Engineering Hand Book
Transcript of Engineering Hand Book
-
7/25/2019 Engineering Hand Book
1/42
Industrial Development & Engineering Associates (IDEA) is a company
specializing in the sourcing and supply of standard and customized products
to the industrial markets of Pakistan, with major focus on Oil & Gas,
Petroleum Refining, Petrochemical, Power , Fer ti lizer, Cement, Chemical
and Textile Industries.
IDEA provides an extensive range of client support services based on the
worldwide information and business expertise of our company. We put
together a world of resources representing leading manufac turers and
trading companies from the world: USA, Canada, Europe, Japan Far
East.
Air and Hydraulic Cylinders
f') Air Compressors
f') Air Filters
f') Air Pollution Control Solutions
~ Aluminium Castings
Bearings
eBelting
Boilers
f') Bolt Fasteners
CNC Machinery
Construction Equipment Supplies
Controls
Corrosion Control Equipment
f') Cutting Tools
f') Elect ric and Electronic Enclosures
Electric Heaters
Electronic Components
~ Flow Meters
Fluid Handling Equipment
Gas Detectors
Gaskets
Gears
Heat Exchangers
o Heat ing Elements
() Hose Fittings
f) HVAC Equipment
.f)
Hydraulic Equipment
Iron and Steel Bars and Rods
f) Loading Arms
f>
Material Handling Equipment
f') Pipe Fittings
f') Pollution Control Equipment
() Precision Guage
tr Y
Pressure Sensors
Pressure Vessels
fi
Printed Circuit Boards
f') Pumps
f')
Reverse Osmosis Plants
f) Stainless Steel
f') Stainless Steel Fitt ings
() Stainless Steel Pipes
o
Steel Forgings
Temperature Sensors
Vacuum Pumps
Variable Speed Drives/Motors
e Waste Water Treatment Plant
Table of Contents
Chapter 1
Definition and Abbreviations for Physical Quantities 1
Chapter 2
Units of Physical Quantities 3
Chapter
3
System of Units 23
Chapter 4
General Mathematical Formulae 27
4.1 Algebra.................. ...... 27
4.2 Geometry .............................................................. 29
4.3 Trigonometry ........................................................... 39
4.4 Logarithm ...... . 40
4.5 Exponents .. ....... .. . .42
4.6 Complex Numbers ....... ........................................ 42
Chapter 5
Engineering Concepts and Formulae .44
5.1 Electricity.. ..................... . 44
5.2 Applied Mechanics 57
5.2.1 Newton'slawsof motion . 57
5.2.2 LinearVelocity And Acceleration 60
5.2.3
5.2.4 Centripetal (Centrifugal) Force . . . 62
5.2.5 Stress,StrainAnd Modulus Of Elasticity.... . 64
5.3 Thermodynamics 64
5.3.1 Laws of Thermodynamics 64
5.3.2 Momentum 65
5.3.3 Impulse . 65
5.3.4 Elastic and Inelastic collision 65
5.3.5 Center of Mass 65
5.3.6 Angu lar Motion 65
-
7/25/2019 Engineering Hand Book
2/42
5.4
5.3.7 Conditions of Equilibrium ..
5.3.8 Gravity.
5.3.9 Vibrations & Waves.
5.3.10 Standing Waves .
5.3.11 Beats..
5.3.12 Temperature and Heat..
5.3.13 IdealGases..
5.3.14 Elastic Deformation .
5.3.15 Temperature Scales.
5.3.16 Sensible Heat Equation .
5.3.17 Latent Heat.
5.3.18 Gas Laws .
5.3.19 Specific Heats Of Gases ..
5.3.20 Efficiency of Heat Engines ..
5.3.21 Heat Transfer by Conduction .
5.3.22 Thermal Expansion of Solids .
5.3.23 Chemical Heating Value of a Fuel.
Fluid Mechanics .
5.4.1 Discharge from an Orifice.
5.4.2 Bernoulli's Theory .
5.4.3 Actual pipe dimensions .
65
66
66
66
66
..67
67
..68
68
68
68
68
69
70
71
72
..72
77
.77
. 78
78
Chap ter 6
References 80
6.1 Periodic Table of Elements 80
6.2 Resistor Color Coding 81
Formulas and Conversions
C
Chapter 1
Def in it ion and Abbrev iat ions for Phys ical Quan ti ti es
Svmb ol Un it
Ouantitv
m meter
l.enqth
kg kilogram
Mass
s second Time
A ampere
Electric current
K
kelvin Thermodynamic temp
cd candela Luminous intensity
Quantity Unit Symbol
Equivalent
Planeangle radian rad
-
Force newton N kg . m/s'
Work, energy heat joule JNm
Power watt W
J/s
Frequency hertz
Hz
s'
Viscosity:
-
m'/s
10 c St
kinematic
(Centistoke)
Viscosity:
-
Ns/rrf
10
3
cP
Dynamic (Centipoise)
Pressure
-
Pa or N/m' pascal, Pa
Symbol
Pr ef ix Fact or by which uni t is
multiplied
T Tera 10
12
G Giaa 10'
M
Mega
10
-1-
-
7/25/2019 Engineering Hand Book
3/42
Formulas and Conversions
Symbol
Prefix
Factorby which uni t i s
multiplied
k Kilo 10
3
h
Hecto 10'
da Deca 10
d Deci
10-
1
c
Centi
10-'
m
Milli
10-
3
jJ
Micro
10-
n
Nano
10-
9
p Pico 10-
1
Quantity
Electrical
Symbol Deri ved
uni t unit
Potential Volt V
W/A
Resista nce Ohm
'Q
VIA
Charge
Coulomb C As
Capacitance
Farad F As;V
Electric field
-
Vim
-
strength
Electric flux
-
C/m'
-
density
Quantity
Magnetic Symbol Deri ved unit
uni t
Magnetic flux
Weber Wb
Vs
=
Nm/A
Inductance Henry H
Vs/A
=
Nm/A'
Magnetic field
- A/m
-
strength
,
Magnetic flux density Tesla T
Wb/m'
=
(N)/(Am)
- 2 -
Formulas and Conversions
[ Chapter 2 r;;) I
Units of Physical Quanti ties
Conversion Factors (general):
1 acre
=
43,560 square feet
1 cubic foot
=
7.5 gallons
1 foot = 0.305 meters
1 gallon
=
3.79 liters
1 gallon
=
8.34 pounds
1 grain per gallon = 17.1 mg/L
1 horsepower
=
0.746 kilowatts
1 million gal lons per day
=
694 gallons per minute
1 pound
=
0.454 kilograms
1 pound per square inch
=
2.31 feet of water
Degrees Celsius = (Degrees Fahrenheit - 32) (5/9)
Degrees Fahrenheit = (Degrees Celsius) (9/5) + 32
1
% =
10,000 mg/L
Name
To convert f rom
To
Multiply
Divide by
bv
Acceleration ft/sec rn/s 0.3048 3.2810
Area
acre m' 4047
2.471E-04
Area ft'
m'
9.294E-02
10.7600
Area
hectare m'
1.000E+04
1.000E-04
Area
in
2
m'
6.452E-04
1550
Density
g/cm
3
kq/rn 1000
1.000E-03
Density
lbrn/ft kq/rn 16.02
6.243E-02
Density lbm/in?
kq/rrr' 2.767E+04
3.614E-05
- 3 -
-
7/25/2019 Engineering Hand Book
4/42
Formulas and Conversions
Name
To co nver t f ro m
To
Multiply
Divide by
by
Density
Ibs'/in
4
kg/m
3
1.069E+07
9.357E-08
Density sluq/ft
kg/m
3
515.40
1. 940E-03
Energy BTU J
1055
9.478E-04
Energy cal J
4.1859 0.2389
Energy erg
J
1.000E-07
1.000E+07
Energy
eV J
1.602E-19
6.242E+18
Energy Ftlbf
J
1.3557
0.7376
Energy
kiloton TNT J
4.187E+12
2.388E-13
Energy
KWhr J
3.600E+06
2.778E-07
Energy
Megaton TNT J 4.187E+15 2.388E-16
Force
Dyne N
1.000E-05
1.000E+05
Force
Lbf N
4.4484
0.2248
Force
Ozf N 0.2780 3.5968
Heat capacity
BTU/lbm . of
J/kg .O(
4188
2.388E-04
Heat transfer coefficient
BTU/hr-ft'.of
W/m'O(
5.6786 0.1761
Length
AU
m
1.496E+ll
6.685E-12
Length
ft
m 0.3048 3.2810
Length
in
m
2.540E-02
39.3700
Length
mile m 1609
6.214E-04
Length Nautical mile
m 1853
5.397E-04
Length
parsec m 3.085E+ 16
3.241E-17
Mass amu
kg
1.661E-27
6.022E+26
Mass
Ibm kg
0.4535
2.2050
Mass
Ibs'/in kg 1200.00
5.711E-03
Mass
slug kg
14.59
6.853E-02
Mass flow rate
lbrn/hr kg/s
1.260E-04
7937
- 4-
Formulas and Conversions
To convert from
To
Multiply
Divide by
Name
by
Mass fl ow r at e
lbrn/sec kg/s
0.4535
2.2050
Moment of inertia
ft -lb s' kgm'
1.3557
0.7376
Moment o f i ne rt ia
inIbs kq-rrr' 0.1130 8.8510
Moment of inertia
.
