeoff. If this happens during flying the object will begin to descend and if it is not corrected then the flying object will crash.

D = Drag Force= A cosα α

α Normal Force N

Axial Force A

L = Lift Force=N cosα

Fluid Mechanics Lab Manual/P. Kalim/Wilkes University-Division of Engineering & Physics-2011

Page-75

EXPERIMENT # - 11

WIND TUNNEL TESTS ON F-16 DELTA DART 1/72 SCALE MODEL

OBJECTIVE:

Determine CD and CL of F-106A Delta Dart airplane model.

APPARATUS:

The Wind Tunnel, 1/72 scale model of the F-16A Delta Dart.

AVAILABLE DATA:

The F-16A Delta Dart is built by the Convair Division of General Dynamics for the US Air Force. Relevant

properties: 38.3 ft. wing span, 70.8 ft. maximum length, 695 sq. ft wing area, 3600 lb. gross weight, Mach

2 class, powered by one P & W J75-P-17 with 24,500 lb. thrust at sea level. The model is exactly 1/72 scale.

INTRODUCTION:

A flowing fluid exerts both pressure and viscous forces on a body. The sum of the forces acting normal to

the free stream direction is the lift, while the sum of the forces acting parallel to the free stream direction is

the drag. Other forces, such as buoyant or gravitational forces, may act on the body. However, by definition,

lift and drag forces are limited to the forces produced by the dynamic action, or movement, of the fluid

itself.

Figure 1. Airfoil differential element

Consider the pressure and viscous forces acting on the differential airfoil element shown in the figure 1.

The pressure force has a magnitude of dFp = p dA, while the viscous force has a magnitude of dFν = τ dA.


Page-76

To define the lift and drag forces, the forces are separated into components that are normal and parallel to

the free stream direction.

So that the differential drag force is

dFD = -p dA cos θ + τ dA sin θ (1)

And the differential lift force is

dFL = -p dA sin θ − τ dA cos θ (2)

The total drag and lift forces can be found by integrating the differential forces over the entire surface of

the airfoil:

FD = ∫ (-p cos θ + τ sin θ) dA (3)

FL = ∫ (-p sin θ − τ cos θ) dA (4)

Performing the integration and applying the equations to the wind tunnel, equations3 and 4 become:

D = A cos α + N sin α (5)

L = N cos α − A sin α (6)

Where D and L are the lift and drag forces, respectively, N and A are the normal and axial force,

respectively, and α is the angle of attack. It is often convenient to use the dimensionless parameters CD,

coefficient of drag, and CL, coefficient of lift, instead of the total forces.

CD = 2

∞ρ V S

D

21 (7)

Where CD is the coefficient of drag, D is the drag force, S is the wing area, ρ is the fluid density, and V∞

is the free stream velocity. This equation could be analogously applied to calculate the lift coefficient as

CL =2

∞ρ V S

L

21 (8)

Dimensionless parameters are also used with pitching and yawing moments. The dimensionless parameter

for pitching moment, Cm, is found by

Cm = 2

∞ρ V c S

M

21

p (9)


Page-77

Where, Cm is the dimensionless coefficient, Mp is the pitching moment, and c is the chord length.

Figure 2. The Balance

Figure 3. The Model Plane Mounted on the Balance in the Test Section

PROCEDURE:

(i) Install the balance as shown in the figure 2. You must refer appendix C before installation of the

balance. The balance is the most fragile part of the system and it will not withstand large forces and

moments or tension either on the balance or on the wiring cable.

(ii) Zero the pressure and airspeed indicators, Refer appendix A

(iii) Zero the force components and angle of attack indicators, Refer appendix B

(iv) Turn the pin located at the rear of the balance in the clockwise direction, so that it points away from

the instrument panel side of the tunnel and tighten the screw located on the back as shown in figure

2.

Balance

Pin

Screw Location

Wires leading to data acquisition System

Strut Tightening Screws to Mount the Balance

Struts

Back Screw

Tightening Screw

Struts


Page-78

(v) Install the Delta Dart model on the balance with collar, in the wind tunnel test section so that the

wingspan is parallel to the floor of the test section and tighten the setscrew located on the upper side

of the model as shown in the figure 3.

(vi) To correct for model weight, record the normal and axial forces, and the pitching moment at 2°

intervals from α = - 4° to 16° with the fan off.

(vii) Refer to appendix A and operate the tunnel at 130 mph.

(viii) Record the normal and axial forces, and the pitching moment at 2° intervals from α = -4° -16°.

Continue pitching model until stall occurs (stall occurs when the lift force is zero or less than the drag

force). Record the airspeed at stall.

RESULTS:

(1) Calculate drag coefficient (CD), lift coefficient (CL), Pitching Moment Coefficient (Cm), using

equations 7, 8, and 9, respectively.

(2) Determine the minimum landing speed of the model. The minimum landing speed of an airplane is

the speed at which the plane stalls. The plane stalls when lift force is zero or less than the drag force.

Find that position by pitching the plane for different angle of attack.

Note: Consider flow of an ideal (non-viscous) fluid over an airfoil. Since the flow is irrotational, the lift and

drag are zero. There are two stagnation points; one on the bottom side near the leading edge, and another

on the topside near the trailing edge. However, this case cannot exist for a non-ideal (real) fluid. The

stagnation point on the upper side near the trailing edge indicates that the fluid must flow from the lower

side around the trailing edge towards the stagnation point. This is impossible since separation occurs at a

sharp edge, in this case the trailing edge of the foil. Because of separation, the stagnation point is moved

further towards trailing edge. This is called the Kutta condition.


Page-79

EXPERIMENT # - 12

UAV TESTING

Objective: Test the UAV as provided. To install the sting Balance see Appendix C.

Sting Balance


Page-80

EXPERIMENT # - 13

DEVELOP OPERATIONAL CHARACTERISTICS OF A CENTRIFUGAL PUMP

OBJECTIVE:

Study variation of pump characteristics such as head (hp), power input (Pin), Overall efficiency (ηo) with

the discharge (Q). The objective of this experiment is to understand the basic operation and characteristics

of a centrifugal pump. There are several major topics that will be looked at in order to better understand

centrifugal pumps:

A comparison of various flow rate measuring devices

The efficiency of the pump

Creating various pump curves consisting of flow rate, pressure head, and efficiency

Comparing operation of both pumps in series or parallel configurations

Verifying the “pump relations” for a constant impeller diameter pump at several rpm values

APPARATUS:

Centrifugal pump, Hydraulic Bench and delivery pipes

INTRODUCTION and THEORY:

The H35 Centrifugal Pump Test Rig Consists primarily of a centrifugal pump, hydraulic bench

and delivery pipes. The centrifugal pump is a type of rotodynamic machinery which creates

hydraulic energy via the rotary motion of its impeller which is run at a constant RPM. Through

this rotary motion the impeller induces an additional centrifugal head which increases both the

kinetic and pressure energy of the fluid.

Centrifugal pumps are very quiet in comparison to other pumps. They have a relatively low operating and

maintenance costs. Centrifugal pumps take up little floor space and create a uniform, non-pulsating flow.

Pumps are used in almost all aspects of industry and engineering from feeds to reactors or distillation

columns in chemical engineering to pumping storm water in civil and environmental. They are an integral

part of engineering knowledge and an understanding of how they work is important for all engineers. The

volute chamber has a uniformly increasing area. This increasing area decreases the fluids velocity, which

converts the velocity energy into pressure energy. The heart of the pump is the impeller, or impellers in

the case of multistage pump. The impeller is fastened to the shaft, which transmits energy to the pump. It


Page-81

is surrounded by a casing, which contains the suction and discharge nozzles. The fluid flows

from the suction nozzle to the eye of the impeller.

The impeller vanes impart velocity or kinetic energy to the fluid. This high velocity fluid is then

captured by the pump casing, which turns high velocity to pressure as it guides the fluid through

the discharge nozzle. All attachments are sealed to prevent any fluid or pressure leakage. Two

characteristics a pump produces are pressure head and volumetric flow.

Figure 1. Engineering Sketch of a Centrifugal Pump

Figure 2- Centrifugal Pump – Cutout Figure 3-Impellers: (a) open, (b) semi-open, and (c) closed

A pump is a device, which converts any other form of energy into hydraulic energy. Centrifugal pump is a

type of Rotodynamic machinery, which is characterized by the rotary motion of the impeller, run at a

constant RPM. This rotary motion of impeller induces an additional centrifugal head on the fluid, thereby

increasing both its kinetic energy and pressure energy. A cutout view of a single stage centrifugal pump is

shown in the figure 2. Different types of impellers are shown in the figures 3a, b and c below.

In figure 1, Fluid enters the inlet duct (D). As the shaft (A) rotates, the impeller (B), which is connected to

the shaft, also rotates. The impeller consists of a number of blades that project the fluid outward when

rotating. This centrifugal force gives the fluid a high velocity. Next, the moving fluid passes through the


Page-82

pump case (C) and then into the volute (E). The volute chamber has a uniformly increasing area. This

increasing area decreases the fluids velocity, which converts the velocity energy into pressure energy.

Two characteristics a pump produces are pressure head and volumetric flow. The pressure head created

from the pump is:

H = Hd – Hs (1)

Where Hd is the discharge pressure head and Hs is the suction head. Head is measured in units of length.

Due to the fact that head is a way of denoting pressure, it can be easily determined using a pressure gauge,

as long as the pressure taps are located at the pump suction and discharge ports. Pumps also deliver a

certain capacity (Q) that is also known as a volumetric flow rate.

Efficiency

The power to drive the pump is always greater than the output power of the fluid being pumped. The

power is usually lost due to hydraulic losses, volumetric losses, and mechanical losses2. Efficiency is a

comparison (ratio) between the power coming out of the system and that put into the system. When the

efficiency is high, the system is minimizing those losses.

