Formulae & Physical Constants_28pg

A P P E N D I X

Formulae and Physical Constants

Table of Contents

Topic Page

Common Units and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

Basic Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

Common Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

Relative Density (Specific Gravity) of Various Substances . . . . . . . . . . . . . . 405

Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

Mathematical Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

Applied Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

Stress, Strain and Modulus of Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

Coefficients of Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422

Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

Periodic Table of the Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

Ion Names and Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

401

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APPENDIX B • FORMULAE AND PHYSICAL CONSTANTS402

Common Units and Abbreviations

foot ftpound lbfoot pound (work) ft•lbpound foot (torque or moment) lb•ftfoot (feet) per second ft/smile mimile per hour mi/h mphhour hinch ininches per minute in/minsecond srevolution per minute r/min rpmhorsepower hphorsepower hour hp•hBritish thermal unit Btuyard ydpounds per square inch psiampere Aampere hour A•hvolt Vwatt Wjoule Jcoulomb Calternating current ACdirect current DC

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APPENDIX B • FORMULAE AND PHYSICAL CONSTANTS 403

Basic Units

U.S. Standard

Distance Conversions:

12 in. 1 ft 1 in. 25.4 mm3 ft 1 yd 1 ft 30.48 cm

5280 ft 1 mile 1 mile 1.61 km100 links 1 chain 1 yd 0.914 m

1 m 3.28 ft

Area Conversions:

1 ft2 144 in.2 1 in.2 6.45 cm2 645 mm2

1 yd2 9 ft2 1 m2 10.8 ft2

1 sq mile 640 acre 1 section 1 acre 0.405 ha1 sq chain 484 sq yds. 1 sq mile 2.59 km2

1 acre 43,560 sq ft.

Volume Conversions:

1 ft3 1728 in.3 1 in.3 16.4 cm3

1 yd3 27 ft3 1 m3 35.3 ft3

1(liquid) U.S. gallon 231 in.3 1 litre 61 in.3

4 (liquid) quarts 1 U.S.gal 3.78 litres1 U.S. barrel (bbl) 42 U.S. gal. 1 U.S. bbl 159 litres1 imperial gallon 1.2 U.S. gal. 1 litre/s 15.9 U.S. gal/min

Mass and Weight Conversions:

2000 lb 1 ton (short) 1 kg (on Earth) results in a weight of2.2 lb

1 long ton 2240 lb

Density Conversions:

weight density (on Earth) a mass density of

r

1 is equivalent to a weight density

of 0.0623

Density

In U.S. Standard the quantity is specific gravity; for solids and liquids a comparison of weight density to that of water.

lbft3

kg

m3wV

a lbft3b

weight

volume

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Common Conversions

1 atmosphere (atmos. press. at sea level) 29.9 ins. mercuryor 760 mm mercuryor 14.696 psi

1 mercury 0.492 psi1 Imp. gal fresh water 10 lbs1 cu ft fresh water 62.4 lbs1 Imp. gal 277 cu ins1 U.S. gal 231 cu ins1 Imp. gal 1.2 U.S. gals1 ft head of water 0.4335 psi1 psi 2.31 ft head of water1 Btu 778 ft-lbs of work1 horsepower-hour (hp-hr) 2545.2 Btu1 horsepower-minute (hp-min) 42.4 Btu1 horsepower 33,000 ft-lbs/min

550 ft-lbs/sec1 horsepower 746 watts

1 watt/min Btu

1 kilowatt/hr

3412 Btu1 lb steam:

Latent heat of steam,from and at 212° F 970.3 Btu

Latent heat of fusion of ice 144 Btu/lb1 ton of refrigeration 144 2000

288,000 Btu

1 ton of refrigeration/24 hrs

12,000 Btu/hr 200 Btu/min

Temperature Scales

Freezing point of water 0° Celsius (Centigrade) 272° Kelvin 32° Fahrenheit 492° Rankine

1° Celsius 1° Kelvin 9/5° Fahrenheit 9/5° Rankine

Velocities

Acceleration due to gravity (g) 32.2 ft/sec2

60 miles per hr 88 ft/secVelocity of sound in air about 1100 ft/sec,

or 750 mph

388,00024

33,000 60 1000746 778

33,000746 778

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APPENDIX B • FORMULAE AND PHYSICAL CONSTANTS

Velocity of light 186,300 miles/sec

Angular Measure

1 revolution 360 degrees 4 right-angles

1 degree 60 minutes1 minute 60 seconds1 radian 57° 1745 or approx.