,
kgm'
7.062E-03
141.60
zm-s
power
BTU/hr
W 0.2931
3.4120
power
hp
W
745.71
1.341E-03
power
tons of refrigeration W
3516
2.844E-04
Pressu re
bar
Pa
1.000E+05
1.000E-05
Pressure
dyne/em
Pa
0.1000
10.0000
Pressure
in. mercury
Pa
3377
2.961E-04
Pressu re
in. water Pa
248.82
4.019E-03
Pressure
kgf/cm'
Pa
9.807E+04
1.020E-05
Pressu re
Ibf/ft'
Pa
47.89
2.088E-02
Pressure
lbf/irr'
Pa
6897
1.450E-04
Pressure
mbar
Pa
100.00
1.000E-02
Pressure
microns mercury
Pa 0.1333
7.501
Pressure
mm mercury Pa
133.3
7.501E-03
Pressure std atm
Pa
1.013E+05
9.869E-06
Specif ic heat
BTU/lbmoF
J/kg .O(
4186
2.389E-04
Spec if ic heat cal/g'O(
J/kg'O( 4186
2.389E-04
Temperature
of
O(
0.5556
1.8000
Thermal conduct iv ity
BTU/hrftoF
W/mO(
1.7307
0.5778
Thermal conductivity BTU in/hrft'oF
W/mO(
0.1442
6.9340
The rmal conductivity cal/cmsO( W/mO( 418.60 2.389E-03
Thermal conduct ivity
cal/fthroF
W/mO( 6.867E-03 145.62
Time
day
S
8.640E+04
1.157E-05
- 5 -
-
7/25/2019 Engineering Hand Book
5/42
I
. .
Formulas and Conversions
Multiply
By To obtain
I
Fathom
1.8288'
meter(m)
Formulas and Conversions
Foot
0.3048' meter(m)
30.48'
Foot
centimeter(cm)
Name To convert from To
Multiply
Di vi de b y
304.8'
by
Foot
millimeter(mm)
Time sidereal year S 3.156E+07
3.169E-08
Inch
0.0254' meter(m)
I
Torque
ftlbf
2.54'
centimeter( cm)
Nm
1.3557
0.7376
Inch
Torque
inlbf
N'm
0.1130 8.8504
Inch
25.4'
millimeter(mm)
Torque
In -ozf
Nm
7.062E-03
141.61
Kilometer
0.6213712 mile(USstatute)
Velocity ft/min rn/s
5.079E-03
196.90
Meter
39.37008 Inch
Velocity
ft/s rn/s 0.3048
3.2810
Meter
0.54680066 Fathom
Velocity
Km/hr rn/s
0.2778 3.6000
1
Meter
3.280840 Foot
Velocity miles/hr rn/s
0.4470
2.2370
Meter
0.1988388 Rod .
Viscosity - absolute
centipose
Ns/m'
1.000E-03
1000
Meter
1.093613
Yard
Viscosity - absolute
q/crns
Ns/m'
0.1000 10
Meter
0.0006213712 mile(USstatute)
Viscosity - absolute
Ibf/ft's
Ns/m'
47.87
2.089E-02
Microinch
0.0254'
microrneterfmicronjfum)
~ o o
iscosity - absolute lbrn/fts
Ns/m'
1.4881
0.6720
micrometer(m icron) 39.37008 Microinch
Viscosity - kinematic
centistoke
m'/s
1.000E-06 1.000E+06
mile(USstatute)
1,609.344 .
meter(m)
Viscosity - kinematic
fe/see
m'/s
9.294E-02
10.7600
mile(USstatute) 1.609344 . kilometer(km)
Volume ft
3
m
3
2.831E-02 35.3200
millimeter 0.003280840 Foot
Volume
in
3
m
3
1.639E-05
6.102E+04
millimeter
0.0397008 Inch
'~
Volume
Liters
m
3
1.000E-03
1000
Rod
5.0292'
meter(m)
~
Volume
U.S. gallons m
3
3.785E-03
264.20
Yard 0.9144'
meter(m)
Volume flow rate
ft
3
/min
m
3
/s
4.719E-04 2119
Volume flow rate U.S. gallons/min
m
3
/s
To Convert
To Mul ti pl y By
6.309E-05
1.585E+04
'-=---
Cables Fathoms
120
A. DISTANCE (Length) Cables
Meters
219.456
.
Conversions
Cables
Yards 240
Multiply By To obtain
LENGTH
Centimeter 0.03280840 foot
- 7 -
Centimeter 0.3937008 inch
- 6 -
.. :. ..
-
7/25/2019 Engineering Hand Book
6/42
Formulas and Conversions
To Convert
To
Multiply By
Centimeters
Meters
0.01
Centimeters
Yards
0.01093613
Centimeters
Feet
0.0328084
Centimeters
Inches
0.3937008
Chains, (Surveyor's)
Rods
4
Chains, (Surveyor's) Meters
20.1168
Chains, (Surveyor's)
Feet
66
Fathoms Meters
1.8288
Fathoms
Feet
6
Feet
Statute Miles
0.00018939
Feet
Kilometers
0.0003048
Feet
Meters
0.3048
Feet
Yards
0.3333333
Feet
Inches
12
Feet
Centimeters
30.48
Furlongs
Statute Miles
0.125
Furlongs
Meters
201.168
Furlongs Yards
220
Furlongs
Feet
660
Furlongs
Inches
7920
Hands (Height Of Horse) Inches
4
Hands (Height Of Horse)
Centimeters
10.16
Inches
Meters
0.0254
Inch es
Yards
0.02777778
Ir.ches Feet
0.08333333
Inches
Centimeters
2.54
Inches
Millimeters
25.4
Formulas and Conversions
- 8-
To Convert
To
Multiply By
Kilometers
Statute Miles 0.621371192
Kilometers
Meters
1000
Leagues, Nautical
Nautical Miles 3
Leagues, Nautical Kilometers
5.556
Leagues, Statute
Statute Miles 3
Leagues, Statute
Kilometers 4.828032
Links, (Surveyor's) Chains 0.01
Links, (Surveyor's) Inches 7.92
Links, (Surveyor's) Centimeters
20.1168
Meters Statute Miles
0.000621371
Meters Kilometers
0.001
Meters Yards
1.093613298
Meters Feet 3.280839895
Meters Inches
39.370079
Meters
Centimeters 100
Meters
Millimeters
1000
Microns
Meters
0.000001
Microns
Inches
0.0000394
Miles, Nautical
Statute Miles
1.1507794
Miles, Nautical
Kilometers
1.852
Miles, Statute
Kilometers
1.609344
Miles, Statute
Furlongs 8
Miles, Statute
Rods
320
Miles, Statute
Meters 1609.344
Miles, Statute
Yards
1760
Miles, Statute
Feet 5280
Miles, Statute
Inches
63360
- 9 -
-
7/25/2019 Engineering Hand Book
7/42
Formulas and Conversions
To Convert
To Multiply By
Miles, Statute Centimeters
160934.4
Millimeters
Inches 0.039370079
Mils Inches 0.001
Mils ~1illimeters 0.0254
Paces(US)
Inches 30
Paces (US) Centimeters 76.2
Points (Typographical) Inches 0.013837
Points (Typographical)
Millimeters
0.3514598
Rods Meters 5.0292
Rods Yards 5.5
Rods Feet 16.5
Spans Inches
9
Spans
Centimeters 22.86
Yards Miles 0.00056818
Yards
Meters 0.9144
Yards
Feet
3
Yards
Inches 36
Yards
Centimeters
91.44
Conversion
Length
1 ft
=
12 in
1 yd = 3 ft
1 cm = 0.3937 in
1 in = 2.5400 cm
1 m
=
3.281 ft 1 ft
=
0.3048 m
1 m
=
1.0936 yd
1 yd
=
0.9144 m
1 km = 0.6214 mile 1 mile = 1.6093 km
1 furlong = 40 rods
1 fathom
=
6 ft
Formulas and Conversions
Conversion
1 statute mile
=
8 furlongs
1 rod = 5.5 yd
1 statute mile = 5280 ft
1 in
=
100 mils
1 nautical mi le = 6076 ft
1 l ight year
=
9.461 x 10
15
m
1 league = 3 miles
1 mil = 2.540 x 10'5 m
Area
1 ft' - 144 in'
1 acre
=
160 rod'
1 yd'
=
9 ft'
1 acre
=
43,560 ft>
1 rod' = 30.25 yd'
1 mile'
=
640 acres
1 cm'
=
0.1550 in'
1 in' = 6.4516 crrr'
1 m'
=
10.764 ft>
1 ft>
=
0.0929 m'
1 krn'
=
0.3861 mile'
1 mile'
=
2.590 km'
Volume
1 ern
=
0.06102 in
3
1 in
3
=
16.387 ern
1 m
3
= 35.31 ft3
1 ft
3
= 0.02832 m
3
1 Litre = 61.024 in
3
1 in
3
=
0.0164 litre
1 Litre
=
0.0353 ft3
1 ft
3
= 28.32 litres
1 Litre
=
0.2642 gal. (U.S.)
1 yd
3
= 0.7646 m
3
1 Litre
=
0.0284 bu (U.s.)
1 gallon (US) = 3.785 litres
1 Litre
=
1000.000 ern?