There are two types of power transformations that occur in this experiment [15]:

• Electrical power, which is transferred into mechanical power via the pump motor, and

• Mechanical power, that rotates the shaft, turns the impeller, and transfers power to the fluid. For

each transition of power there is efficiency, including an overall efficiency.

•

The following diagram shows the power distribution and the related efficiency.

Electrical Power Mechanical Power Output Power

Shaft Efficiency Thermodynamic Efficiency

Overall Pump Efficiency


Page-83

Figure 4a, b. Component parts of a Centrifugal Pump

The electrical power is the power needed to run the pump. This is calculated by multiplying the input

current times the input voltage.

Power electrical = I V (2)

Where Powerelectrical is in Watts, V is Voltage , and I is the Current in Amperes

Powermechanical = 2 π N T/60 (3)

This is given in the experiment

Powermechanical is in Watts, N = Speed [rpm’s], T = Torque [N*m]

The fluid output power of the pump is combination of the flow rate and the pressure head created by the

pump. This is the primary function of the pump. The equation for the fluid output power is:

Powerfluid = g Q h ρ water (4)

Where: g = 9.81 m/s2, Q = Flow quantity [m3/s], h =Pressure head [m], ρwater = density of water

Therefore the maximum power required to drive the pump will occur as the flow quantity approached

Qmax. The efficiency of the pump is the ratio of the output power to the input power of the pump. The

three types of efficiencies for each power transition for the overall centrifugal pump system are as

follows.

Shaft efficiency:

Casing (C)

Impeller

Shaft (A)

Suction (D)

outlet or discharge nozzle

Impeller Eye

Volute or Diffuser (E)


Page-84

ηshaft = (Power mechanical/Power electrical)*100 % (5)

Thermodynamic efficiency :

ηthermodynamic = (Power fluid/Power mechanical)⋅ ∗100% (6)

Overall efficiency :

ηoverall = (Power fluid/Power electrical)⋅ ∗100% (7)

A centrifugal pump is designed for maximum overall efficiency (ηo), corresponding to the efficiency (ηo),

the design discharge (Q), maximum power input required (P) and maximum design head (H). But during

actual operation of the pump, it is not necessary that it be always at the design values. In fact, frequently

the centrifugal pump gets operated at different discharges than the design discharge. Hence the operating

curves of a centrifugal pump show graphically behavior and performance of the pump under various

conditions of operation for a constant rpm of the impeller. These curves in the non-dimensional form help

to predict the pump performance when run at any other discharge, than the design discharge.

The centrifugal pump is one of the most widely used pumps for transferring liquids. The basic components

of a centrifugal pump are depicted in the figure 1 and 2. The principle operation of a centrifugal pump is to

convert fluid velocity into pressure energy. The pump consists of three components, an inlet duct, an

impeller, and a volute. Fluid enters the inlet duct (D). As the shaft (A) rotates, the impeller (B), which is

connected to the shaft, also rotates. The impeller consists of a number of blades that project the fluid outward

when rotating. This centrifugal force gives the fluid a high velocity. Next, the moving fluid passes through

the pump case (C) and then into the volute (E). Sample characteristics curve for a centrifugal pump is shown

in the figure 5.

Figure 5- Centrifugal Pump Characteristics Curves


Page-85

Once the pump is primed I suggest that a set of six tests should be run to find six different flow rates,

three at 2000 rev/sec and three at 1500 rev/sec. (NOTE: these speeds seem to produce the most

consistent data.) This should produce six sets of values for six separate flow rates, from which, a

characteristic curve for both motor speeds can then be generated. (NOTE: for the purposes of my

experiment I ran a total of 18 tests, 3 for each flow rate, so that I could generate an average. When the

students run the experiment, 6 tests should be sufficient, but if time permits they should repeat my full

procedure to ensure accuracy.)

First turn on the test set via the switch on the back of the console. The volumetric bench does not need

to be turned on for the experiment. (NOTE: The switch which turns on the wind tunnel also turns on this

pump.) Next ensure that both the inlet and outlet valves are fully open and the volumetric bench is

empty prior to starting the pump. Now, two steps need to be preformed simultaneously; the pump

speed needs to be turned up to the desired speed, say 2000 rev/sec, and the volume gauge needs to be

watched to judge when to begin timing. The timing should begin once water begins to fill the guage at

the zero level, NOT as soon as the pump is turned on, as it takes time for water to flow through the

pump and pipes. Once timing begins allow the tank to fill to the 35 lt mark. Now the water may shoot

up fast at first but it will level out so only stop timing once the water remains consist at the 35 lt mark.

(NOTE: This may be hard to judge at first so the test may need to be run once or twice to ensure

accurate readings are taken, this is where an averaging may be necessary.) While one student takes the

time to fill the tank another should be taking the values for torque, inlet and outlet pressures. When the

bench is filled turn the pump speed down to zero and proceed to empty the tank by lifting the gray

drainage tube.

Now adjust the pump outlet valve to a slightly more closed position to vary the flow rate. (NOTE: Make

sure the valve is not fully closed, this will damage the pump.) By taking values for different flow rates a

characteristic curve can then be generated for this pre-determined motor speed. Run the test again for

this new flow rate, recording the time taken to fill the tank to 35 liters mark, the motor torque, and the

inlet and outlet pressures. A total of at least three flow rates should be found for each motor speed.

Tables 1 and 2 list the values taken from the pump test set, and the calculated flow rates for each test.

The flow rates were calculated by simply dividing the total liters collected by the time taken to collect

that volume.


Page-86

Figure 7. Centrifugal Pump and the hydraulic Bench Setup

𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 = 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝐶𝐶𝐶𝐶𝑉𝑉𝐶𝐶

𝑇𝑇𝑇𝑇𝑉𝑉𝑉𝑉 𝑅𝑅𝑉𝑉𝐶𝐶𝑉𝑉𝑅𝑅𝐶𝐶𝑉𝑉𝐶𝐶= 35𝑉𝑉𝐶𝐶

16.50𝑠𝑠𝑉𝑉𝐶𝐶= 2.12 𝑉𝑉𝐶𝐶

𝑠𝑠𝑉𝑉𝐶𝐶 =0.00212 m3/sec

(1)

Table 1: Recorded Values from Bench for 2000 rev/sec

Motor Speed: 2000 (rev/sec)

FlowRate (lt/sec)

Average FlowRate

(lt/sec)

Time (sec)

Torque (N-m)

Suction Pressure

(bar)

Delivery Pressure

(bar)

2.12 2.00

16.50 0.48 -0.90 0.05 1.94 18.00 0.53 -1.02 0.05 1.93 18.10 0.54 -1.02 0.05 1.68

1.67 20.80 0.53 -1.00 0.10

1.68 20.80 0.52 -1.10 0.10 1.65 21.20 0.52 -1.10 0.09 0.73

0.72 47.80 0.42 -0.40 0.40

0.72 48.30 0.41 -0.50 0.39 0.71 49.40 0.41 -0.40 0.39

Discharge Pressure

Power Inlet Pressure


Page-87

Table 2: Recorded Values from Bench for 1500 rev/sec


FlowRate (lt/sec)

Average FlowRate

(lt/sec)

Time (sec)

Torque (N-m)

Suction Pressure

(bar)

Delivery Pressure

(bar)

1.02 1.04

34.30 0.30 -0.09 0.05 1.05 33.20 0.28 -0.09 0.04 1.04 33.50 0.29 -0.08 0.05 0.94

0.92 37.40 0.28 -0.09 0.08

0.92 38.20 0.27 -0.08 0.09 0.91 38.40 0.27 -0.09 0.09 0.70

0.70 50.20 0.24 -0.03 1.60

0.71 49.40 0.25 -0.03 1.70 0.70 50.00 0.25 -0.03 1.60

Results: Using the data collected from the pump test rig, various pump characteristics can be determined,

including the fluid power, shaft efficiency, thermodynamic efficiency and overall efficiency. Also,

several affinity relations can be verified, such as flow rate, head loss and power output. From these we

can illustrate a characteristic curve for the pump.

First, the mechanical power of the pump must be determined using equation 1, where (N) is the motor

speed and (T) is the torque.

𝑃𝑃𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑉𝑉𝑉𝑉𝐶𝐶ℎ𝑎𝑎𝑎𝑎𝑇𝑇𝐶𝐶𝑎𝑎𝑉𝑉 = 2 ∙ 𝜋𝜋 ∙ 𝑁𝑁 ∙ 𝑇𝑇60

= 2 ∙ 3.14 ∙ 2000 ∙ .4860

= 100.48 Watts (1)

With (Q), the volumetric flow rate, the fluid power can then be found knowing (g) to be the gravitational

constant, 9.81 m/s2, (h) the pressure head which is the difference between delivery pressure and suction

pressure, (NOTE: watch your sign convention, in this case we have [Delivery Pressure – Suction

Pressure]), and ρ is the density of water, taken to be 990 kg/m3.

𝑃𝑃𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑓𝑓𝑉𝑉𝑉𝑉𝑇𝑇𝐶𝐶 = 𝑔𝑔 ∙ 𝑄𝑄 ∙ ℎ ∙ 𝜌𝜌𝑤𝑤𝑎𝑎𝐶𝐶𝑉𝑉𝑅𝑅 = (9.81 ∙ 2.12 ∙ 0.95 ∙ 990)/1000 = 19.57095 watts (2)


Page-88

With the values for both mechanical and fluid power, and the estimated electrical power of 500 and 375

watts for motor speeds of 2000 rev/sec and 1500 rev/sec respectively, (P=VI, V=220; I=2.27), various

efficiency characteristics are found, shown in equations 3 through 5.

Note: Use ohm/amp reader to determine the electrical power provided to the pump for each test.

These calculated values for pressure head and power can be found in tables 3 and 4.