57.3°

Base of Napierian Logarithms 2.7183Loge (In) 2.3 Log10

Relative Density (Specific Gravity) of Various Substances

Water (fresh) . . . . . . . . . . 1.00 Mica . . . . . . . . . . . . . . . 2.9Water (sea average) . . . . . 1.03 Nickel . . . . . . . . . . . . . . 8.6Aluminum . . . . . . . . . . . . 2.56 Oil (linseed) . . . . . . . . . 0.94Antimony . . . . . . . . . . . . 6.70 Oil (olive) . . . . . . . . . . . 0.92Bismuth . . . . . . . . . . . . . 9.80 Oil (petroleum) . . . . . . . 0.76–0.86Brass . . . . . . . . . . . . . . . . 8.40 Oil (turpentine) . . . . . . 0.87Brick . . . . . . . . . . . . . . . . 2.1 Paraffin . . . . . . . . . . . . . 0.86Calcium . . . . . . . . . . . . . . 1.58 Platinum . . . . . . . . . . . . 21.5Carbon (diamond) . . . . . 3.4 Sand (dry) . . . . . . . . . . . 1.42Carbon (graphite) . . . . . . 2.3 Silicon . . . . . . . . . . . . . 2.6Carbon (charcoal) . . . . . . 1.8 Silver . . . . . . . . . . . . . . 10.57Chromium . . . . . . . . . . . 6.5 Slate . . . . . . . . . . . . . . . 2.1–2.8Clay . . . . . . . . . . . . . . . . . 1.9 Sodium . . . . . . . . . . . . . 0.97Coal . . . . . . . . . . . . . . . . 1.36–1.4 Steel (mild) . . . . . . . . . . 7.87Cobalt . . . . . . . . . . . . . . . 8.6 Sulfur . . . . . . . . . . . . . . 2.07Copper . . . . . . . . . . . . . . 8.77 Tin . . . . . . . . . . . . . . . . 7.3Cork . . . . . . . . . . . . . . . . 0.24 Tungsten . . . . . . . . . . . . 19.1Glass (crown) . . . . . . . . . 2.5 Wood (ash) . . . . . . . . . . 0.75Glass (flint) . . . . . . . . . . . 3.5 Wood (beech) . . . . . . . . 0.7–0.8Gold . . . . . . . . . . . . . . . . 19.3 Wood (ebony) . . . . . . . 1.1–1.2Iron (cast) . . . . . . . . . . . . 7.21 Wood (elm) . . . . . . . . . 0.66Iron (wrought) . . . . . . . . 7.78 Wood (lignum-vitae) . . 1.3Lead . . . . . . . . . . . . . . . . 11.4 Wood (oak) . . . . . . . . . . 0.7–1.0Magnesium . . . . . . . . . . . 1.74 Wood (pine) . . . . . . . . . 0.56Manganese . . . . . . . . . . . 8.0 Wood (teak) . . . . . . . . . 0.8Mercury . . . . . . . . . . . . . . 13.6 Zinc . . . . . . . . . . . . . . . 7.0

405

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Greek Alphabet

Alpha Iota Rho Beta Kappa Sigma , Gamma Lambda Tau Delta Mu Upsilon Epsilon Nu Phi , Zeta Xi Kai Eta Omicron Psi Theta Pi Omega ,


Mathematical Formulae

Algebra

1. Expansion Formulae

(x ! y)2 x2 ! 2xy ! y2

(x " y)2 x2 " 2xy ! y2

x2 " y2 (x " y) (x ! y)

(x ! y)3 x3 ! 3x2y ! 3xy2 ! y3

x3 ! y3 (x ! y) (x2 " xy ! y2)

(x " y)3 x3 " 3x2y ! 3xy2 " y3

x3 " y3 (x " y) (x2 ! xy ! y2)

2. Quadratic Equation

If ax2 ! bx ! c 0,

Then x

Trigonometry

1. Basic Ratios

Sin A , cos A , tan A

2. Pythagoras’ Law

x2 ! y2 h2

3. Trigonometric Function Values

Sin is positive from 0° to 90° and positive from 90° to 180°

Cos is positive from 0° to 90° and negative from 90° to 180°

Tan is positive from 0° to 90° and negative from 90° to 180°

yx

xh

y

h

"b # 2b2 " 4ac2a

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4. Solution of Triangles

a. Sine Law

b. Cosine Law

c2 a2 ! b2 " 2 ab Cos C

a2 b2 ! c2 " 2 bc Cos A

b2 a2 ! c2 " 2 ac Cos B

aSin A

b

Sin B

cSin C

407

Geometry

1. Areas of Triangles

a. All Triangles

Area

Area

and,

Area

where, s is half the sum of the sides, or s

b. Equilateral Triangles

Area 0.433 side2

2. Circumference of a Circle

C pd

3. Area of a Circle

A pr2 d2 0.7854d2

4. Area of a Sector of a Circle

A

A r2 ( angle in degrees)