1 gallon (US) = 3.785 X 10'3 m
3
1 Litre
=
1.0567 qt. (liquid) or
1 bushel (US)
=
35.24 litres
0.9081 qt. (dry)
1 oz (US fluid) = 2.957 X 10'5 m
3
1 stere
=
1 m
3
Liquid Volume
1 gill = 4 fluid ounces
1 barrel
=
31.5 gallons
1 pint = 4 gills
1 hogshead = 2 bbl (63 gal)
1 quart = 2 pints
1 tun = 252 gallons
1 gallon = 4 quarts
1 barrel (petrolum) = 42 gallons
- 11 -
- 10 -
-
7/25/2019 Engineering Hand Book
8/42
Formulas and Conversions
Conversion
Dry Volume
1
quart =
2
pints
1
quart =
67.2
in'
1
peck =
8
quarts
1
peck =
537.6
in'
1
bushel =
4
pecks
1
bushel
= 2150.5
in'
B. Area
Conversions
Multiply
By
To obtain
AREA
acre
4,046.856
meter> (rn)
acre
0.4046856
hectare
centimeter> 0.1550003
inch'
centimeter>
0.001076391
foot>
foot'
0,09290304' meter' (rn)
foot'
929.0304'
centimeter> (ern)
foot'
92,903.04
millimeter> (rnrn)
hectare
2.471054
acre
inch'
645.16'
millimeter> (rnm)
inch'
6.4516
centimeter> (ern)
inch'
0,00064516
meter> (rn)
meter'
1,550.003 inch'
meter'
10.763910
foot>
meter'
1.195990
yard'
meter'
0.0002471054
acre
millimeter>
0,00001076391
foot'
millimeter> 0.001550003
inch'
yard'
0.8361274
meter> (rn')
- 12 -
Formulas and Conversions
c . Volume
Conversions
MetricConversionFactors:Volume(includingCapacity)
Multiply
By
To obtain
VOLUME(including CAPACITY)
centimeter'
0.06102376
inch
foot'
0.028311685
meter' (rn)
foot'
28,31685
liter
gallon (UK liquid)
0,004546092
meter (rrr')
gallon (UK liquid)
4,546092
litre
gallon (US liquid)
0,003785412
meter' (rn)
gallon (USliquid)
3,785412
liter
inch'
16,387,06
millimeter' (rnrn)
inch'
16,38706
centimeter' (ern)
inch?
0,00001638706
meter? (rn)
Liter
0,001 '
meter? (rn)
Liter
0,2199692
gallon (UK liquid)
Liter
0,2641720
gallon (US liquid)
Liter
0,03531466
foot
3
meter'
219,9692
gallon (UK liquid)
meter'
264,1720
gallon (US liquid)
meter'
35,31466
foot'
meter'
1,307951
yard
3
meter'
1000:
liter
meter'
61,023,76
inch'
millimeter'
0,00006102376
inch?
Yard
3
0,7645549
meter' (rrr')
D. Mass and Weight
Conversions
- 13 -
-
7/25/2019 Engineering Hand Book
9/42
Formulas and Conversions
To Convert To Multiply By
Carat
Milligrams 200
Drams, Avoirdupois
Avoirdu pois Ounces 0.06255
Drams, Avoirdupois
Grams
1.7718452
Drams, Avoirdupois Grains 27.344
Drams, Troy Troy Ounces
0.125
Drams, Troy
Scruples 3
Drams, Troy
Grams
3.8879346
Drams, Troy Grains
60
Grains
Kilograms
6.47989E-05
Grains Avoirdupois Pounds
0.00014286
Grains
Troy Pounds
0.00017361
Grains
Troy Ounces
0.00208333
Gra ins Avoirdupois Ounces
0.00228571
Grains
Troy Drams
0.0166
Grains Avoirdupois Drams
0.03657143
Grains Pennyweig hts
0.042
Grains
Scruples
0.05
Grains Grams
0.06479891
Grains Milligrams 64.79891
Grams
Kilograms 0.001
Grams Avoirdupois Pounds
0.002204623
Grams Troy Pounds
0.00267923
Grams Troy Ounces
0.032150747
Grams Avoirdupois Ounces
0.035273961
Grams Avoirdupois Drams
0.56438339
Grams Grains
15.432361
- 14 -
Formulas and Conversions
To Convert
To
Multiply By
Milligrams 1000
Grams
Hundredweights, Long
Long Tons
0.05
Hundredweights, Long
Metric Tons
0.050802345
Hundredweights, Long
Short Tons
0.056
Hundredweights, Long
Kilograms
50.802345
Hundredweights, Long
Avoirdupois Pounds
112
Hundredweights, Short
Long Tons
0.04464286
Hundredweights, Short
Metric Tons
0.045359237
Hundredweights, Short
Short Tons
0.05
Hundredweights, Short
Kilograms
45.359237
Hundredweights, Short
Avoirdupois Pounds
100
Kilograms
Long Tons
0.0009842
Kilograms
Metric Tons
0.001
Kilograms
Short Tons
0.00110231
Kilograms
Short Hundredweights
0.02204623
Kilograms
Avoirdupois Pound~ 2.204622622
Kilograms
Troy Pounds
2.679229
Kilograms Troy Ounces
32.15075
Kilograms
Avoirdupois Ounces
35.273962
Kilograms
Avoirdupois Drams
564.3834
Kilograms
Grams
1000
Kilograms
Grai ns
15432.36
Milligrams
Grains
0.015432358
Ounces, Avoirdupois
Kilograms
0.028349523
Ounces, Avoirdupois
Avoirdupois Pounds
0.0625
Ounces, Avoirdupois
Troy Pounds
0.07595486
Ounces, Avoirdupois
Troy Ounces
0.9114583
- 15 -
-
7/25/2019 Engineering Hand Book
10/42
Formulas and Conversions
To Convert To
Multiply By
Ounces, Avoirdu pois Avoirdupois Drams
16
Ounces, Avoirdupois
Grams
28.34952313
Ounces, Avoirdupois Grains 437.5
Ounces, Troy Avoirdupois Pounds 0.06857143
Ounces, Troy
Troy Pounds 0.0833333
Ounces, Troy Avoirdupois Ounces
1.097143
Ounces, Troy
Troy Drams
8
Ounces, Troy Avoirdupois Drams 17.55429
Ounces, Troy
Pennyweights
20
Ounces, Troy
Grams
31.1034768
Ounces, Troy
Grains
480
Pennyweig hts Troy Ounces
0.05
Pennyweights Grams
1.55517384
Pennyweig hts
Grains
24
Pounds, Avoirdupois Long Tons
0.000446429
Pounds, Avoirdupois Metric Tons
0.000453592
Pounds, Avoirdupois
Short Tons
0.0005
Pounds, Avoirdupois
Quintals
0.00453592
Pounds, Avoirdupois Kilograms
0.45359237
Pounds, Avoirdupois
Troy Pounds 1.215278
Pounds, Avoirdupois
Troy Ounces 14.58333
Pounds, Avoirdupois Avoirdu pois Ounces
16
Pounds, Avoirdupois
Avoirdupois Drams 256
Pounds, Avoirdu pois
Grams 453.59237
Pounds, Avoirdupois
Grains 7000
Pounds, Troy Kilograms
0.373241722
Pounds, Troy Avoirdupois Pounds 0.8228571
- 16 -
Formulas and Conversions
To Convert
To
Mu lt ip ly By
pounds, Troy
Troy Ounces
12
pounds, Troy
Avoirdu pois Ounces
13.16571
pounds, Troy
Avoirdupois Drams
210.6514
pounds, Troy Pennyweights
240
pounds, Troy
Grams
373.2417216
Pounds, Troy
Grains
5760
Quintals
Metric Tons
0.1
Quintals
Kilograms
100
Quintals
Avoirdupois Pounds
220.46226
Scrupies
Troy Drams 0.333
Scruples
Grams
1.2959782
Scru pies
Gra ins
20
Tons, Long (Deadweight) Metric Tons
1.016046909
Tons, Long (Deadweight) Shor t Tons
1.12
Tons, Long (Deadweight) Long Hundredweights 20
Tons, Long (Deadweight)
Short Hundredweights
22.4
Tons, Long (Deadweight)
Kilograms
1016.04691
Tons, Long (Deadweight)
Avoirdupois Pounds 2240
Tons, Long (Deadweight)
Avoirdupois Ounces
35840
Tons, Metric
Long Tons
0.9842065
Tons, Metric
Short Tons
1.1023113
Tons, Metric
Quintals
10
Tons, Metric
Long Hundredweights
19.68413072
Tons, Metric
Short Hundredweights
22.04623
Tons, Metric
Kilograms 1000
Tons, Metric
Avoirdupois Pounds
2204.623
Tons, Metric
Troy Ounces
32150.75
- 17 -
-
7/25/2019 Engineering Hand Book
11/42
Formu las and Conversions
To Multiply By
long Tons 0.8928571
Metric Tons 0.90718474
Long Hundredweights 17.85714
Short Hundredweights 20
Kilograms
907.18474
Avoirdu pois Pounds 2000
To Convert
Tons, Short
Tons, Short
Tons, Short
Tons, Short
Tons, Short
Tons, Short
E. Density
Conversions
To Convert To Multi ply By
Grains/imp. Gallon Parts/million 14.286
Gra ins/US ga lion Parts/million 17.118
Grains/US ga llon Pounds/million ga I 142.86
Grams/cu. Cm Pounds/mil-foot
3.405E-07
Grams/cu. Cm Pounds/cu. in 0.03613
Grams/cu. Cm Pounds/cu. ft
62.43
Grams/liter Pounds/cu. ft 0.062427
Grams/liter
Pounds/1000 gaI 8.345
Grams/liter
Grains/gal
58.417
Grams/liter Parts/million
1000
Kilogra rns/cu meter
Pounds/mil-foot
3.405E-10
Kilograrns/cu meter Pounds/cu in
0.00003613
Kilogra rns/cu meter
Grams/cu cm 0.001
Kilogra rns/cu meter
Pound/cu ft 0.06243
Milligrams/liter Parts/million 1
Pounds/cu ft
Pounds/mil-foot
5.456E-09
Pounds/cu ft Pounds/cu in
0.0005787
- 18-
Formulas and Conversions
To convert
To
Multiply By
Pounds/cu ft
Grarns/cu cm
0.01602
Pounds/cu ft
Kqs/cu meter
16.02
Pounds/cu in
Pounds/mil-foot
0.000009425
Pounds/cu in
Gms/cu cm
27.68
Pounds/cu in
Pounds/cu ft
1728
Pounds/cu in
Kgs/cu meter
27680
F. Relative Density (Speci fic Gravity) Of Various Substances
Substance
Relative
Density
Water (fresh)
1.00
Mica
2.9
Water (sea average)
1.03
Nickel
8.6
Aluminum 2.56
Oil (linseed) 0.94
Antimony 6.70
Oil (olive) 0.92
Bismuth
9.80
Oil (petroleum)
0.76-0.86
Brass
8.40
Oil (turpentine)
0.87
Brick
2.1
Paraffin
0.86
Calcium
1.58
Platinum
21.5
Carbon (diamond)
3.4
- 19 -
Formulas and Conversions
-
7/25/2019 Engineering Hand Book
12/42
Substance
Relative
Density
Sand (dry)
1.42
Carbon (graphite)
2.3
Silicon
2.6
Carbon (charcoal)
1.8
Silver
10.57
Chromium
6.5
Slate
2.1-2.8
Clay
1.9
Sodium
0.97
Coal
1.36-1.4
Steel (mild)
7.87
Cobalt
8.6
Sulphur
2.07
Copper
8.77
Tin
7.3
Cork
0.24
Tungsten
19.1
Glass (crown)
2.5
Wood (ash)
0.75
Glass (flint)
3.5
Wood (beech)
0.7-0.8
Gold
19.3
Wood (ebony)
1.1-1.2
Ir on ( cast)
7.21
Wood (elm)
0.66
Iron (wrought)
7.78
- 20 -
Formulas and Conversions
Substance
Relative
Density
Wood (lignum-vitae)
1.3
Lead
11.4
Magnesium
1.74
Manqanese
8.0
Mercury
13.6
Lead
11.4
Magnesium
1.74
Manganese
8.0
Wood (oak)
0.7-1.0
Wood (pine)
0.56
Wood (teak)
0.8
Zinc
7.0
Wood (oak)
0.7-1.0
Wood (pine)
0.56
Wood (teak)
0.8
Zinc
7.0
Mercury
13.6
G. Greek Alphabet
Name
Lower
Upper
Case
Case
Alpha
o
A
Beta
~
B
Gamma
y
r
Delta
1 5
D .