Table 3: Calculated values for 2000 (rev/sec) Motor Speed: 2000 (rev/sec)

Average FlowRate

(lt/sec)

Pressure Head (bar)

Average Pressure

Head (bar)

Power Electrical (Watts)

Power Mechanical

(Watts)

Average Power

Mechanical (Watts)

Power Fluid

(Watts)

Average Power Fluid

(Watts)

Table 4: Calculated values for 1500 (rev/sec)


Average FlowRate

(lt/sec)

Pressure Head (bar)

Average Pressure

Head (bar)

Power Electrical (Watts)

Power Mechanical

(Watts)

Average Power

Mechanical (Watts)

Power Fluid

(Watts)

Average Power Fluid

(Watts)

Now with the calculated powers, various efficiencies of the pump can be determined, as shown in equations 3, 4 and 5.

1. The following affinity relations can be found in most references and books on centrifugal pumps.

They are valid for the same pump at various rpm values. Verify these relations and substantiate their

basis in theory.

Flow Rate 𝑄𝑄2𝑄𝑄1

= �𝑁𝑁2𝑁𝑁1�, Capacity varies directly as the speed ratio

Head/Pressure Drop across pump 𝐻𝐻2𝐻𝐻1

= �𝑁𝑁2𝑁𝑁1�2, Head varies as the squrare of the speed ratio

Power 𝐻𝐻𝐻𝐻2𝐻𝐻𝐻𝐻1

= �𝑁𝑁2𝑁𝑁1�3, HP varies as the cube of the speed ratio


Page-89

2. Draw the characteristics curves of flow rate vs. head, then compare with the curves given in figure 6.

Figure 6. Characteristics Curve Shaft efficiency:

ηshaft= �𝐻𝐻𝑉𝑉𝑤𝑤𝑉𝑉𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚𝑎𝑎𝑎𝑎𝐻𝐻𝑉𝑉𝑤𝑤𝑉𝑉𝑅𝑅𝑚𝑚𝑎𝑎𝑚𝑚𝑚𝑚𝑒𝑒𝑒𝑒𝑎𝑎𝑚𝑚𝑎𝑎𝑎𝑎

� ∙ 100% = ��108.16500

� ∙ 100� = 21.62% (3) Thermodynamic efficiency:

ηthermodynamic= � 𝐻𝐻𝑉𝑉𝑤𝑤𝑉𝑉𝑅𝑅𝑓𝑓𝑎𝑎𝑓𝑓𝑎𝑎𝑓𝑓

𝐻𝐻𝑉𝑉𝑤𝑤𝑉𝑉𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚𝑎𝑎𝑎𝑎� ∙ 100% = ��19.95720

108.16� ∙ 100%� = 18.45231% (4)

Overall efficiency:

ηoverall= � 𝐻𝐻𝑉𝑉𝑤𝑤𝑉𝑉𝑅𝑅𝑓𝑓𝑎𝑎𝑓𝑓𝑎𝑎𝑓𝑓

𝐻𝐻𝑉𝑉𝑤𝑤𝑉𝑉𝑅𝑅𝑚𝑚𝑎𝑎𝑚𝑚𝑚𝑚𝑒𝑒𝑒𝑒𝑎𝑎𝑚𝑚𝑎𝑎𝑎𝑎� ∙ 100% = ��19.95720

100� ∙ 100� = 39.9144% (5)

Tables 5 and 6 lists the values computed for both motor speeds.

Table 5: Various Efficiencies According to Varied Flow Rates for 2000 (rev/sec) Motor Speed: 2000 (rev/sec)

Average Flow Rate (lt/sec)

Shaft Efficiency

Thermo Efficiency

Overall Efficiency

2.00 21.63 18.4 39.9

Table 6: Pump Efficiencies

Motor Speed: 1500 (rev/sec) Average FlowRate (lt/sec)

Shaft Efficiency

Thermo Efficiency

Overall Efficiency


Page-90

Lastly, using the values obtained throughout the lab the affinity relations can be verified for the pump, as shown in equations 6 through 8, where (Q) is the volumetric flow rate, (N) is the motor speed, and (HP) is the horse power. *Note: 1 horsepower = 745.699872 watts

Flow Rate: 𝑄𝑄2𝑄𝑄1

= �𝑁𝑁2𝑁𝑁1�

2.001.04

≠ �20001500

� Almost equal Pump Head

𝐻𝐻2𝐻𝐻1

= �𝑁𝑁2𝑁𝑁1�2

0.131.03

≠ �15002000

�2

Power:

𝐻𝐻𝑃𝑃2𝐻𝐻𝑃𝑃1

= �𝑁𝑁2𝑁𝑁1�3

1.8126.76

≠ �15002000

�3

RESULTS: 3. Calculate Powerfluid, PowerMechanical, Shaft efficiency, and Overall efficiency.

4. Use either an ohm reader or consult factory specifications for the electrical power supplied to

the pump.

CONCLUSION:

1. Calculate Powerfluid , Shaft efficiency, Thermodynamic efficiency, and Overall efficiency.

2. The following affinity relations can be found in most references and books [3, 4, 7, 8, 11, 12-

15] on centrifugal pumps. They are valid for the same pump at various rpm values. Verify

these relations and substantiate their basis in theory?

Flow rate

=

1

2

1

2NN

QQ , Capacity varies directly as the speed ratio

Head/Pressure Drop across Pump 2

1

2

1

2NN

HH

= , Head varies as the square of the speed

ratio


Page-91

Power HPHP

NN

2

1

2

1

3

=

, HP varies as the cube of the speed ratio.

3. Draw the characteristics curves.

References:

1. Dr. Kalim, S. Perwez. Fluid Laboratory (ME323) Manual, Fall 2009 2. H35/36 Centrifugal Pump Test Rigs. Tecquipment Limited, Bonsall Street, Long Eaton,

Nottingham, NG10 2AN, England


Page-92

EXPERIMENT # 14

CALIBRATION OF YAW PROBE

OBJECTIVE:

Calibrate a cylindrical yaw probe to measure fluid free stream velocity.

APPARATUS:

Wind tunnel, cylindrical yaw probe, Bubble handheld protractor

INTRODUCTION:

Yaw head shown in the figure 1 (a) and (b) is used to measure fluid stream velocity. The cylindrical yaw

probe has three orifices, or pressure sensing holes, at the tip. It has a center orifice, an orifice at −45 degree

from the center, and another orifice at 45 from the center as shown in the figure 2. The center sensing orifice

reads total head. The two outer sensing orifices read static pressures. If the flow is directed along the yaw

axis and the two outer holes are placed, at equal angles, the two outer orifices will read equal pressures.

Thus, difference in pressures between these two outer orifices will be zero. But there will be a difference

in the pressures between center sensing orifice and one of the outer sensing orifices. It will give a different

value of ∆p for each degree the flow is off center. In other words, ∆p will be a function of angle α. ∆p can

be expressed non-dimensionally by dividing it by the dynamic pressure, q = ½ρV2. Thus, rotating the yaw

head at a single location in the air stream different qp∆ can be calculated at different angle of attack α.

Plotting qp∆ against the angle of attack α is used to calibrate the yaw head.

PROCEDURE:

(i) Insert the yaw head into one of the threaded openings so that the sensing holes are in the center of the

test section, and so that the center hole of the yaw head is directed along the axis of air flow so that

the other sensing holes will be oriented at + 45 and -45 degrees to the center hole. This will be the

erect position.

(ii) Connect the two pressure measuring leads from the +45 and -45 degree holes to the 24-input rotary

dial pressure system. These +45 and -45 degree holes shown in the figure Operate the tunnel at 80

mph. Record the static ring pressure. The static ring pressure may be considered as dynamic pressure.

Record the center hole pressure. It should be close to static ring pressure.


Page-93

(iii) Rotate the yaw head at 2 degrees increments to +10 degrees angle of attack and record the pressures

from the other two sensing holes each time. The difference between two pressures is ∆p.

Figure 1 (a) Yaw Probe

Pressure Lead Connections

Pressure Sensing holes

Center Orifice

Figure 1 (b) Yaw Probe - Sketch

Figure 2. Yaw head – Magnified

Pressure Leads or Connections from two Pressure Sensing holes Located at +45 and –45 Degrees

+45 and –45 degrees Pressure Leads that Connects to the Rotary Dial.

Threaded Fitting Mounted in the Test Section

Pressure Sensing holes

Pressure Sensing holes at – 45o

Pressure Sensing holes at 0o

Pressure Sensing holes at + 45o

Yaw Head


Page-94

(iv) Repeat the process in the negative direction in -2 degrees decrements from the horizontal to -10

degrees angle of attack.

(v) Insert the yaw head into the threaded opening of the test section on the other side. This process is

termed as the inverted position of the yaw head. Repeat the procedure for the inverted position.

RESULTS:

(1) From the central pressure tap data of the yaw head, determine and verify the velocity of airflow.

(2) Assume that dynamic pressure q is equal to the static ring pressure. Then using the pressure data from

two 45 degrees aligned holes of the yaw head, evaluate ∆p/q (the pressure difference between the two

outer sensing holes divided by the dynamic pressure q) at each angle α. Then plot the coefficient of

pressure Cp = q/p∆ versus the angle of attack α. A sample graph is depicted in the figure 3. Plot both

erect and inverted positions on the same graph and scale.

(3) Determine the instrument error. It is determined where the erect position plot crosses the inverted

position plot, as shown in the sample graphs.

(4) Find the calibration factor k = α

∆d

)q/p(dtaken near zero alpha. What do you conclude with the

calibration factor for erect and inverted positions? The k is found by determining the slope of the curves

in both positions.

(5) Optional: Determine the air stream inclination. It is determined from the readings obtained in the erect

and inverted position readings (qp∆

) at α = 0°. The minimum difference between two readings shows

air stream inclination.

Figure 3. Variation of Cp vs. the Angle of Attack


Page-95

EXPERIMENT # 15

VISCOCITY EXPERIMENT

OBJECTIVE:

Determine and compare the SAE 30 Oil viscosity at different temperatures.