A ( angle in radians)°r2

2

°360

arc r2

p

4circumference r

2

a ! b ! c2

2s(s " a)(s " b)(s " c)

bc Sin A2

ab Sin C

2

ac Sin B2

base perpendicular height

2

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5. Area of a Segment of a Circle

A area of sector " area of triangle

Also approximate area h2

6. Ellipse

A Dd

Approx. circumference

7. Area of Trapezoid

A h

8. Area of Hexagon

A 2.6s2 where s is the length of one side

9. Area of Octagon

A 4.83s2 where s is the length of one side

10. Sphere

Total surface area A 4r2

Surface area of segment As dh

Volume V r3

Volume of segment

Vs (3r " h)

Vs (h2 ! 3a2) where a radius of segment baseh6

h2

3

43

aa ! b2b

(D ! d)2

4

Adh

" 0.60843

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11. Volume of a Cylinder

V d2L where L is cylinder length

12. Pyramid

Volume

V base area perpendicular height

Volume of frustum

VF A ! a ! where h is the

perpendicular height, A and a are areas as shown

13. Cone

Area of curved surface of cone:

A

Area of curved surface of frustum

AF

Volume of cone:

V

Volume of frustum:

VF

Applied Mechanics

Scalar —a property described by a magnitude only

Vector —a property described by a magnitude and a direction

Velocity—vector property equal to

The magnitude of velocity may be referred to as speed or

Speed of sound in dry air is 1085.7 at 32°F and increases by about 1.4 for

each °F rise

fts

fts

mih

fts

displacement

time

perpendicular height (R2 ! r2 ! Rr)

3

base area perpendicular height

3

(D ! d)L2

DL2

B2AaAh3

13

4

409

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Acceleration—vector property equal to

Acceleration due to gravity, symbol “g”, is 32.2

Linear Velocity and Acceleration

u initial velocity

v final velocity

t elapsed time

s displacement

a acceleration

Angular Velocity and Acceleration

angular displacement (radians)

angular velocity (radians/s); 1 initial, 2 final

angular acceleration (radians/s2)

2 1 ! t

t

1 t ! 1/2 t2

22 1

2 ! 2

linear displacement, s r

linear velocity, v r

linear, or tangential acceleration, aT r

Tangential, Centripetal and Total Acceleration

Tangential acceleration aT is due to angular acceleration

aT r

Centripetal (Centrifugal) acceleration ac is due to change in direction only

ac v2/r r 2

Total acceleration, a, of a rotating point experiencing angular acceleration isthe vector sum of aT and ac

a aT ! ac

Force

Vector quantity, a push or pull which changes the shape and/or motion of anobject

The unit of force is the pound lb

1 ! 2

2

fts2

fts2

change in velocity

time

v u ! at

s t

s ut ! at2

v2 u2 ! 2 as

12

av ! u2b

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Weight

The gravitational force of attraction between a mass, m, and the mass of theEarth

The mass of an object (rarely used), in slugs, can be calculated from the knownweight in pounds

m g 32.2

Newton’s Second Law of Motion

An unbalanced force F will cause an object of weight w to accelerate a, accord-ing to:

F a, where w is weight

Torque Equation

T where T is the acceleration torque, I is the moment of inertiain lb ft2 and is the angular acceleration in radians/s2

Momentum

Vector quantity, symbol p,

p v, where w is weight

Work

Scalar quantity, equal to the (vector) product of a force and the displacementof an object. In simple systems, where W is work, F force and s distance

W F s ft-lb

Energy

Energy is the ability to do work, the units are the same as for work; ft-lb

Kinetic Energy

Energy due to motion

Ek v2 where w is weightw2g

wg

Iag

wg

fts2

Weight

g

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Kinetic Energy of Rotation

ER k22 where k is radius of gyration, is angular velocity in rad/s

or

ER I2 where I k2 is the moment of inertia

Centripetal (Centrifugal) Force

FC where r is the radius

or

FC 2 r where is angular velocity in rad/s

Potential Energy

Energy due to position in a force field, such as gravity

Ep w h

where w is weight, and h is height above some specified datum

Thermal Energy

The units of thermal energy are British Thermal Units (Btu)