Epsilon
E
E
Zeta
~
Z
~ .
- 21 -
-
7/25/2019 Engineering Hand Book
13/42
Formulas and Conversions
Name
Lower
Upper
Case
Case
Eta
~
H
Theta
e
e
Iota
I
I
Kappa
K
K
Lambda
A
r ;
Mu
~
M
Nu
v
N
Xi
~
-
Omicron
0
0
Pi
n
n
Rho
p
P
Sigma
a
and c ;
L
Tau
T
T
Upsilon
u
y
Phi
'P
< P
Chi
X
X
Psi
Ii
4J
Omega
w
Q
- 22 -
Formulas and Conversions
[ Chapter 3 '
I
Sy st em of Uni ts
The two most commonly used systems of units are as follows:
SI
Imperial
SI: The International System oflnits (abbreviated SI ) is a scientific method of expressing
the magnitudes of physIca l quant rues. TIllS system was formerly called the meter-kilogram-
second (l\1KS) system.
Imperial: A unit of measure for capacity officially adopted in the British Imperial System;
British units are both dry and wet
Metr ic system
Exponent
Numerical
Representation
value
eauivalent
Example
Tera
10
12
1000000000000
T
Thz (Tera
hertz)
Giga
10
1000000000
G
Ghz (Giga
hertz)
Mega
10
1000000
M
Mhz (Mega
hertz)
Unit
1
hz (hertz)
quantity
1
F (Farads')
Micro
10'
0.001
,I
,IF (Micro
farads)
Nano
10-
0,000001
n
nF (Nano
farads)
Pico
10-
12
0.000000000001
pF (Pico
p
farads)
Conversion Char t
~
Into
Into
Into
Into
Into Into
Into
I2 Y
Mill i
Centi
Oed
MGL* Oeca
Hecto Kilo
To
convert
10
10
5
10'
10
3
10
2
10'
1
Kilo
- 23 -
-
7/25/2019 Engineering Hand Book
14/42
Formulas and Conversions
ul tply Into
Into Into
Into Into Into Into
I
bv
Milli Centi
Oeci
MGL* Oeca Hecto
Kilo
To
Formulas and Conversions
convert
10
s
10'
10
3
102
10
'
1
10-
1
I
Hecto
i
To
Symbolic
I
convert
10'
10
3
102
10
'
1
10-
1
10-
2
Name
Representation
Numerical Equivalent
Oeca
I
Acceleration due to gravity on
9.80 m S-2
To
I
g
convert 10
3
102
10
'
1
10-
1
10'2 10-
3
Earth
MGL*
cceleration due to gravity on the
g
1.62 m S-2
To
Moon
convert
102 10' 1 10-1 10-2 10-3 10-4 Radius of the Earth RE 6.37
X
10 m
Oeci
Massof the Earth
ME
5.98 x 102 (1 Kilo X 10
6
) Milligrams
Earth-Sun distance
1.50 x 10 m
Physical constants
Speed of li ght i n air
c
3.00 x 10
8
m s
Symbolic
Numerical Equivalent
Electron charge
e -1.60 x 10-
1
C
Name
Representation
Mass of electron
rn,
9.11 x 10-
31
kg
Avogadro's number N
6.023 x 10
2
/Ckg mol)
:~
lanck's constant
h
6.63 x 10-
34
J s
Bohr magneton B
9.27 x 10-2
-
7/25/2019 Engineering Hand Book
15/42
Formulas and Conversions
Name
Symbolic
__Rel r esentation
Numeric al Equivalent
Electron ic rest mass
m e
Electronic charge to mass ratio
e/rn,
9.109 X 10'31kg
1.759 X 10 C/kg
Faraday constant
F
Permeability of free space
~IO
9.65 X 10
7
C/(kg mol)
4n x 10'7 H/m
Permittivity of free space
E o
8.85
X
10'1' F/m
Pianck's consta nt
h
Proton mass
mp
Proton to electron mass ratio
m p/m e
6.626 X 10'34 J s
1.672 X 107 kg
1835.6
Standard gravitational
acceleration
g
Universal constant of g ravitation
G
Universal gas constant
R o
9.80665 rn/s, 9.80665 N/k
6.67
x
10-11 N m'/kg'
8.314 kJ/(kg mol K)
Velocity of light in vacuum
C
Temperatu re
c
2.9979
x
10 m/s
5/9(OF - 32)
Temperature
K
5/9(OF + 459.67), 5/9
0
R , -c
273.15
Speed of liqht i n air
c
Electron charge e
Mass of electron
m e
3.00 x 10 m s'
-1.60
X
109 C
9.11 X 10'31kg
Planck's constant h
Universal gravitational constant
G
Electron volt
1eV
Mass of proton
m p
- 25 -
6.63
X
10'34J s
6.67
X
10' N m' kg
1.60 X 109 J
1.67 X 107 kg
[ Chapter 4 .- I
General Mathematical Formulae
4.1 Algebra
A Expansion Formulae
square of summati~n 2
(x
Y ) 2
= x + Zxy +
Y
square of difference
(x - y) 2= x2 - 2xy +
i
Differenceof squares
.x
2
-i=(x+y)(x-y)
Cube of summation
(x + y)' = x
3
+ 3x
2
y + 3xi + y'
Summationof two cubes
x' + y' = (x + y) (x
2
- xy +
i)
Cube of difference
(x - y) 3 = X _ 3x
2
y + 3xy2 _ y'
Differenceof two cubes
x' - y' = (x - y) (x
2
+ xy +
i)
B.
Quadratic Equation
Ifax
2
+ bx + C = 0,
-b
J b
2
''- --4-a-c
Then X
=-------
2a
TIle b .
CtSH ; algebraic pro erties ot real numbers 3, band care:
Property
Description
Closure
a + band ab are real numbers
Commutative
a + b
=
b + a, ab
=
ba
Associative
(a+b) + c = a + (b+c), (ab)c = a(bc)
Distributive
(a+b)
=
ac+bc
- 27 -
Formulas and Conversions
-
7/25/2019 Engineering Hand Book
16/42
Identity
a+O = O+a = a
Inverse a + (-a) = 0, a(l/a) = 1
Ca ncellation
If a+x=a+y, then x=y
Zero-fa ctor
aO = Oa = 0
Negation
-(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab
Algebraic Combinations
Factors with a common denominator can be expanded:
a+ b a b
--=+
C C C
Fractions can be added by finding a common denominator:
a b ad+ bc
-+=--
c d cd
Products of fractions can be carried out directly:
a b ab
c d cd
Quotients of fractions can be evaluated by inverting and multiplying:
a d ad
r, ;= bx-;;-= bc
Radical Combinations
V a b = V a V b
Va =a
1/11
~=~
v;;; = a~
a = M r a
- 28 -
10
::I
ell
u ::
+
Gl
E
~
I
~
:I
Z
z
'0
>
III
Gl
. .
~
Gl
~
I
~
0>
. . ,
Z Z
rv
III
. .
. .
::I
III
I
:5
'C
II
I
I
OJ
~oo
Gl
I
N
00-
. .
V
~-'
~
~11
'
:
OJ
~
Gl
I
. . , . .
C Gl
Gl
I
C D
:. ,
Gl
. ..
J E
Qj
V
I
+
; :
v
E
: :I G l
~
0
..,Il.
N
Q I
.:
-
7/25/2019 Engineering Hand Book
17/42
eaJV
Ja~aw Jad /
wan
aJn6::I
awnloA
eaJ a:>elJ
a:>ua.laJwn:>.II,:)
Item
I Circumference 1
Area
ISurface Area Vo me
Figure
/ Perimeter
, ( > )( s
b)(\
0)
- O -
i N
i N
5
+
-
7/25/2019 Engineering Hand Book
18/42
VN
VN
pIL
=
J
ilPJ )
z-lIL
= V
JILZ
=
J
~lre3 lZ:.'Il
{ _ Z
) = 1 7
are < 1 > pu e
e
; Ja I lA \
plozildeJJ.