INTRODUCTION

An applied shearing force which produces flow in a fluid is resisted by a force proportional to the gradient

of the flow velocity. The proportionality constant is known as viscosity. The flow of a fluid is said to be

"laminar", if points in the fluid move smoothly in layers. When one layer flows past another, an internal

viscous force is produced that slows down the faster layer and speeds up the slower one. To overcome

this drag and maintain a constant velocity gradient between layers, an external force must be exerted.

Newton deduced a relationship between the velocity gradient (du/dx) and the shearing force (F) which

produces it. If (A) is the area of contact between the moving layers of fluid, the Newton's Law of

Viscosity is,

F = μ A du/dx

where the factor of proportionality "μ" is called the viscosity of the fluid.

Viscosity of a fluid depends on temperature, pressure and composition. A fluid is said to be a Newtonian

fluid if, in laminar flow, μ is an independent of the velocity gradient (Shomaker, 1974). There are several

experimental methods for the determination of the viscosity of fluids. The methods used are: 1. Flow

through the capillary tubes 2. Fall of solid spheres through fluids 3. Torque or viscous drag on a rotating

disk or cylinder immersed in the fluid 4. Flow of fluids through an aperture in a plate

Capillary-Flow Method

The Ostwald-Fenske method makes use of the Hagen-Poiseuille equation for the determination of liquid

viscosities by measuring the time of flow of a given volume liquid through a vertical capillary tube under

the influence of gravity. For a virtually incompressible fluid this flow is governed by the Poiseuille's Law

in the form of (Moore 1962) dV/dt = (π r4 Δ P) / (8 μ L) (1.1)

where (dV/dt) is the rate of liquid flow through a cylindrical tube of radius ‘r’ and length ‘L’, and ΔP is

the pressure difference between two ends of the tube, when ΔP is constant the equation (1.1) becomes


Page-96

μ = (π r4 ΔP) t

8VL

(1.2)

where ‘t’ is the time required for the liquid to fall from the upper to the lower level, V is the volume of

liquid flowing out of the cylindrical tube (constant in this case), ΔP = ρ g h, ‘ρ’ being the density and ‘h’

is the height of the tube as shown in the figure below. Thus, equation (1.2) can be written with some

simplifying assumptions as

μ = π r4ρ g t8V

(1.3)

Procedure

1. Determine the radius r and height h of the copper tube from top to bottom.

2. Determine the volume of the liquid that would fill the copper tube.

3. Record the fluid temperature.

4. Find time that would be needed to drop this fixed volume of liquid from

the tube into the beaker below by opening the valve slightly.

5. Find the viscosity of the fluid from equation 1.3.

6. Repeat the procedure at three different temperatures.

Results:

1. Plot the variation of viscosity with temperature.

2. Compare your data with theoretical data available in text books or on web.

3. Verify the unit of viscosity in equation 1.3.

h


Page-97

EXPERIMENT 16

DEMONSTRATION OF

REYNOLDS NUMBER AND TRANSITIONAL FLOW OBJECTIVE:

Demonstrate how the conditions in a pipe vary with flow velocity and that the changes occur over a range

of velocities and therefore changing the Reynolds number.

INTRODUCTION:

The TecQuipment H215 Reynolds number and Transitional Flow Demonstration Apparatus™

demonstrate the dependence of the flow rate on the Reynolds number. The apparatus enables the nature of

the flow in a pipe to be studied by observing the behavior of a dye injected into a tube with water flowing

through it. This enables the observer to see the type of flow (Laminar, Transitional and Turbulent) that is

present in the tube. Figure .1 shows the differences in the dye that can be seen in the tube.

Figure. 1. Laminar, Transitional and Turbulent flow

Reynolds was the first to determine the values of non-dimensional number that can predict that nature of

the flow. He postulated that the nature of the flow depended on the ratio of inertia forces (related to

turbulent flow) and viscous forces (laminar flow). This dimensionless number is known as the Reynolds

number,

Re=µ

ρDV (1)


Page-98

Figure 2. Reynolds Experiment - Demonstration Unit.

Where ρ is equal to the density of the fluid, D is equal to the diameter, μ is a constant for a given fluid at a

given temperature, and V is the velocity of the fluid in the pipe. The term ρ/μ is known as the Kinematic

Viscosity v and it is more convenient to write Re as:

Re=ν

DV (2)

The important discovery made by Reynolds was that the transition of a flow from laminar to transitional

to turbulent and vice versa always happens at particularly the same value of Re regardless of the fluid or

the size of the pipe.

The figure 2 depicts the apparatus details. This apparatus consists of a precision bore of 12mm internal

diameter glass tube, which is supported in a large shroud of rust proof material. This shroud is open at the

front and the inside surface is a light color to assist in the visualization of the flow. At the top of the

shroud is a large tank from which there is a constant supply of water for the specially shaped bell

mouthed shroud entry. Water is supplied to the tank through a diffuser and a region of glass beads that

provides a uniform flow of water to all sides of the bell mouth. The supply to the tank is at the rear of the

Dye injector

Dye

Thermo-meter

Bell-mouth entry

Water Supply

Constant Head Tank

Overflow Pipe

Overflow to Drain

Discharge Control Valve to

Drain

Glass Test Pipe


Page-99

apparatus and is connected to the hydraulic bench. A fixed over flow pipe is also fitted to the tank to

ensure a steady and constant supply of water for the glass shroud. The flow through the glass tube is

controlled by a valve at the bottom of the apparatus, which leads to another tube, which is used for the

measurement of the flow rate for each of the different conditions that are achieved in the apparatus. It is

important to note that the water level in the constant head tank must always be above the overflow pipe to

ensure a constant fluid flow. The behavior of the flow can clearly be seen by the dye injection apparatus,

which can be found on the top of the apparatus. This apparatus supplies a constant stream of water-

soluble dye that shows the observer the type of flow that is experienced.

PROCEDURE:

1. Partially open the valve at the bottom of the glass shroud assembly and then turn the hydraulic

bench to give a small amount of flow to the apparatus (Make sure that the flow rate coming from

the bench is small enough so that the diffuser and bed of glass beads are not greatly disturbed by

the sudden rush of water. The flow rate from the bench my be adjusted by using the valve knob

found on the upper right of the bench.)

2. Adjust the water supply until the level in the constant head tank is just above the overflow pipe

and is maintained at this level by a small flow down the overflow pipe. This condition is required

for all tests and at different flow rates through the tube; the supply will need to be adjusted to

maintain it. At any given condition the overflow should only be just sufficient to maintain a

constant head in the tank.

3. Open and adjust the dye injector valve to obtain a fine filament of dye in the flow down the glass

tube. If the dye is dispersed in the tube, meaning that the dye is sprayed and covers the whole

tube, reduce the flow rate in the tube by closing the valve slightly at the bottom of the apparatus.

The flow rate must also be adjusted at the bench so a constant head is always present in the tank.

A laminar flow condition should be achieved in which the filament of dye passes the complete

length of the tube without disturbance.

4. When this is achieved, record the flow rate by timing the discharge of water in the 1000 ml

cylinder through the outlet that is found on the back bottom of the apparatus. The bench should

not be used to collect the water and measure the flow rate because that water that exits the

apparatus has dye in it and will turn the water in the bench black. The water should be collected


Page-100

in a large bucket and drained in the sink and new water added to the bench so that the bench does

not run out of water.

5. Slowly increase the flow rate by opening the valve found at the bottom of the apparatus and

repeat step four.

6. Repeat steps 4 and 5 until all three conditions of flow can be seen.

RESULTS:

Table – 1. Experimental data and calculated results Time -

Sec

Amount - kg u - m/sec v*10^6 Re Condition

13.68 175 0.113167 1.06 1281.136 Laminar

23.38 410 0.155134 1.06 1756.235 Laminar

29.06 300 0.091326 1.06 1033.877 Laminar

17.35 570 0.290632 1.06 3290.172 Transitional

19.19 470 0.216666 1.06 2452.822 Transitional

8.12 700 0.762623 1.06 8633.467 Turbulent

10.13 400 0.349316 1.06 3954.52 Turbulent

CONCLUSION:

Since the critical value of the Reynolds number is 2000 for flow through a pipe the overall experiment

was a success with the exception of the one transitional value. This may be due to the fact that using the

collection cylinder and timing the flow is very cumbersome for one person to handle. Over all the

experiment was a success. What the table demonstrates are the values that are obtained from using the

values obtained from the experiment with the given values of v, which at normal room temperature is 1.06

*10-6 m2/sec.


Page-101

DEMONSTRATION - PELTON WHEEL TURBINE

Cavitation in Turbine

o η

Elevation

Pipe and penstock length in thousands of feet or meters.

DAM

friction loss in pipe & penstock = h

Lake

concrete

H

Pipe Diameter (D) Jet or Nozzle

d jet

Turbine Buckets

WHP

P j P e

h n η

t η

h

Shaftwork to generator

SHP m η

V p V j H

L

SHP P t

P t


Page-102

Appendix - A OPERATION OF THE WIND TUNNEL

Before operating the AEROLAB wind tunnel, the airspeed and pressure readouts must be zeroed. To zero

the airspeed readout, turn the airspeed indicator knob until the reading on the LED display just reaches

zero. NOTE: Due to internal square root function, the knob must only be turned until the reading is a

positive zero. Repeat this procedure with the pressure indicator knob.

Turn the fan speed control knob on the instrument panel counter-clockwise until it stops. Then connect

the tube from the static ring of the test section to the tee fitting on the line, which connects behind the

instrument panel. Then, flip the switch below the fan speed control knob up to turn the fan on. Slowly

turn the fan speed control knob clockwise until the desired speed is indicated on the airspeed readout. To

record the test section (static ring) pressure, turn the 24-input rotary dial to any unconnected input. Turn

the fan off by flipping the switch below the fan speed control knob down.

Differential Transducer Pressure:

It must be noted that the pressure read by the 24-input rotary dial is actually a differential pressure. The

pressure shown on the LED pressure readout is actually the difference in pressure between the static ring

and whatever is connected to the 24-input rotary dial. For example, the pressure read by the total-head

sensing hole of the Pitot-static tube is actually the difference between the static ring pressure and the

actual pressure at the total head-sensing hole.