Conversions: 1 Btu 778 ftlb

Electrical Energy

The unit of electrical energy is the kWh

Conversions: 1 kWh 3,412 Btu 2.66 106 ftlb

Power

A scalar quantity, equal to the rate of doing work

The units are:

Mechanical Power— , horsepower hp

Thermal Power—

Electrical Power—W, kW, or hp

Conversions: 746 W 1 hp

1 h.p. 550 ,

1 kW 0.948 Btu

s

ftlbs

Btus

ftlbs

wg

wv2

gr

wg

12

wg

12

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Pressure

A vector quantity, force per unit area

The basic unit is the pound per square inch, psi

Atmospheric Pressure

At sea level atmospheric pressure equals 14.7 psi

Pressure Conversions

Pressure may be expressed in standard units, or in units of static fluid head.

Common equivalencies are:

1 kPa 0.294 in. mercury 7.5 mm mercury

1 kPa 4.02 in. water 102 mm water

1 psi 2.03 in. mercury 51.7 mm mercury

1 psi 27.7 in. water 703 mm water

1 m H2O 9.81 kPa

Other pressure unit conversions:

1 bar 14.5 psi 100 kPa

1 kg/cm2 98.1 kPa 14.2 psi 0.981 bar

1 atmosphere (atm) 101.3 kPa 14.7 psi

Simple Harmonic Motion

Velocity of P

Acceleration of P 2 x

The period or time of a complete oscillation

seconds

General formula for the period of S.H.M.

T 2

Simple Pendulum

T 2 T period or time in seconds for a double swing

L length in feet

ALg

Adisplacementacceleration

2

1R2 " x2

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The Conical Pendulum

R/H tan Fc/W 2 R/g

Lifting Machines

W load lifted, F force applied

M.A.

V.R. (velocity ratio)

efficiency

1. Lifting Blocks

V.R. number of rope strands supporting the load block

2. Wheel & Differential Axle

Velocity ratio

2 R

Or, using diameters insteadof radii,

Velocity ratio

3. Inclined Plane

V.R.

4. Screw Jack

V.R. circumference of leverage

pitch of thread

length

height

2D(d " d1)

2Rr " r1

2R2(r " r1)

2

M.A.V.R.

effort distanceload distance

WF

loadeffort

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Indicated Horse Power

I.H.P. where I.H.P. is power in W, Pm is mean or “average” effec-tive pressure in psi, A is piston area in in2, L is length ofstroke in ft and N is number of power strokes per min

Brake Horse Power

B.H.P. T

for prony brake D w is weight on rim s is balance readingon other side

Stress, Strain and Modulus of Elasticity

Direct stress

Direct strain

Modulus of elasticity

E

Shear stress

Shear strain

Modulus of rigidity

G

Thermodynamics

Temperature Scales

°C (°F " 32) °F °C ! 32

°R °F ! 460 (R Rankine) K °C ! 273 (K Kelvin)

Sensible Heat Equation

Q wcT

w is weight

c is specific heat

T is temperature change

95

59

shear stressshear strain

xL

forcearea under shear

PLA¢/

P/A¢//L

direct stressdirect strain

extensionoriginal length

/L

loadarea

PA

(w " s) (speed of rim in ft per min)

33000

PmA L N33000

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Latent Heat

Latent heat of fusion of ice 144 Btu/lb

Latent heat of steam from and at 212°F 1,207,385 Btu/lb

1 ton of refrigeration 31,753 Btu/day

220 Btu/min

Gas Laws

1. Boyle’s Law

When gas temperature is constant

PV constant or

P1V1 P2V2

where P is absolute pressure and V is volume

2. Charles’ Law

When gas pressure is constant, constant

or , where V is volume and T is absolute temperature

3. Gay-Lussac’s Law

When gas volume is constant, constant

Or , where P is absolute pressure and T is absolute temperature

4. General Gas Law

constant

P V w R T where P absolute pressure (lb/ft2)

V volume (ft3)

T absolute temp (°R)

w weight (lb)

R characteristic constant (ftlb/lb°R)