I
\
/
VN
VN
( u t S o n ]
+C J
\+-1-iqv
iun6 ::1
ea.llf
.Ia~aW.Iad /
a:Jua.lajwn:1.ID
- l -
~
I
Item
Circumference ~
I
Perimeter Area
Surface Area
Volume
Figure
A=
arc x
r
2
-
7/25/2019 Engineering Hand Book
19/42
\
/
'VN
'VN
l/ Zq
+
lq )~
= V
sapis lie jo wnS
piozad
eJ.l
1
iun6;j
awnlo/\
eaJ V a:>ejJns
eaJV
Ja~aw Jad /
wan
a:>ua.laJwn:>.I0
Item
Circumference
Area
J
Perimeter
Su fa eAr
Volume figure
- r - r
- v[-
apis
ljO
4~6uill
il4~
s 5
ilJil4M
zS9 'Z =
If
59
'V N
u06eXilH
'V N
A
=
4,83
52
-
7/25/2019 Engineering Hand Book
20/42
- 9 -
V'N
V'N
V'N
PIOS
4 x M
I
V'N J~ln5u~pil~
D
p
Z
+
4
M
Z
+
4H
.Ia~awl.1ad /
Item
Circumference
Area Surface Area
Volume
Figure
/ Perimeter
;0
'O~
Formulas and Conversions
-
7/25/2019 Engineering Hand Book
21/42
~
. ,
Vi ::J
30
c:
sr
0
~
~
+
zr
z
z
z
i
w
e x >
' -
l
Iv
tr
N
1 / 1
:i'
I
e
+
. .
N
Q T
~
t\
+
III
N
)0
:: E
I
i
r
-
=
useful f lux per pole (webers). entering or leaving the armature
p = number of pairs of poles
I\' =
speed (revolutions per minute)
Generator Tenninal volts EG JaRa
~lolor Terminal volts = EB - JaRa
- 4S -
Formulas and Conversions
-
7/25/2019 Engineering Hand Book
25/42
Formulas and Conversions
Where EG
=
generated e.m.f.
EB generated back c.m.f.
la
=
armature current
Ra = armature
resistance
Alternating Current
R.\lS value of sine curve
=
0.707 of maximum value
Mean Value of Sine wave
=
0.637 of maximum value
Form factor = RMSvalue MeanValue = 1.11
Frequency of Alternator =
pN
cycles per second
. 60 .
Where p ISnumber of pairs of poles
)J
is the rotational speed in r rnin
Slip of Induction Motor
[ISlip speed of the field - Speed of the rotor) I Speed of the Field] x 100
Induclors and Induclive Reaclance
Physical Quantity
Equation
Inductors and Inductance
V
L
= L
ii.
d I
Inductors in S eries: LT= L, + L, + L3 + , ..
Inductor in Parallel:
1 1
1
I
-=-+-+-+ ..
LT
L, L, L,
Current build up
,
(switch initially closed after having
At vL(t)=Ee';
been opened)
t
YR(t)=E(l-e ')
. E '
I(t)=-(l-e ')
R
L
T = -
R
Current decay
,
(switch moved to a new position)
i(l) 1 0 e t
v.(t) = R i(t)
VL(t) =
RTi(t)
~cal
Quantity
f = lIT
rn =
2][ f
Equation
L
T'= ~
L .- --
Alternating current
L .- --
complex Numbers:
C=a+jb
C =
M
cos
e
+ j
M
sin
e
M=,/a'+b'
e = lan '('.)
a
polar form:
C
=
M ~
e
Inductive Reactance
IXcI
=
00 L
Capacitive Reactance
IXcl =
1 /
(00
C)
Resistance
R
Impedance
Resistance: Z. = R ~Oo
Inductance: ZL = XL
L90
=
00
L
L900
Capacitance: Zc = Xc ~-90 = 1/ (we)
L. -90
0
Quantity
Equation
Ohm's Law for AC
V=IZ
Time Domain
vet) = Vm sin (00 t
< 1
i(t) = 1msin (00 t < 1
Phasor Notation
V = V,m, L
V = Vm - < I >
Compon ents in Series
ZT = Z, + Z, + Z3 + .
Voltage Divide r Rule
V =V ~
x
T
Z T
Components in Parallel
1
1
1
1
-=-+-+-+ ..
ZT Z,
Z,
Z,
- 47-
Formulas and Conversions
-
7/25/2019 Engineering Hand Book
26/42
Quantity Equation
Current Divider Rule
IT ~~
,
Two impedance va lues in
Z _ l,Z,
parallel
T Z, + Z,
Capacitance
Capacitors
C=
Q
[F] (Farads)
v
Capacitor in Series
I I I l
..
C
T
C,
C,
C,
Capacitors in Parallel
CT=C,+C,+C
J
+
Charging a Capacitor
E .. ...
i(t)= R e RC
,
v
R
(t)
E e RC
,
vc(t)=E(l-eOCj
T = RC
Discharging a
\
.'
Capacitor
i(t)=
-....e
r'
R
,
vR(t)=-V. eO;'
,
vc(t)
\0
e r
t= R-rC
Quantity
Equation
Capacitance
C=
V
- 48 -
Formu las and Conversions
Quantity
Equation
Capacitance of a
C=e4
Parallel-plate Ca pacitor
d
E
= ~
d
Isolated Sphere C = 4nEr
Capacitors in parallel
C = C
,
+ C, + C,
Capacitors in series
I
I
1
I
=
C
C,
C,
C,
Energy stored in a
charged capacitor
IT =~= .. .C -, =.. .QV
2C 2 2
If the ca pacitor is
isolated
w=~
2C
If the capacitor is
W =...CV
connected to a battery
2
For R C circuits
Q = Qo (1 - e-'1
R
c);
Charging a capacitor
V =
v ,
(1 - e-
t
/
RC
;
Discharging a capacitor
Q
=
Qo
e-'1
R
C
V = Vo
e- '1
R
C
If the capacitor is isolated, the presence of the dielectric decreases the potential
difference between the plates
If the capacitor is connected to a battery, the presence of the dielectric increases the
charge stored in the capacitor.
TI,e introduction of the dielectric increases the capacitance of the capacitor
- 49 -
Formulas and Conversions
power dissipation
-
7/25/2019 Engineering Hand Book
27/42
Formulas and Conversions
Current in AC Circuit
RMSCurrent
In Ca rtesia n
1= V
1 2 [R-l(WL- ~)]
orm -
[R' + ( wL -
C& C ) ]
Amperes
In polar form
I -
_ - 1/ > ,Amperes
j t (
1 r
R' + (oL-- 1
we)
. [ d
R ~l
here 1 /> ,
=
1311-
Modulus
I I I
I -
Amperes
~R'
+ (
mL- ~ J
Complex Impedance
In Cartesia n
Z =
R + l( mL- ~) Ohms
form
In pola r form
Z=~R'+(mL- ~ J - I/> ,
Ohms
[ 1 1
L - -
Where 1/ > ,
=
lan' R C & C
Modulus
I
r
1 r
Z
=
V[R' - \ (iJL- C &C 1 Ohms
,- -
Average power, P
= / f
cos
Watts
power d issipat ion in a
I 1 R Watts
resistor
-
Rectification
controlled half wave
I -
Average DC voltage
(I
j
cosa)
rectifier
2
Volts
~ontrolled full wave /
Average DC voltage
(ltcosa)rectifier
n
Volts
powerFactor
DC
I'R
1-
Power
Pi
11
R
AC
Pac
=Re(I-.)=
I J
cos
Power
Powerin ac circuits
Quantity
Equation
Resistance
The mean power
=
P
=
I,,,,, V,,,,,
=
I,m,2R
Inductance
The insta ntaneous power = (10 sin wt) (Vo sin (wt +
n)
The mean power
p
= a
Capacitance
The i nstantaneous power
=
(10 sin (wt + n/2)) (Vo sin
wt)
The mean power
P =
a
Formula f or a .c.
The mean power
=
P
=
I,,,,, V,,,,, cos
ower
- 51 -
ormu as an onversons
Three Phase Alternators
-
7/25/2019 Engineering Hand Book
28/42
Star connected
Line voltage = 3 . phase voltage
Line current
=
phase current
Delta connected
Line voltage = phase voltage
Line current = 3 . phase current
Three phase power
P
=
3 EL IL cos
EL
=
line voltage
lL
=
line current
cos
=
power factor
Electrostatics
Quantity Equation
Instantaneous current,
I
=
dq
=
C dv Amperes
dt dt
Permittivity o f free space
10
9
_
10-
12
Farads
=--=8.8)
o 3 6 1 1
(meters)
Energy stored in a
=..CV,
Joules
capacitor
2
Quantity Equation
Coulomb's law
F=k
Q,Q
,
r
Electric fields
E=f.
q
Due to a point charge
E=-Q-
4JT6 r2
Due to a conducting sphere carrying charge
E
=
0
Q Ins ide the sphere
- S2 -
/
Formulas and Conversions
I ' Quantitv
Equation
outsi de t he sphere
E
Q
4ne r'
Just outside a uniformly charged conducting
E
cr
sphere or plate
c
Anelectric field E is a vector
TI,e electric field strength is directly proportional to the number of electric f ield l ines
per unit cross-sectional area.
The electric field at the sur face ofa conductor is perpendicular to the surface.
TI,e electric field is z ero i nside a conductor.