Therefore, it can be shown that the pressure indicated on the LED readout from the total head sensing

hole of the Pitot-static tube is actually the dynamic pressure, or total head pressure minus static pressure is

dynamic pressure.

(Po + 12

ρV2) - Po =21 ρV2 (A)

Similarly, it can be shown that the pressure indicated by the static sensing hole of the Pitot-static tube

should be approximately zero.


Page-103

APPENDIX - B Zeroing Angle Of Attack

1. To zero the angle of attack you need to use a level or bubble protractor. Turn the angle of attack knob

while the level sets on the balance; observe when the bubble is centered. After the bubble is centered

use the knob below the angle of attack display and set the reading to zero.

2. To zero the normal force use the knob below the display by turning the knob till the readout displays

0.000.

3. Repeat same procedure can be used for the axial force and pitching or yawing moment.

Calibrating the Normal and Axial Force, Pitching and Yawing Moment

1. First zero the normal and axial forces and the pitching moment by referring to appendix B.

2. The normal force is to be calibrated by adding a known weight to the sting, with the calibration barrel

in place, on the center groove. The normal force display should show 100 times the amount of pounds.

If there is a problem with the display ask the lab instructor or assistant for help.

3. The pitching moment is to be calibrated by moving the weight 2 grooves forward from the center

groove. The pitching moment should display should read 2 times the weight. If there is a problem with

the display ask the lab instructor or assistant for help.

4. The axial force is to be calibrated by changing the angle of attack to positive 30 degrees and then the

weight should be added to the center groove. The axial force display should show half the magnitude

of the weight. If there is a problem with the display ask the lab instructor or assistant for help.


Page-104

APPENDIX - C INSTALLING AND REMOVING THE BALANCE

1. Removing the balance requires Philips screwdriver. The screws must be loosened and removed from

the bottom of the sting which is labeled 'a' in the figure below. Once the screws are removed, very

gently remove the balance from the struts (black balance supports), which are labeled 'b' in the figure.

Now turn the knob (labeled as 'c' in the figure), which controls the angle of attack. Now the balance

mechanism can be pulled out gently from the bottom of the test section through the slot and the rubber

gasket. Then disconnect the bus plug from the balance, which is labeled 'd' in the figure. Again note

that connection ‘d’ is under the test section. The position c and d do not exist in the figure.

Use extreme caution when removing the balance because the balance is very

sensitive to forces, moments, and tensions. The balance and wiring cable are the most

fragile part of the system and cannot withstand large forces, moments, any shock, or

impact.

Figure 1. Balance Mechanism

2. Installing the balance requires Philips screwdriver. First place the balance gently back in the test

section through the bottom plate of the test section. Turn the knob labeled 'c' in the figure, which

controls the angle of attack, so that the struts are reinserted back into the test section. After the balance

and struts are inserted back in the tunnel, place the balance in the struts. Insert the screws back in the

area labeled 'a' in the figure and tighten. Then plug the wire bus in the bus connector labeled 'd' in the

figure.

a

b Rubber Gasket

d

c under the

test


Page-105

Appendix D USE OF MANOMETER

1. Fill manometer with the blue solution so that the fluid level is at about 6 inches. This is done by

pinching off one of the "T" tubes and placing the opposite side tube in the solution and applying a

suction to the open "T" tube.

2. Hook one of the manometer tubes with the "T”. The other end of the "T" will be used to apply suction

by mouth. The other tube of the manometer is open to air.

3. Zero both the airspeed and pressure displays refer appendix A. After they are zeroed apply suction to

the suction tube so that the solution has a total displacement of more than 5 inches and less than 10

inches. Then lock the suction tube at that position.

4. Read the total displacement and the pressure reading, they should be approximately the same value.

Use the displacement reading to look up the corresponding value for airspeed. Compare this value to

the actual airspeed if there is a large discrepancy. See the lab instructor or the lab assistant.

5. A graph is supplied to convert pressure measured from the manometer in ∆h inches of water to miles

per hour (mph).


Page-106

Appendix - E HYDRAULIC BENCH OPERATING INSTRUCTIONS

INSTALLATION

The Hydraulic Bench is already installed, however instructions are provided in case any problem arises.

Assembling the Drain Valve

(a) Remove and discard the straps securing the bench top to the sump tank.

(b) Remove the bench top and lift it off on to a suitable support. Do not stand or drop the top on its edge.

(c) Assemble the drain valve into the hole in the weigh tank as shown in the figure E 1.

Electrical Mains Connection

(a) Check that the voltage engraved on the manufacturer's plate is the same as the mains electrical supply,

to which the equipment will be connected.

(b) A three-core cable is fitted to the bench as standard.

Checking, Weighing and Draining Operations

With the bench top removed, ensure that both sump and weigh tank are clean and free from dust and that

the pump passageway is not blocked.

Figure E 1 - Hydraulic Bench

Weight Power Supply

Water In Water Out to system

Bench Supply Valve

Power Switch For the Pump

Stopper


Page-107

(a) Fill the sump tank with cold water to the level label (160 liters). Mix the stain/deposit preventer in the

correct proportion to the contents of the sump tank. This solution will prevent impurities depositing in

the manometer tubing and other parts of the hydraulic range of equipment. The solution is especially

desirable in hard water areas.

(b) The valve assembly (A) is dropped into the hole in the weigh tank (B). The rubber seal, plus the weight

of the valve assembly, ensures a good seal.

(c) Close bench supply valve.

(d) Connect bench to the mains and start pump motor by twisting the red button on the starter. Check hose

clips for leaks.

(e) Direct supply hose into weigh tank and slide weigh beam stop over beam. No weights need be added

for this test.

(f) Open bench supply valve and fill the weigh tank with water to approximately 25 mm from the top.

(g) Close the bench supply valve, check that the drain valve is closed, and not leaking.

(h) To drain the weigh tank, depress the weigh beam above the weight hanger and slide the beam stop

away. Gently release the weigh beam and the water will commence to drain. To finish draining lift the

weigh beam for 10 or 15 seconds. Note: There will always be water in the drain valve tube and some

residual water in the bottom of the weigh tank after draining.

WEIGHING TECHNIQUE

The precision weighing unit of the Hydraulic Bench, which has a 3:1 arm ratio, is designed for accurate

measurement of relatively large quantities of water up to a maximum of 36 kg. With the supply valve fully

open, a flow of 30 Kg in 38 sec is usual. Before proceeding with any experimental work on the bench,

students should familiarize themselves with the following technique:

(a) Close the bench supply valve and direct the supply hose into the weigh tank via the center of the bench

top.

(b) Slide the weigh beam stop out of line of the beam and lift the beam for 10-15 seconds to ensure the

weigh tank is empty.

(c) The weigh beam will be in its lower position with only the weight carrier on (fig E 1). Slide the weigh

beam stop above the weigh.

(d) Switch on the pump.

(e) Open the bench supply valve.

(f) Start timing the instant the weigh beam comes horizontal and place selected mass immediately on to

the weight hanger. (See figs 2b and 2c).


Page-108

(g) When the mass of water collected balances the mass of the weight hanger, the beam will rise again to

the horizontal position (fig 2d). At this instant, stop the timer and record the timing interval. Note: The

mass of water collected is three times the mass used on the weight hanger.

(h) Close supply valve or switch off the pump.

(i) To drain weigh tank, depress weigh beam above weight hanger and slide weigh beam stop away. Gently

let weigh beam rise until it stops against the sump tank. Remove weights and tank will continue

draining. As the weigh beam returns to the horizontal, lift it for 10-15 seconds to drain final amount

from weigh tank (fig 2e).

ADDITIONAL SUMP OUTLET

An additional sump outlet is provided so that the pump can be by-passed and the water directed through

any hydraulic circuit required. The procedure for connection is as follows: -

(a) Remove the bench top.

(b) A stack pipe from the outlet is located adjacent to the normal delivery pipe. It is secured with a plastic

clip and a worm drive hose clip.

(c) Remove the worm drive clip and slide the pipe through the hole in the tank and out of the plastic clip.

The stack pipe can now be connected to the external circuit. Note: The outlet can be connected with the

sump tank full of water if the connection can be made above the level of the sump tank water.

(d) Replace the bench top. The replacement of the stack pipe is the reverse of the above procedure.

Appendix F Conversion Factors and Units

1 Btu = 778 ft-lb = 1055 J

1 HP = 550 ft-lb/sec = 746 watts = 2545 Btu/hr

1 liter = 0.264 gal = 0. 001 meter3 = 0.2642 in3

1 atm = 2116 Psf = 29.92 in Hg = 101325 Pa = 14.7 Psi, 1" of Water = 0.036 Psi

1 m3/sec = 35.32 (ft3/sec), 1 ft3/sec = 449 Gal/min.


Page-109

REFERENCES

1. Operating Instructions for the AEROLAB Educational Wind Tunnel.

2. Low Speed Wind Tunnel Testing, Alan Pope, and John J. Harper, John Wiley & Sons, 1966.

3. Experiments in Fluid Mechanics, Robert A. Granger, HRW Inc. 1988.

4. Engineering Fluid Mechanics, John A. Roberson and Clayton T. Crowe, Houghton Mifflin Co.,

2000.

5. Introduction to Flight, John D. Anderson, Jr. McGraw Hill, 1989.

6. Experiments for AEROLAB Educational Wind Tunnel.

7. Principles of Fluid Mechanics, Wen-Hsiung Li and Sau-Hai Lam, Addison Wesley Publishing

Co. Inc., 1964.

8. Operation and Maintenance Manual,P. A. Hilton Ltd, 1996

9. http://www.math.csusb.edu/faculty/stanton/m262/regress/regress.html

10. http://www2.chass.ncsu.edu/garson/pa765/regress.htm

11. TecQuipment Inc – Brochures and discussions.

12. http://www.PumpWorld.com, Pump World.