P1V1

T1

P2V2

T2

P1

T1

P2

T2

PT

V1

T1

V2

T2

VT

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Efficiency of Heat Engines

Carnot Cycle

Air Standard Efficiencies

1. Spark Ignition Gas and Oil Engines (Constant Volume Cycle orOtto Cycle)

1 " where rv compression ratio

2. Diesel Cycle

1 " where r ratio of compression

R ratio of cut-off volume to clearance volume

3. High Speed Diesel (Dual-Combustion) Cycle

1 "

where rv

k

volume at end of constant P heating (combustion)

clearance volume

absolute pressure at end of constant V heating (combustion)

absolute pressure at beginning of constant V combustion

cylinder volume

clearance volume

k " 1rv

"1 [(k " 1) ! k(b " 1)]

(R " 1)rv

"1 (R " 1)

specific heat (constant pressure)

specific heat (constant volume)

cylinder volume

clearance volume1

rv( "1)

where T1 and T2 are absolute temperatures ofheat source and sink

T1 " T2

T1

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4. Gas Turbines (Constant Pressure or Brayton Cycle)

1 "

where rp pressure ratio

Heat Transfer by Conduction

Q

where Q heat transferred in Btu

thermal conductivity or coefficient of heat transfer in

A area in ft2

t time in hr

T temperature difference between surfaces in °F

d thickness of layer in ft

Btu ftft2 n °F

AtTd

compressor discharge pressure

compressor intake pressure

1

rp

a "1 b

Coefficients of Thermal Conductivity

Material Coefficient ofThermal Conductivity

Aluminum 230Brick 0.4Concrete 0.54Copper 398Cork 0.026Felt 0.03Glass 0.5Glass, fiber 0.63Iron, cast 60Tin 20Wood 0.20Wallboard, paper 0.034

Btu ft(n•ft2)(°F/ft)

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Thermal Expansion of Solids

Increase in length L (T2 – T1)

where L original length

coefficient of linear expansion

(T2 – T1) rise in temperature

Increase in volume V (T2 – T1)

Where V original volume

coefficient of volumetric expansion

(T2 – T1) rise in temperature

coefficient of volumetric expansion coefficient of linear expansion 3

3

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Chemical Heating Value of a Fuel

Chemical Heating Value Btu/lb of fuel 145000 C ! 53400 !4000 S

C is the mass of carbon per lb of fuel

H2 is the mass of hydrogen per lb of fuel

O2 is the mass of oxygen per lb of fuel

S is the mass of sulfur per lb of fuel

Theoretical Air Required to Burn Fuel

Air (lb per lb of fuel)

Air Supplied from Analysis of Flue Gases

Air in lb per lb of fuel

C is the percentage of carbon in fuel by weight

N2 is the percentage of nitrogen in flue gas by volume

CO2 is the percentage of carbon dioxide in flue gas by volume

CO is the percentage of carbon monoxide in flue gas by volume

Boiler Formulae

Equivalent evaporation

Factor of evaporation

Boiler efficiency

where mass flow rate of steam

h1 enthalpy of steam produced in boiler

h2 enthalpy of feedwater to boiler

mass flow rate of fuelw#

f

w#

s

#ws (h1 " h2)#

wf calorific value of fuel

(h1 " h2)970.3 Btu/lb

#ws (h1 " h2)970.3 Btu/lb

N2

33 (CO2 ! CO) C

c 83

C ! 8 aH2 "O2

8b ! S d 100

23

aH2 "O2

8b

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Fluid Mechanics

Discharge from an Orifice

Let A cross-sectional area of the orifice (/4)d2

and Ac cross-sectional area of the jet at the vena contracta = ((/4)

then Ac CcA

or Cc

where Cc is the coefficient of contraction

At the vena contracta, the volumetric flow rate Q of the fluid is given by

Q area of the jet at the vena contracta actual velocity

Acv

or Q CcACv

The coefficients of contraction and velocity are combined to give the coefficientof discharge, Cd

i.e. Cd CcCv

and Q CdA

Typically, values for Cd vary between 0.6 and 0.65

Circular orifice: Q 0.62 A

Where Q flow (ft3/s) A area (ft2) h head (ft)

Rectangular notch: Q 0.62 (B H)

Where B breadth (ft) H head (ft above sill)

Triangular Right Angled Notch: Q 2.635 H5/2

Where H head (ft above sill)

22gh23

22gh

22gh

22gh

Ac

A adc

db 2

d2c

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Bernoulli’s Theory

H h !