Quantity
Equation
Suppose a point charge
Q
is at A. The work done in
11
Qq
bringing a charge
q
from infinity to some point a distance
4ne,
from A is
Electric potentia I
/. = ~
q
Due to a point charge
v = Q
4ne r
Due to a conducting sphere, of radius a, carrying charge
1=-'
:
4ne anside the sphere
Outside the sphere
r
Q
4ne,
I f
the potential at a point is
V,
then the potential energy
U
=
qV
of a charge
q
at that point is
Work done in br inging charge
q
from A of potential
VA
to
W =
q (V B - VA )
POint B of potential
VB
- S3 -
Formulas and Conversions
PhysicalQuantity
-
7/25/2019 Engineering Hand Book
29/42
Formulas and Conversions
Quantity Equation
Relation between E a nd V dV
E=--
dx
For unifo rm e lectric field
E = ~
d
Magnetostatics
Physical Quantity
-
Equation
Magnetic flux density (also called the B-
B=F
field) is defined as the force acting per unit
current length.
t e
Force on a current-carrying conductor in a
F = I
e
BF = I
.
B
magnetic field
And Magnitude of F = F = I B
sin e
Force on a moving charged particle in a
F=qvB
magnetic field
Circulating Charges
,
mv
qvB=-
r
Calculation of magnetic flux density
Physical Quantity Equation
Magnetic f ields around a long straight wire
B =
JL o l
carrying current
I
7
where a
=
perp. distance from a
very long straight wire.
Magnetic fields inside a long solenoid,
I:B = ~ n I,where n = number of
carrying current turns per unit length.
Hall effect
OVH =OvB
and
At equilibrium
- d -
VH = B v d
The current in a,mater ial isgiven by
1= nQAv
- S4 -
Theforces between two current-carrYing
conductors
I~,
.1l1,l,f
2,m
Equation
~
.---- lt
Physical Quant i y
Equation
~ torque on a rec tangular coil In a magnetic
T
=
Fb sin e
field
=
N IeBb sine
= NIA B sine
I T
t he co il i s in a radial f ield and the pl ane of the
T
=
NIA B s in e
coil is always paral le l to the field, then
=
N
I
A B sin 90
0
= NIA B
Magnetic flux
-
7/25/2019 Engineering Hand Book
30/42
Energy stored in an inductor:
U =...L/'
2
Tra nsformers: I
N:
- - - - -
=
lip
Np
The L R (d.c.) ci rcuit:
1 =~(l_e-Rr ')
R
When a g reat load (or smaller
II -8
res is ta nce) is con nected to
v; -Ep. 'R; 1 =~
the secondary coil, the flux in
the cor e dec reases. The
e.m.f.,
Ep,
in the primary coil
falls.
Kirchoff's laws
Kirchoff's firs t l aw (Junction Theorem)
At a junct ion, t he to ta l cur rent entering the junction is equal to the total
cur rent l eavi ng t he j unct ion.
Kirchoff's second law (Loop Theorem)
The net e.m.f. round a circuit is equal to the sum of the p.d.s round the loop.
Physical Quantity
Equation
Power
W
P=-=VI
t
Electr ic cur rent
1=3.
t
Work
W=qV
Ohm's Law
V =IR
Resists nces in Series
RT = R, + R,,,.
Resista nces in Paral lel
1 1 1
-=-+-.
RT
R,
R,
Magnetic flux
=BA
- 56-
/
Formulas and Conversions
Electroma g n etic
Emf=-N (< >,-,l
induction
t
emf = IvB
Magnetic force
F=IIB
T ransf orme r t ur ns r at io
Vs = Ns
Vp
Np
Electromagnetic spectrum
Frequency
Wavelength
10
2
10
I I
).(m)
1
I
10-
1
10-
2
10-
3
10-
4
10-
5
10-
6
10-
7
108 10-9 10-1010-11
I
I I I I I I I I
I
- ' -- r
10
16
, - - - - - - ,
10
17
10
18
10
19
10
20
r ad lo fr ea uenC les
I
,
,
,
,
, '
, ,
, ,
,
'
ii
: :
:
:
:.; Inrrartdradia ion
, ,
,
:
gamm a ra ys
&Lm
lo.rea of
Ispectrum
,
,
; I m lcr o w ay s
:.
.
,
15 : . U ftre vi ol e l :
:~: rad jallon ,
- ,
10
7
10
8
I I I I I I
10
9
10lD 1011 10
12
10
13
1014
(Hz)
10
10
15
Note: 1. Shaded areas represent regions of overlap.
2. Gamma rays and X-rays occupy a common region.
5.2 Applied Mechanics
5.2.1 Newton 's laws of motion
Newton' first law of motion
The inertia ofa body is the reluctance of the body to change its state of rest or motion.
Mass is a measure of inertia.
Newton's second law of motion
F
_mv-mu.
- tit
F = m a
Formulas and Conversions
,--
-
7/25/2019 Engineering Hand Book
31/42
Formulas and Conversions
Impulse = force' time = change of momentum
Ft=mv-mu
Newton's third law of motion
When two objects interact, the y exert equal and opposite forces on one another.
Third-law pair of forces act on two different bodies.
Universal Law
F
=
Gm,mp/d
2
m, is the mass of the sun.
mp is the mass of the planet.
The Universal law and the second law must be consistent
Newton's Laws of Motion and Their Applications
Physical Quantity Equations
s v + u
V V t
verage velocity
2
Acceleration
v-u
a=--
t
Momentum
p=mv
Force F=ma
Weight
weight =mg
Work done W =
Fs
Kinetic energy
EIo; =tmv2
Gravitational potential energy
E, = mgh
v-u
a=--'
t
s
=
ut + tatl ;
v
2
=
u
2
+2a5
quations of motion
Centripeta I acceleration
v
a=-
r
Centripetal force
F=ma= mv'
r
Newton's Law of Universal
Gravitation
F=Gm,m,
r
. . . . .
g=G~
r
Physical Quantity
Equations
. . . -
Gravitational field strength
Physical Quantity
Equations
Moment of a force
M=rF
Principle of
l:M=O
moments
Stress
Stress =
.
A
Strain
Strain = ~
I
Young's Modulus
F /A
y=--
~III
Scalar: a property described by a magnitude only
Vector: a property described by a magnitude and a direction
ity: vector property equal to displacement
I
time
The magnitude of velocity may be referred to as speed
In SI the basic unit is m s, in Imperial ftls
Other common units are
kmlh,
miJh
Conversions:
Im 1 s = 3.28 ftls
lkm/h = 0.621 mi/h
Speed of sound in dry air is 331 m s at OC and increases by about 0.6 I m s for each 0C
rise.
Speed oflight in vaccum equals 3
x
108
m1s
Acceleration: vector property equal to change in velocity time.
In SI the basic unit is m/s '
lIT Imperial ftls
2
- 59 -
Formulas and Conversions
Conversion:
-
7/25/2019 Engineering Hand Book
32/42
lm~'28.fi
s _
Sl
Acceleration due to gravity. g is 9.81 m s'
5.2.2 Linear Velocity and Acceleration
Quantity Equations
If u initial velocity and v final velocity,
5=(; tl ~
then displacement
s,
If t is the elapsed time
1 ,
s=ut+-at-
2
If a is the acceleration
, =11' +2as
Angular Velocity and Acceleration
Quant ity Equations
B angular displacement
c
1 +
lU
(radians)
f
2
w angular velocity (radians s):
w ,
= initial, W2 = final
I
)=iJ\t+-at
2
a angular a cc eler at ion
liJ,=iJ\
+2aB
(radians/5
2
)
Linear displacement s = r
B
Linea r velocity
v = r
w
Linear, or tangential
aT = r a
acceleration
Tangential, Centripetal and Total Acceleration
Quantity
Equations
Tangential acceleration aT is due to angular acceleration
aT = ra
a
- 60 -
Formulas and Conversions
~tripetal (Centrifugal) acceleration ac is due to change
Iin direction onlv
ac = v2/r = r
w
2
t70.tal acceleration, a, of a rotating point experiencing
I angular acceleration is the vector sum of aT and ac
a
=
aT + ac
5.2.3 Force
Vector quantity, a push or pull which changes the shape and/or motion of an object
In SI the unit of force is the newton, N, defmed as a kg m
In Imperial the unit offorce is the pound Ib
Conversion: 9.81 N = 2.21b
Weight
The gravitational force of attraction between a mass, m, and the mass of the Earth
In SI weight can be calculated from Weight = F =mg, where g = 9.81 m/s2
In Imperial, the mass of an object (rarely used), in slugs, can be calculated from the
known weight in pounds
weight
n1=---
g
g
=32 2 ft
. 5
Torque Equation
T
= I
Cl
where
T
is the acceleration torque in Nm, I is the moment of inertia in kg m2 and
C l is the angular acceleration in radians/s
2
Momentum
Vector quantity, symbol p.
p =mv (Imperial p = (w/g)v, where w is weight]
in SI unit is kgm / s
Work
Scalar quantity, equal to the (v ector) product of a force and the displacement of an
object. In simple systems. where W is work,
F
force and s distance
W = F
s
In SI the unit of work is the joule, J, or kilojoule, kJ
1
J
= 1
Nm
In Imperial the unit of work is the ft-lb
Energy
Energy is the ability to do work, the units are the same as for work; J, kJ, and ft-lb
Formulas and Conversions
A scalar quantity, equa l to the rate of doing work
In SI the unit is the Watt W (or kW)
-
7/25/2019 Engineering Hand Book
33/42
Formulas and Conversions
Kinetic Energy
1
E. =-mk'6J'
2
Where k is radius of gyration. (()is angular velocity in rad/s
Kinetic Energy of Rotation
Er=~/6J'
2
Where 1
=
mt? is the moment of inertia
5.2.4 Centripetal (Centri fugal) Force
F,
mv'
r
Where r is the radius
Where
co
is angular velocity in rad/s
Potential Energy
Quantity Equation
Energy due t o position in a force Ep = m g h
field, such as gravity
In Imperial this is us ually expressed Ep = w h
Where
w
is weight, and h is height
above some sp ec if ie d da tum
Thermal Energy
In SI the common units of thermal energy are 1. and kJ, (and kJlkg for specific
quantities )
In Imperial, the units of thermal energy a re British Thermal Units (Btu)
Conversions
I Btu = 1055 J
1Btu = 778 ft lb
Electrical Energy
In SI the units of electrical energy are 1. k J a nd kilowatt hours kWh. In Imperial, the unit
of electrical energy is the kWh
Conversions
I k\Vh = 3600 kJ
I k\\ll 3412 Btu
=
2.66
X
10
6
ft-Ib
Power
- 62 -
IW=I.-
s
In Im peria l, th e un its ar e:
Mechanica l Power - (ft - lb) s, horsepower h.p.