13. Understanding Pump Curves, Engineered Systems, Kunz David. 1997, Volume 14.

14. Hydraulic Engineering, Roberson, John A., Cassidy, John J., Chaudhry, M.Hanif, 2nd edition,

1997, John Wiley & Sons, Inc. New York.

15. Fluid Mechanics for Engineers, Albertson, Maurice L., Barton, James R., Simons, Daryl B.,

1960, Prentice-Hall Inc., New Jersey.

16. http://en.wikipedia.org/wiki/Linear_regression

17. http://www.ncsu.edu/labwrite/res/gt/gt-reg-home.html or click here Regression with Excel

18. Engineering Tool Box Site: http://www.engineeringtoolbox.com/fluid-mechanics-t_21.html

19. LMNO Engineering, Research, and Software, Ltd. http://www.lmnoeng.com/

http://www.math.csusb.edu/faculty/stanton/m262/regress/regress.html

http://www2.chass.ncsu.edu/garson/pa765/regress.htm

http://www.pumpworld.com/

http://en.wikipedia.org/wiki/Linear_regression

http://www.ncsu.edu/labwrite/res/gt/gt-reg-home.html

http://www.engineeringtoolbox.com/fluid-mechanics-t_21.html

http://www.lmnoeng.com/


Page-110

Appendix G

Sample Report 1

A sample laboratory report written by a student

Title Page

LAB - 1

Experiment # CV1 Title : Free and Forced Convection

by

Ryan C.

SUBMITTED TO DR. P. KALIM

Date: --------------------


Page-111

LAB # 1

EXPERIMENT # CV1 – FREE AND FORCED CONVECTION

Abstract

The experiment helps verify the Newton’s law of cooling in which when the air speed is increased

the surface temperature of the heat exchanger is decreased. In other words the convection heat transfer is

increased as the flow velocity is increased. Results obtained were satisfactory and they were found to be

within acceptable range.

Introduction

This experiment addresses how the heat transfer coefficient of a medium surrounding an object

with internal heat generation affects the surface temperature of the object. The experiment uses fixed power

inputs and monitoring of surface temperature and air speed to develop relationships between the heat

transfer coefficient and air speed. The phenomenon of convection is a constant force in the world. The very

existence of the world as we know it is shaped by this force of nature. The weather patterns of the world

are heavily influenced by convection; both the atmosphere and the oceans of the world are important heat

transfer mechanisms [2]. In this experiment the effects of convection on a metal heat exchanger are studied.

The effects of free and forced convection are looked at with an analytical eye toward determining the

change in heat transfer rates produced when natural convection is replaced with free convection.

Procedure and Experimental Data

The convective heat transfer apparatus in the Wilkes University Heat and Mass Transfer Lab was

used for this experiment. The apparatus consists of a vertically mounted rectangular tube capable of

housing an extended surface heat exchanger. The apparatus has a blower that circulated air thru the tube

and thus over the extended heat surfaces. Appropriate provisions were made for monitoring both air

velocity and temperature [1].

The basic procedure of the experiment was to apply a constant electric power supply to the

resistance element within the heat exchanger. This element produces heat within the element, which is

then transferred from the element body to the surrounding air by convection. The temperature of the

surface of the heat exchanger is monitored for various input powers with both forced and free convection.


Page-112

The data was collected for2 power settings, 20 watts and 40 watts. For both power settings the

temperature was allowed to settle near steady state for both free and forced convection. The first set of

reading displayed in Table 1 is recorded with the heat exchanger in an initial ambient condition. Twenty

watts of power are then applied and the heat exchanger is allowed to heat until a new steady state is

reached. Table 2 shows that 20 watts power applied to reach steady state condition with free convection.

Forced convection (with velocity of 0.1 m/sec) is then started at time = 0 and the surface temperature

decreases to near steady state. The following data were collected. The data in Tables 3 and 4 were

collected using the same procedure as outlined for the previous readings with the exception that the power

supply is increased to 40 watts.

Table 1. Temperature Data at 20 Watt Power supply

Time in

Minutes

Temperature in

Celsius

Time in

Minutes

Temperature

in Celsius

1 26 19 39.5 2 27.1 20 40 3 28.3 21 40.4 4 29.3 22 40.8 5 30.2 23 41.2 6 31.1 24 41.6 7 31.9 25 42 8 32.7 26 42.3 9 33.5 27 42.6 10 34.2 28 42.9 11 34.9 29 43.2 12 35.6 30 43.4 13 36.2 31 43.6 14 36.8 32 43.8

Table 2. 20 Watt Power supply forced convection

Time in Minutes

Temperature in Celsius

Time in Minutes


1 44.3 9 37.6 2 42.8 10 37.2 3 41.7 11 36.9 4 40.7 12 36.4 5 39.9 13 36.2 6 39.3 14 36 7 38.7 15 35.9 8 38.1 16 35.8


Page-113

Table 3. 40 Watt Power supply free convection

Table 4. 40 Watt Power supply forced convection

Time in Minutes


Time in Minutes


0 60.2 10 45.3 1 55 11 44.9 2 52.6 12 44.5 3 50.7 13 44.2 4 49.3 14 43.8 5 48.5 15 43.6 6 47.8 16 43.4 7 47 17 43.2 8 46.3 18 42.5 9 45.9 19 42.8

Results, Discussions, and Analysis:

Must use trendline equations to determine the steady state temperature.

Not done in this report The results tabulated in the preceding section of this report are effectively visualized in the following

graphs. Figure 1 presents the data from Table 1 graphically along with a power trend line. Figure 2

presents the data from Table 2 graphically along with a logarithmic trend-line. The results from the

experiment with the power input at 40 watts were presented in Tables 3 and 4 respectively. Those Tables

are graphically presented in figures 3 and 4 respectively.

Time in Minutes


in Minutes


Time in Minutes


0 36 11 50.6 22 57.5 1 38.1 12 51.4 23 57.8 2 39.8 13 52.2 24 58.2 3 41.5 14 53 25 58.8 4 43.2 15 53.5 26 59.1 5 44.4 16 54.3 27 59.4 6 45.6 17 54.8 28 59.6 7 46.7 18 55.4 29 59.8 8 47.6 19 56 30 60.1 9 48.8 20 56.5 31 60.2 10 49.7 21 57


Page-114

A) MathCAD3 Calculations

(1)

Where: Q= heat transfer rate, A= Area of surface, t = temperature in degrees Celcius and

h = Convection heat transfer coefficient.

Equation 1 was used to calculate the heat transfer coefficient1 between the object and the air at both

free and forced convection conditions. For example the convection coefficient of air for free

convection was found as follows (sample calculations must be done for each category). The h

values obtained from the four experiments are tabulated in Table 5. It is noted that the airflow for

forced convection for both experiments was measured as Watts per Meter squared * Kelvin.

tsurface 316.6 K⋅:= Tsurroundings 300 K⋅:=Q 20W:= A 1319.6 cm2⋅:=

Given Q h A⋅ tsurface Tsurroundings−( )⋅ Find h( ) 9.13W

m2 K⋅=

Using the regression capabilities an equation relating temperature to q” is obtained and displayed

on each chart. It is noted that the equation modeling the data in figure 5 has a lower power than that of

figure 1. The trendline shows that R2 coefficient [1] is almost equal to 1 (0.9837), which suggests that the

data fit (trendline) is very good.

Figure 1. 20 watt power supply to steady state temperature - free convection

Q h A⋅ t surface t surroundings−( )⋅

2527293133353739414345

0 5 10 15 20 25 30 35 40

Tem

p. Ii

n D

egre

es C

elci

us

Time in Minutes

Insert a trend line and display equation and R2 value


Page-115

Figure 2. 20 watt power supply to steady state temperature - forced convection

Error analysis:

At this point in the semester all the h values we have worked with have been given. A search was

made for a typical h value of air it appears that the values of h are dependent on a number of

conditions and there is no set value for which to compare. In place of comparing the h value

obtained to an expected value the percent error between the readings will be calculated using

equation 2 [1].

Percent error = Larger_value Smaller_value−

accecpted_value100⋅ ⋅

(2)

A sample calculation is provided below

tsurface 316.6 K⋅:= Tsurroundings 300 K⋅:=Q 20W:= A 1319.6 cm2⋅:=

Given Q h A⋅ tsurface Tsurroundings−( )⋅ Find h( ) 9.13W

m2 K⋅=

The error between the free convection readings for several power settings was very small 0.3 %.

The error for the forced convection was significantly higher at 8.82%. This higher error is

attributed to the inaccuracy in obtaining equal flows of air for each experimental setup. It is

suspected that a ruler with a narrower range would produce better results.

3536373839404142434445

0 5 10 15 20

Tem

p. Ii

n D

egre

es C

elci

us

Time in Minutes


Page-116

Figure 3. 40 Watt power supply ambient to steady state temperature - free convection

Figure 4. 40 watt supply, to steady state temperature - forced convection

Table # 5 - Calculated Values of h

Experiment Type

“h” Value-

W/(m2 K) Experiment Type

Value of “h”

W/(m2 K)

free convection 20 watts 9.13 forced convection 20 watts 17.831

free convection 40 watts 9.103 forced convection 40 watts 19.556

30

35

40

45

50

55

60

65

0 5 10 15 20 25 30 35Te

mp.

Iin

Deg

rees

Cel

cius

Time in Minutes

40

42

44

46

48

50

52

54

56

58

60

0 2 4 6 8 10 12 14 16 18 20

Tem

p. Ii

n D

egre

es C

elci

us

Time in Minutes


Page-117

Figure 5. 40 watt power supply steady state temperature - free convection

(must insert trendline with fitting equation and regression coefficient- Excel)

Conclusions

It was observed that the higher values of “h” result in lower values of surface temperature. This

is an important result as the implications have far reaching effects in the engineering field. Should a part

need to have a lower surface temperature then the option of increasing the coefficient of heat transfer is a

plausible answer to the problem. This verifies the Newton’s law of cooling that the heat transfer by

convection increases as temperature gradient is increased or convection heat transfer is increased.