H total head (ft) w specific weight (lb/ft3)

h height above datum level (ft) v velocity of water (ft per second)

P pressure (lb/ft2)

Loss of Head in Pipes Due to Friction

Loss of head in meters f

L length in ft v velocity of flow in ft per second

d diameter in ft f constant value of 0.01 for large pipes to 0.02for small pipes

Note: This equation is expressed in some textbooks as

Loss 4f where the f values range from 0.0025 to 0.005

Electricity

Ohm’s Law

I

or E IR

where I current (amperes)

E electromotive force (volts)

R resistance (ohms)

Conductor Resistivity

R

where specific resistance (or resistivity) (ohm inches, Ω·in)

L length (inches)

a area of cross-section (square inches)

Temperature correction

Rt Ro (1 ! t)

where Ro resistance at 0°C ()

Rt resistance at t°C ()

La

ER

Ld

v2

2g

Ld

v2

2g

Pw

!v2

2g

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temperature coefficient which has an average value for copper of0.004 28 (/°C)

R2 R1

where R1 resistance at t1 ()

R2 resistance at t2 ()

Dynamo Formulae

Average e.m.f. generated in each conductor

where Z total number of armature conductors

c number of parallel paths through winding between positive andnegative brushes where c 2 (wave winding), c 2p (lap winding)

useful flux per pole (webers), entering or leaving the armature

p number of pairs of poles

N speed (revolutions per minute)

Generator Terminal volts EG " IaRa

Motor Terminal volts EB ! IaRa

where EG generated e.m.f.

EB generated back e.m.f.

Ia armature current

Ra armature resistance

Alternating Current

R.M.S. value of sine curve 0.707 maximum value

Mean value of sine curve 0.637 maximum value

Form factor of sinusoidal

Frequency of alternator cycles per second

Where p number of pairs of poles

N rotational speed in r/min

pN

60

R.M.S. valueMean value

0.7070.637

1.11

2NpZ

60c

(1 ! t2)(1 ! t1)

Values /ºC

copper 0.00428platinum 0.00385nickel 0.00672tungsten 0.0045aluminum 0.0040

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Slip of Induction Motor

100

Inductive Reactance

Reactance of AC circuit (X) 2fL ohms

where L inductance of circuit (henries)

Inductance of an iron cored solenoid henries

where T turns on coil

magnetic permeablility of core

A area of core (square centimeters)

L length (centimeters)

Capacitance Reactance

Capacitance reactance of AC circuit ohms

where C capacitance (farads)

Total reactance ohms

Impedence (Z)

Current in AC Circuit

Current

Power Factor

p.f.

also p.f. cos , where is the angle of lag or lead

Three Phase Alternators

Star connected

Line voltage phase voltage

Line current phase current

Delta connected

Line voltage phase voltage

Line current phase current23

23

true wattsvolts amperes

impressed volts

impedance

AR2 ! a2fL "1

2fCb 2

ohms

2(resistance)2 ! (reactance)2

a2fL "1

2fCb

12fC

1.256T2 AL 108

Slip speed of field " speed of rotor

Speed of field

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Three phase power

P EL IL cos

EL line voltage

IL line current

cos power factor

23

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Ion Names and Formulae

Monatomic Polyatomic

Ag! silver ion BO33" borate ion

Al3! aluminum ion C2H3O2" acetate ion

Au! and Au2! gold ion ClO" hypochlorite ionBe2! beryllium ion ClO2

" chlorite ionCa2! calcium ion ClO3

" chlorate ionCo2! and Co3! cobalt ion ClO4

" perchlorate ion Cr2! and Cr3! chromium ion CN" cyanide ionCu! and Cu2! copper ion CO3

2" carbonate ionFe2! and Fe3! iron ion C2O4

2" oxalate ionK! potassium ion CrO4

2" chromate ionLi! lithium ion Cr2O7

2" dichromate ionMg2! magnesium ion HCO3

" hydrogen carbonate or bicarbonate ionNa! sodium ion H3O! hydronium ionZn2! zinc ion HPO4

2" hydrogen phosphate ionH2PO4

" dihydrogen phosphate ionHSO3

" hydrogen sulfite or bisulfite ionHSO4

" hydrogen sulfate or bisulfate ionMnO4

" permanganate ionN3

" azide ionNH4

! ammonium ionNO2

" nitrite ionNO3

" nitrate ionO2

2" peroxide ionOCN" cyanate ionOH" hydroxide ionPO3

3" phosphite ionPO4

3" phosphate ionSCN" thiocyanate ionSO3

2" sulfite ionSO4

2" sulfate ionS2O3

2" thiosulfate ion

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