Thermal Power - Btu s
Electrical Power - W.kW. or h.p.
Conversions
746W =Ih.p.
ih.p. = 550
ft
-Ib
s
IkW
= 0.948
8m
s
Pressure
A vector quantity. force per unit area
In SI the basic units of pressure are pascals Pa and kPa
lPa=l~
m
In Imperial, the basic unit is the pound per square inch, psi
Atmospheric Pressure
At sea level atmospheric pressure equals 101.3 kPa or 14.7 psi
Pressure Conversions
I psi = 6.895 kPa
Pressure may be expressed in standard units, or in units of static fluid head, in both SI
and Imperial systems
Common equivalenc ies a re:
1kPa = 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 H20 = 9.81 kPa
Other pressure unit conversions:
1 bar
=
14.5 psi
=
100 kPa
1 kg/ern
2
= 98.1 kPa = 14.2 psi = 0.981 bar
- 63 -
Formulas and Conversions
01 atmosphere (atm) 10 1.3 kPa 14.7 psi
-
7/25/2019 Engineering Hand Book
34/42
Simple Harmonic Motion
Velocity ofP _
li J J R 2 - - ; ;
m
s
5.2.5 Stress, Strain And Modulus Of Elasticity
Young's modulus and the breaking stress for selected materials
Material
Young modulus
B reak ing stress
x 10 Pa
x 10 Pa
Aluminium 0.70
2.4
Copper
1.16
4.9
Brass 0.90 4.7
Iron (wrought)
1.93
3.0
Mild steel 2.10
11.0
Glass 0.55 10
Tungsten 4.10 20
Bone 0.17
1.8
5.3 Thermodynamics
5.3.1 Laws ofThermodynamics
oW =P(\V
o(\U
= Q -
W
o W = nR T InV v 'V ;
oQ
=
C n( \T
oCv= 312R
oCp= 512R
o
C p lC
v
= y= 5/3
o e = I - Qe /Q = W /Qh
oe,
=
I-
TelT
o
CO P
=Q,
W
(refrigerators)
o
CO P
=
Qh
W (heat pumps)
o Wm ax= (I T ,nh)Qh
o(\S = QrT
-64-
Formulas and Conversions
5.3.2 Momentum
op =
mv
oLF
=
(\pl (\t
5.3.3 Impulse
I ~ F.,A
t ~
rnv, -
m v,
5.3.4 Elastic and Inelastic collision
rnjV + m2v2 ::;mtVf + m2v2f
(2) mjVli2 + (' 2) m2V212::; 12 mlVl? + 12m2
V
2f
2
o m;vl; + m2v2;
=
(m 1 + m2)Vr
5.3.5 Center of Mass
Xcm~ L:mxIM
oV'm~LmvlM
Acm
=
~malM
o MAcm = Fn
-
7/25/2019 Engineering Hand Book
35/42
Formulas and Conversions
5.3.10 Standing Waves
ofn= nfl
of
n
= nv.Zl, (air column, string fixed both ends) n = 1.2,3,4...
ofn = nval, (open at one end) n = 1,3,5.7 ..
ol:
r, =
0
ol: r
= 0
(any axis)
5.3.8 Gravi ty
of = Gmlmvr2
oT =
21 t1
..Jr
3
/GM,
oG = 6.67
x
1O-
II
N_m
2
ikg
2
og = GME/R\
oPE = - Gmlm,l r
ov, = ..J2GM
E
IRE
ov,=..JGME/r
oME = 5.97 X 10
24
kg
oRE = 6.37
X
10
6
m
5.3.9 Vibrations &W aves
of =-kx
oPE, =' ,kx
2
ox = Acos9 = Acos(rot)
e v = -Aesinnct)
oa = -Aro
2
cos(rot)
oro=
vk
m
of=
1 T
oT = 21t..Jm k
oE=',kA
2
-T
= 21t..JL
I
g
.V
m ax
=
Am
eam ax
=
Au /
ov= Af v
=..J FT /fl
ofl = mIL
01
= PIA
o P = IOlog(lII
o
)
010
=
Ix
10.
12
W/m'
of = f[(1
vJv)/(l
+
v,iv)]
oSurface area of the sphere = 4m
2
oSpeed of sound waves = 343 mls
5_3.11 Beats
ofb ,= fl-f,
oFluids
oP'
1n1
= 1.0I x lO
s
Pa = 14.7 Ih/in2
oFB= prVg = Wr(weight of the displaced fluid)
o pJpr = V
rN 0
(floating object)
o pweee = 1000 kg/rn
3
.W.=W-F.
Equation of Continuity: Av = constant
Bernoulli's equation: P + Y, pv
2
+ pgy = 0
5.3.12 Temperature and Heat
oT,,= 9/5T
c
+32
o
T
c=
5/9(T F-3 2)
o
L '. T F
=
9/5L '.T
c
oT=Tc+273.15
o p=
mlv
o L'.L= ctLoL'.
oM= yAoL'.T
oL'.V=PVoL'.Tp=3a
oQ = mcL'.T
oQ=mL
olkcal=4186J
o Heat Loss = Heat Gain
o
Q
=
(kM
T)t/L,
oH =
Q/t
=(kAL'.T)/L
oQ = earAt
-P>
QII
oP=aAer
oP n.,= aAe(T4-Ts4)
o a = 5.67
x
10-
8
W/m
2K4
5.3.13 Ideal Gases
oPV=nRT
-R
= 8.31
J/mol
K
oPV = NkT
o
NA
= 6.02
x
1023molecules/mol
ok = 1.38 x 10-
23
JIK
oM=NAm
o(KE)ov=(
1/2mv2
).v= 312kT
oU= 312NkT = 3/2nRT
- 67 -
- 66-
Formulas and Conversions
5.3.14 Elastic Deformation
.P= F A
.y
= FL
o
A6L
-
7/25/2019 Engineering Hand Book
36/42
.s =
Fh/A~x
.B=-V~/MV
Volume of the sphere =
4m .3
3
.1 atm = LOI x 10
5
Pa
5.3.15 Temperature Scales
.oC =
5/9
(OF-32)
.oF
=
5/9
(OC+ 32)
.OR = of +
460
(R Rankine)
K = C
+
273 (K Kelvin)
5.3.16 Sensible Heat Equation
.Q=mc~T
.M=mass
C=specific heat
~T=temperature chance
5.3.17 Latent Heat
Latent heat of fusion of ice = 335 kJlkg
Latent heat of steam from and at lOOC= 2257 kJlkg
.1
tonne of r efrigeration = 335
00 0
kJ day = 233 kJ/min
5.3.18 Gas Laws
Boyle's Law
When gas temperature is constant
PV = constant or
PlVl = P2V2
Where P is absolute pressure and V is volume
Charles' Law
When gas pressure is constant,
V
-=consl.
T
or
~=v,
T . ,
T,
where V is volume and T is absolute temperature
- 68 -
/
Formulas and Conversions
Gay-Lussac's Law
When gas volume is constant,
P
-=consl.
T
or
l=
P,
T, T,
where P is absolute pressure and T is absolute temperature
General Gas Law
P,V,
=
P,V, const.
T, T,
P V
=
m R T wher e P = absolute pressure (kPa)
V = volume (m')
T = absolute temp (K)
m = mass (kg)
R
=
characteristic constant (kJ/kgK)
Also
PV = nRoT where P = absolute pressure (kPa)
V = volume (m)
T = absolute temperature K
N = the number ofkmoles of gas
Ro = the universal gas constant
8.314
kJ/kmollK
5.3.19 Specific Heats Of Gases
Specific Heat Specific Heat
at Constant at Constant Ratio of
GAS Pressure Volume
Specific
kl/kgK
or
kl/kgK
or
v =
cp / cv
kl/kg C kl/kg C
Air
1.005
0.718
1.40
Ammonia
2.060
1.561
1.32
Carbon Dio xi d e 0.825 0.630
1.31
Carbon
1.051
0.751
1.40
Monoxide
Formulas and Conversions
Where rv=cylinder volume clearance volume
k = absolute pressure at the end of constant V heating (combustion) absolute pressure at
the beginning of constant V combustion
~ =
volume at the end of constant P heating (combustion) / clearance
-
7/25/2019 Engineering Hand Book
37/42
Fo rmu las and Conversions
Specif ic Heat Specific Heat
at Constant
at Constant Ratio of
GAS Pressure
Volume
Specific
kl/kgK
or
kl/kgK or
v= cp / cv
kl/kg DC kl/kg DC
Helium
5.234 3.153
1.66
Hydrogen
14.235
10.096
1.41
Hydrogen
1.105
0.85
1.30
Sulphide
Methane
2.177
1.675
1.30
Nitrogen
1.043
0.745
1.40
Oxygen
0.913 0.652
1.40
Sulphur Dioxide 0.632
0.451
1.40
5.3.20
Efficiency of Heat Engines
Carnot Cycle
T,-T,
1=--
T,
where T, and T2 are absolute temperatures of heat source and sink
Air S tandard Eff iciencies
Spark Ignition Gas and Oil Engines (Constant Volume Cycle)
1
1=1-0
r.