References

1. Heat and Mass Transfer Lab Manual, P. Kalim, Wilkes University, 2009

2. University Physics Young, D. ninth edition, John Wiley & Sons, 1995.

3. Fundamentals of Heat and Mass Transfer, F. D. Incropera and D. P. Dewitt, John Wiley and

Sons, Fifth Edition, 2002.

4. MATH CAD, www.ptc.com/mathcad

y = 1E-17x7.6814 , R2 = 0.9837

0

100

200

300

400

500

600

700

320 330 340 350 360 370 380 390

q'' i

n W

atts

per

met

er s

quar

ed

Temp in Kelvins

http://www.ptc.com/mathcad


Page-118

Sample Report 2

A sample laboratory report written by a student

LAB # 2

Experiment # HX1 Title: Concentric Tube (Parallel Pipe) Heat Exchanger

Student

Course Name

Submitted

Dr. P. Kalim


Page-119

Abstract

Hot and cold water temperature was recorded for a single-pass aluminum parallel concentric tube heat

exchanger at different flow rates flowing through the concentric tube. The effectiveness ε of the heat

exchanger was calculated using LMTD method. Also NTU and overall heat transfer coefficient UA was

calculated. The calculations produced reasonable and satisfactory results and the error was within

acceptable limits.

Introduction

Heat exchangers work by transferring heat from a warmer to a cooler substance. As the

instrument is placed into a thermal transfer system the temperature drops. This transfers heat and the

longer the heat exchanger, the more transfer of heat will occur. A heat exchanger is an instrument in

which water flows through different tubes to measure the flow rates and temperature at different points on

the instrument2.

The heat exchanger had different types of tubes in that they are of various types of metal and

configuration. Proper tubes for the intended experimentation are selected by opening and closing

designated valves on the heat exchanger. In current experimentation, the parallel pipe aluminum tube was

utilized. The shell and tube heat exchanger was also used which is the most common.

On a heat exchanger, usually the only readable temperatures are at the entrance and the exit of the

tubes. These temperature readings are used to ascertain the load using the average of the temperatures.

The heat load facilitates calculation of overall heat transfer coefficient helps understand that the heat flux

fluctuates with the resistance between the different temperatures at the inlet and outlet of the tubes1.

Procedure and Experimental Data

In this experiment the parallel flow aluminum concentric tube heat exchanger was used. From the

faucet, specified flow rates of hot (2.05 gpm) and cold water (1.94 gpm) was allowed to flow through the

Heat Exchanger (HX) and then let it stabilize. Temperature readings were taken at certain points of the

heat exchanger every five minutes for thirty consecutive minutes. These points were the inlet and outlet

points of both hot (TC-12 and TC-13) and cold water (TC-14 and TC-15). Hot water was also measured

at the entrance to the heat exchanger, TC-1. This entire process was again completed for a different flow

rate of 1.35 gpm and TC-1 temperature of 47.2 ° C. Also, temperatures were taken along the length of the

heat exchanger tube in fifteen centimeter intervals.


Page-120

Tables 1 and 2 show the temperature at given time interval at 2 gpm and 1.35 gpm respectively. Table 3

shows the temperature per distance on the tube and table 4 shows the temperature for TC-1. Tables 5, 6

and 7 show the same temperature measurements, but in Celsius form.

Table 1 - Temperature Data - Flow Rate 2 gpm

Time Cold Water (oF)

Cold Water t (oF)

Hot Water (oF)

Hot Water out (oF)

(min) (TC-12) TC-13) (TC-14) (TC-15) 0 77.6 89.5 122.6 115.7 5 76.2 88.0 120.8 112.4 10 75.8 86.8 120.0 112.0 15 75.4 86.5 118.9 111.0 20 75.2 86.3 117.5 108.5 25 75.1 86.2 117.0 108.0 30 75.0 86.0 116.6 107.0

Table 2 – Temperature Data - Flow Rate 1.35 gpm

Time Cold Water (oF)

Cold Water out (oF)

Hot Water (oF)

Hot Water out (oF)

(min) (TC-12) (TC-13) TC-14) (TC-15) 0 75.5 86.1 116.2 110.0 5 75.3 86.0 115.3 108.7 10 75.2 86.0 115.0 108.3 15 75.1 85.9 114.3 108.1 20 75.0 85.8 114.2 107.8 25 75.0 85.7 114.1 107.6 30 74.9 85.6 114.0 107.5

Table 3 –LMTD along the length of the HX.

Distance from Left End of the HX

Temp (oF)

0 113.8 15 111.9 30 110.5 45 109.3 60 108.6 75 107.8 90 107.7

105 107.4 120 107.2


Page-121

Table 4 – Temperature readings for TC1

Flow Rate TC1 - Temp (GPM) (oF) (oC)

2.0 123.0 50.6 1.5 116.9 47.2

Table 5 - Temperature readings at various locations- Flow Rate 2 gpm

Time Water in Tube (oC)

Water out Tube ( oC )

Hot Water

Hot Water

(min) (TC-12) (TC-13) (TC-14) (TC-15) 0 25.3 31.9 50.3 46.5 5 24.6 31.1 49.3 44.7 10 24.3 30.4 48.9 44.4 15 24.1 30.3 48.3 43.9 20 24.0 30.2 47.5 42.5 25 23.9 30.1 47.2 42.2 30 23.9 30.0 47.0 41.7

Table 6 - Temperature readings at various locations- Flow Rate 1.35 gpm

Time Water in Tube (oC)

Water in Tube (oC)

Hot Water

Hot Water

(min) (TC-12) (TC-13) (TC-14) (TC-15) 0 24.2 30.1 46.8 43.3 5 24.1 30.0 46.3 42.6 10 24.0 30.0 46.1 42.4 15 23.9 29.9 45.7 42.3 20 23.9 29.9 45.7 42.1 25 23.9 29.8 45.6 42.0 30 23.8 29.8 45.6 41.9

Table 7 – Temperature readings along the length of Heat Exchanger

Distance from Left End of the HX Temp (oC)

0 45.4 15 44.4 30 43.6 45 43.0 60 42.6 75 42.3 90 42.0

105 41.9 120 41.8


Page-122

Results Discussion and Analysis

The heat exchanger2 load was calculated using equation 1 in which the temperature differences

from the input to output was averaged per the LMDT method and the density of water at 50° C is 1080

kg/m3 and at 25°C is 1180 kg/m3 is used to find mass flow rate ‘m’ (kg/sec) along with the specific heat

‘C’ (J/kg.K) which was 4181 for the hot water and 4180 for cold. Log mean temperature difference2 is

calculated through temperature change in equation 2 and the overall heat transfer coefficient ‘UA’ 2 is

calculated through equation 3 using the heat load and LMTD. Heat transfer effectiveness, ε [2] was found

using specific heat and temperature data in equation 4 and NTU2 was found using UA and minimum heat

capacity (Cmin) from equation 5.

)()( cicopcchohiphh TTCmTTCmq −=−= (1)

)ln(1

2

12

TT

TTLMTD

∆∆

∆−∆= (2)

)()( cicopcchohiphh TTCmTTCmq −=−= =UA LMTD (3)

)()(

)()(

minminmax cihi

cicoc

cihi

hohih

TTCTTC

TTCTTC

qq

−−

=−

−==ε (4)

minCUANTU = (5)

Sample Calculations

For the flow rate of 2 gpm, Q was found to be 0.000126 m3/sec and density was 1080 kg/m3 making

mass flow rate m=0.13608 kg/sec (m=Qρ). Equation 1 was used to find the heat load2 while Cp is the

specific heat found from a table in the ‘Fundamentals of Heat and Mass Transfer2.’

)()( cicopcchohiphh TTCmTTCmq −=−=

q= (0.13608)(4181)(50.33-46.50)=2179 Watts

LMTD2 is then found through equation 2 taking temperature differences and UA2 is found through

equation 3 and used LMTD found in the previous equation.


Page-123

)ln(1

2

12

TT

TTLMTD

∆∆

∆−∆=

3.19

)94.3150.46)33.2533.50(ln(

)94.3150.46()33.2533.50(=

−−

−−−=LMTD

)()( cicopcchohiphh TTCmTTCmq −=−= =UA LMTD

85.2123.19

4108===

LMTDqUA

Heat transfer effectiveness2 was found through equation 4 using the Cc and Cmin along with

temperature changes. The cold specific heat is 621.482 and the minimum is 568.95 which are found

from the mass flow rate with the hot or cold specific heat.

)()(

)()(

minminmax cihi

cicoc

cihi

hohih

TTCTTC

TTCTTC

qq

−−

=−

−==ε

2888.0)33.2533.50(95.568)33.2594.31(482.621

=−−

=ε

Finally NTU2 is found from equation 5 using Cmin and UA

min

UA 212.75NTU 0.374C 568.95

= = =

Table 8 - Heat Exchanger Load: 2 GPM

q (Watts) (TC-12) (TC-13) q (Watts) (TC-14) (TC-15) 4101.78 25.30 31.90 2162.01 50.30 46.50 4039.64 24.60 31.10 2617.17 49.30 44.70 3791.04 24.30 30.40 2560.28 48.90 44.40 3853.19 24.10 30.30 2503.38 48.30 43.90 3853.19 24.00 30.20 2844.75 47.50 42.50 3853.19 23.90 30.10 2844.75 47.20 42.20 3791.04 23.90 30.00 3015.44 47.00 41.70

As seen in table 8 and 9, the heat exchanger load was found for each temperature change and

for the tube and the shell for the flow rates of 2 gpm and 1.35 gpm. All of the data and heat loads


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were found to be very consistent for both hot and cold water but with the cold load always bigger

than the hot. LMTD is shown in table 10 and is the same for over time for the temperature changes.

The overall heat transfer coefficient was calculated both through experimental and theoretical

conclusions for both flow rates and can be seen in table 11 and 12. Once again, the cold water has a

higher value than the hot and the conclusions are consistent, among time change and theoretically as

well as experimentally.

Table 9 - Heat Exchanger Load:1.35 GPM

q (Watts) (TC - 12) (TC-13) q (Watts) (TC-14) (TC-15)

3666.75 24.20 30.10 1991.33 46.80 43.30 3666.75 24.10 30.00 2105.12 46.30 42.60 3728.89 24.00 30.00 2105.12 46.10 42.40 3728.89 23.90 29.90 1934.43 45.70 42.30 3728.89 23.90 29.90 2048.22 45.70 42.10 3666.75 23.90 29.80 2048.22 45.60 42.00 3728.89 23.80 29.80 2105.12 45.60 41.90

Table 10 – Log Mean Temp Difference

LMTD 19.3 Δ T1 14.6 Δ T2 25.0

Table 11 - Calculate UA (2 GPM)

Experimental UA (TC-12) (TC-13) UA (TC-14) TC-15)

212.53 25.30 31.90 112.02 50.30 46.50 209.31 24.60 31.10 135.60 49.30 44.70 196.43 24.30 30.40 132.66 48.90 44.40 199.65 24.10 30.30 129.71 48.30 43.90 199.65 24.00 30.20 147.40 47.50 42.50 199.65 23.90 30.10 147.40 47.20 42.20 196.43 23.90 30.00 156.24 47.00 41.70

Theoretical UA (TC-12) (TC-13) UA (TC-14) (TC-15)

210.49 25.30 31.90 111.99 50.30 46.50 207.30 24.60 31.10 135.57 49.30 44.70 194.55 24.30 30.40 132.63 48.90 44.40 197.74 24.10 30.30 129.68 48.30 43.90 197.74 24.00 30.20 147.36 47.50 42.50 197.74 23.90 30.10 147.36 47.20 42.20 194.55 23.90 30.00 156.20 47.00 41.70


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Table 12 - Calculate UA (1.35 GPM)

Experimental UA (TC-12) (TC-13) UA (TC-14) (TC-15)

189.90 24.20 30.10 103.18 46.80 43.30 189.90 24.10 30.00 109.07 46.30 42.60 193.11 24.00 30.00 109.07 46.10 42.40 193.11 23.90 29.90 100.23 45.70 42.30 193.11 23.90 29.90 106.13 45.70 42.10 189.99 23.90 29.80 106.13 45.60 42.00 193.21 23.80 29.80 109.07 45.60 41.90

Theoretical UA (TC-12) (TC-13) UA (TC-14) (TC-15)

189.99 24.20 30.10 103.15 46.80 43.30 189.99 24.10 30.00 109.05 46.30 42.60 193.21 24.00 30.00 109.05 46.10 42.40 193.21 23.90 29.90 100.21 45.70 42.30 193.21 23.90 29.90 106.10 45.70 42.10 189.99 23.90 29.80 106.10 45.60 42.00 193.21 23.80 29.80 109.05 45.60 41.90

Heat exchanger effectiveness as seen on table 13 shows the value ascertained through the specific

heats and cold water temperature change. Only one value was needed to be found since it is for the

effectiveness of the entire system. This value, 0.288 seems to show that the system worked well. Tables

14 and 15 calculate the NTU values for the flow rates of 2 gpm and 1.35 gpm respectively. NTU values

were also very consistent with the cold water values again being slightly higher than all of the hot water

values for both flow rates. Error between the experimental and theoretical UA values were judged in

tables 16 and 17 for the flow rates of 2 gpm and 1.35 gpm respectively. This error was almost nonexistent

and showed that good data was gained and the instrument worked well. Finally tables 18 and 19 show the

overall heat transfer coefficient ‘UA’ without the area. The diameter of the tube was given in the lab

manual and was used to the find the area and taken away from ‘UA.’

Table 13 - Heat Exhanger Effectiveness

ε Ch Cc Cmin

0.2888 568.95 621.48 568.95


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Table 14 - Calculate NTU for 2 GPM

NTU (TC-12) (TC-13) NTU (TC-14) (TC-15) 0.37 25.30 31.90 0.20 50.30 46.50 0.36 24.60 31.10 0.24 49.30 44.70 0.34 24.30 30.40 0.23 48.90 44.40 0.35 24.10 30.30 0.23 48.30 43.90 0.35 24.00 30.20 0.26 47.50 42.50 0.35 23.90 30.10 0.26 47.20 42.20 0.34 23.90 30.00 0.27 47.00 41.70

Table 15 - Calculate NTU for 1.35 GPM

NTU (TC-12) (TC-13) NTU (TC-14) (TC-15)

0.33 24.20 30.10 0.18 46.80 43.30 0.33 24.10 30.00 0.19 46.30 42.60 0.34 24.00 30.00 0.19 46.10 42.40 0.34 23.90 29.90 0.18 45.70 42.30 0.34 23.90 29.90 0.19 45.70 42.10 0.33 23.90 29.80 0.19 45.60 42.00 0.34 23.80 29.80 0.19 45.60 41.90

Table 16 - Error on UA (2 GPM)

% Error (TC-12) (TC-13) % Error (TC-14) (TC-15) 0.96 25.30 31.90 0.02 50.30 46.50 0.96 24.60 31.10 0.02 49.30 44.70 0.96 24.30 30.40 0.02 48.90 44.40 0.96 24.10 30.30 0.02 48.30 43.90 0.96 24.00 30.20 0.02 47.50 42.50 0.96 23.90 30.10 0.02 47.20 42.20 0.96 23.90 30.00 0.02 47.00 41.70

Table 17 - Error on UA (1.35 GPM)

% Error (TC-12) (TC-13) % Error (TC-14) (TC-15) 0.05 24.20 30.10 0.02 46.80 43.30 0.05 24.10 30.00 0.02 46.30 42.60 0.05 24.00 30.00 0.02 46.10 42.40 0.05 23.90 29.90 0.02 45.70 42.30 0.05 23.90 29.90 0.02 45.70 42.10 0.00 23.90 29.80 0.02 45.60 42.00 0.00 23.80 29.80 0.02 45.60 41.90


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Table 18 - U find the known value of A=0.00090746: 2 GPM

U (TC-12) (TC-13) U (TC-14) (TC-15) 231959.43 25.30 31.90 123415.41 50.30 46.50 228444.89 24.60 31.10 149397.60 49.30 44.70 214386.74 24.30 30.40 146149.82 48.90 44.40 217901.28 24.10 30.30 142902.05 48.30 43.90 217901.28 24.00 30.20 162388.69 47.50 42.50 217901.28 23.90 30.10 162388.69 47.20 42.20 214386.74 23.90 30.00 172132.01 47.00 41.70

Table 19 - U value 1.35 GPM

U (TC-12) (TC-13) U (TC-14) (TC-15) 209361.13 24.20 30.10 113672.09 46.80 43.30 209361.13 24.10 30.00 120167.63 46.30 42.60 212909.62 24.00 30.00 120167.63 46.10 42.40 212909.62 23.90 29.90 110424.31 45.70 42.30 212909.62 23.90 29.90 116919.86 45.70 42.10 209361.13 23.90 29.80 116919.86 45.60 42.00 212909.62 23.80 29.80 120167.63 45.60 41.90

Temperature profile for the flow rates of 2 gpm and 1.35 gpm can be seen in figures 1 and 2 while the

surface probe data can be seen in figure 3.

Figure 1. Temperature Profile

Figure 2 is missing

Figure 1 - Temperature Profile: 2 GPM Flow Rate

y = -0.0421x + 24.94

y = -0.0579x + 31.448

y = -0.1524x + 45.984

y = -0.1115x + 50.038

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0 5 10 15 20 25 30 35

Temperature (C)

Tim

e (m

inut

es)

TC-12

TC-13

TC-14

TC-15

Linear (TC-12)Linear (TC-13)Li (TC


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Figure 2. Surface Probe Data, LMTD

Try to Fit a logarithmic Curve, since LMTD is log mean temperature difference

Conclusions

Heat load2 was analyzed for the cold water in the tube and hot water in the shell in an aluminum

parallel tube in a heat exchanger. After the heat load was found using the LMTD method of the mean of

the input and output of temperatures, other data could be found. This included the log mean temperature

difference, overall heat transfer coefficient and NTU. All of this data was very consistent among time and

temperature change. Although the data was so consistent throughout all the calculations, it was

consistently found that the cold water in the tube always possessed higher values in the calculations than

the hot water in the shell which could have been due to a more even flow.

Using the heat exchanger effectiveness formula, the instrument seemed to have a good value

which was aided in this determination by the consistency of results and graphs. Also in performing some

error analysis, it was almost nonexistent, which is much less then other labs and findings done in the past

on other experiments.

The temperature profiles show that with a greater flow rate (2 gpm), there is more variation in the

temperature change over time than for the less flow rate (1.35 gpm) in which there is almost no variation

Figure 3 - Surface Probe Data

y = -0.0291x + 44.737

41.0

41.5

42.0

42.5

43.0

43.5

44.0

44.5

45.0

45.5

46.0

0 20 40 60 80 100 120 140

Length of HX (cm)

Tem

pera

ture

(C)

HX Temperature ProfileLinear (HX Temperature Profile)Linear (HX Temperature Profile)


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in temperature change. This shows that the slower the flow, the slower the transfer of heat through a

system. Surface probe data varies logarithmically as it should, per the lab manual. Temperature decreases

faster at first and then slows down farther in distance in the tube. This shows that the temperature varies

much more closely to the entrance of flow.

References

1. Incropera, Frank P., DeWitt, David P., Bergman, Theodore L., Lavine, Adrienne S. Fundamentals of

Heat and Mass Transfer. Sixth Edition. 2007.

2. Dr. Kalim, S. Perwez. Heat and Mass Transfer Laboratory (ME326) Manual, Fall 2009,. August

2007

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