ro=
compression ratio
y
= specific heat (constant pressure) I Specific heat (constant volume)
Diesel Cycle
1=1-
Ry-I)
r:-y(R-I)
Where r = ratio of c ompression
R
=
ratio of cut-off volume to clearance volume
High Speed Diesel (Dual-Combustion) Cycle
kpr
-I
I] - Ic; ;
- -: [(k -1) + jk(P -I)]
volume
Gas Turbines (Constant Pressure or Brayton Cycle)
1}=1__ I_
(
L: )
rp ,
where
Fp
= pressure ratio = compressor discharge pressure I compressor intake pressure
5.3.21 Heat Transfer by Conduction
Material
Coeff icient o f Thermal
Conduct ivity
W/m c
Air
0.025
Brass
104
Concrete
0.85
Cork
0.043
Glass
1.0
Iron, cast
70
Steel
60
Wallboard, 0.076
paper
Aluminum
206
Brick
0.6
Copper
380
Felt 0.038
Glass, fibre
0.04
Plastic, cellu la r
0.04
Wood
0.15
- 71 -
Formulas and Conversions
5.3.22 Thermal Expansion of Solids
Increase in length
=
L (l (T, - Tj)
Where L = original length
(l = coefficient of linear expansion
: >
0
, 0
~c
u '
hMlh~
'-----
00
.s
-
7/25/2019 Engineering Hand Book
38/42
(T, - T.) = rise in temperature
Increase in volume
=
V ~ (T, - T
I
Where V
=
original volume
P
=
coefficient of volumetric expansion
(T, - T.) = rise in temperature
Coefficient of volumetric expansion =Coefficient of linear expansion x 3
~ = 30
5.3.23 Chemical Heating Value ofa Fuel
hemical Heating Value MJ per kg of fuel
=
33.7C + 144(H, _ 0,) + 9.3S
8
C is the mass of carbon per kg of fuel
H, is the mass of hydrogen per kg of fuel
0, is the mass of oxygen per kg of fuel
S is the mass of sulphur per kg of fuel
Theoretical Air Required to Burn Fuel
. [ 8 ] 1 0 0
lr(kgperkgoffuel)= 3C+8(H,-O,)+S 23
Air Supplied from Analysis of Fl ue Gases
Air in kg per kg offuel
= N,
xC
33(CO, +CO)
Boiler Form~lae
. . m
1 1 -11 )
Equivalent evaporation
=
,I ,
22 57 kJ I kg
( -h)
Factor of evaporation
= '
22 5 7kJ I kg
Boi ler E ff iciency
m,( ,
-h,)
mf x (calorific value)
Where
m,
=
mass flow rate of steam
hi = enthalpy of steam produced in boiler
h,
=
enthalpy offeedwater to boiler
mr =mass flowrate of fuel
- 72-
>
~
8
:>
~
Q : '
o
h-
I
8
10
;
.E t > -
c'
. . . .
., .,
, c
cc,
u'
I I
0.
:E
II
C
o
~ D.
. ,
,
II: ~
~
Ii .
. E > -
. ,E -
, , , ,
c. c
, '
cC
u '
. ,
c
o
'C
o f
o
~
1 1
'C
'C
i
: z :
. ,
c
iij
> 0
'O~
., . ,
E
U
' f
o.
~
II.
h-
I
8
~
10
;
h-
I
8
; : : ;
~:o~ -;}
~.- c c
S ~ 8 8
g?(;~~
0 __
~~i
0 '''0
o
0
~~~~
'E
QJ & . & .
ca.. orl){I)
~ l; j II II
OuJ J
*
Q)
I =
h-
I
8
. .
10
Ii;
h-
I
8
- r
Ii;
~
o
';;
:; ;
~
o
()
~
~
~
o
II.
hM
I
h-
~ T 1
,
.
~T~
---J
II
h- Ih '
.
r:1~
---J
II
0.,-10;
. . . .
u ~
.~ II s
1ii
> 6 : c
~ 8
M
.. .
-
7/25/2019 Engineering Hand Book
39/42
Formulas and Conversions
Specific Heat and Linear
Mean Specific Heat between oe
Coefficient of Linear Expansion
Expansion of Solids
and lOOe kl/kgK or kl/kge
between
oe
and
lOOe
(mult ip ly by
10-
6
)
Aluminum 0.909 23.8
Antimony 0.209 17.5
Bismuth 0.125
12.4
Brass 0.383
18.4
Carbon 0.795 7.9
Cobalt
0.402
12.3
Copper
0.388 16.5
Glass 0.896 9.0
Gold 0.130 14.2
Ice (between -20C & OC) 2.135
50.4
Iron (cast)
0.544
10.4
Iron (wrought)
0.465
12.0
Lead 0.131 29.0
Nickel
0.452
13.0
Platinum
0.134 8.6
Silicon
0.741 7.8
Silver
0.235 19.5
Steel (mild)
0.494
12.0
Tin
0.230 26.7
\
Zinc 0.389
16.5
~r
- 75
-
7/25/2019 Engineering Hand Book
40/42
C I l
c
o
C])
>
c:
o
(J
0
c:
I l
..
: :J
E
&
Formulas and Conversions
5.4 F lu id Mechanics
5.4.1 Discharge from an Ori fice
Let A
=
cross-sectional area of the orifice
=
..d '
4
And Ac = cross-sectional area of the jet at the vena
d'
conrtacta
4 '
Then Ac
=
CcA
OrC
= ~ = ( d ' r
Ii d
Where C, is the coefficient of contraction
C I l
0
'5
C
:. :;
e
0
ii i
e
10
c . . . .
)(.,
Q j l
E>
:I Q
=
v
N
0 0
:
r-,
0>
. ..
N
co .co.
N
r v i
>ii
. .. . .. . ..
. ..
. , .
0 >
-
o~
:I
c : : : E :
Q j
' ij
It
8
u
u
.
. .
CI
1 0 . . . . . \1 :
Qj U .....
:1: . ~
0
, . . . . ,
co
, . . . . ,
0 >
, . . . . ,
I L l
, .. ..,
0
, ... .,
~e .
r-- r--
, . . . .,
v
, ... . ,
, . . . ., ,.. .. ,
0 >
0
co
= N 0
: :
. ..
~
. ..
. ..
=
co
. ..
u ~
N
0
. ..
,. . . . ,
0
. ..
N N
. ..
v
~~ CI
/I ~
. ..
~
C ])
-0
.
'x
E
Q)
C ])
z -
Q)
c:
0
;;;
c:
c:
0
0
: : J
c:
:;:;
. ..
5
.c:
0
'N
0
::J
Q)
Q)
0
c:
2 :
c :r
0..
e
C ])
r o
u
c:
II)
:J
ct
E
Q)
0
C ])
0
4 i
r o
1 : -
:;:
ct:
co
- e
: :; :
(,)
: :J
0-
I-
r o
U
.. .
s
c
o
'iij
c:
~
x
W
C])
E
::J
~
0
c:
o
C ])
:c
o
Ii:
c
~
e n
h
d
\
Ve na c on tr ac ta
At the vena contracta, the volumetric flow rate Q of the fluid is given by
o Q = area of the jet at the vena contracta . actual velocity = A,\'
oOrQ= C
c
AC .,.j2 gh .
o
Typically, values for Cd vary between 0.6 and 0.65
oCircular orifice:
Q
= 0.62 A 2gh
o Where Q = flow (m
3
s) A area ( rn') h = head (m)
o Rectangular notch: Q = 0.62 (B . H) 2/3 v2gh
- 77-
Formulas and Conversions
. -
Nominal
Outside
Inside
Wall
pipe size
diameter
diameter
thickness
Flow area
(in)
(mm)
(mm)
(mm)
(m')
-
7/25/2019 Engineering Hand Book
41/42
Formulas and Conversions
Where B = breadth (m)
H head (m above s ill)
Triangular Right Angled Notch: Q = 2.635H'
2
Where H = head (m above sill)
5.4.2 Bernoulli's Theory
P
v
H=h.,.-+-
W 2g
H = total head (meters)
w
= force ofgravity on 1 m
3
of fluid (N)
h = height above datum level (meters)
v = velocity of water (meters per second)
P = pressure (N/m
2
or Pal
Loss of Head in Pipes Due to Friction
L \.2
Loss of head in meters =
f--
d 2g
L = length in meters
v = velocity of flow in meters per second
d = diameter in meters
f= constant value of 0.01 in large pipes to 0.02 in small pipes
5.4.3 Actual pipe dimensions
Nominal
Outside
Inside Wall
Flow area
p ip e s ize diameter
diameter thickness
(m ')
(in) (mm)
(mm) (mm)
1/8
10.3 6.8
1.73
3.660
10.
5
1/4
13.7
9.2 2.24
6717 . 10'5
3/8
17.1 12.5
2.31 1.236
10
1/2
21.3 15.8 2.77
1.960
10
3/4
26.7
20.9 2.87
3.437 . 10
1
33.4
26.6 3.38 5.574
10
1I.
42.2 35.1 3.56 9.653
10
1'12
48.3 40.9 3.68
1.314 10'3
2
60.3 52.5 3.91 2.168
10'3
- 78 -
2'12
73.0
62.7
5.16
3.090
10'3
3
88.9
77.9
5.49
4.768
10'3
3'12
101.6
90.1
5.74
6.381
10-
3
4
114.3
102.3
6.02
8.213
10'3
5
141.3
128.2
6.55
1.291
10
6
168.3
154.1
7.11
1.864
10
8
219.1
202.7
8.18
3.226
10
10
273.1
254.5
9.27
5.090
10
12
323.9
303.2
10.31
7.219
10'2
14
355.6
333.4
11.10
8.729
10'2
16
406.4
381.0
12.70 0.1140
18
457.2
428.7
14.27
0.1443
20
508.0
477.9
15.06
0.1794
24
609.6
574.7
I
17.45
0.2594
- 79 -
. .
Formu las and Conversions
I J
-
7/25/2019 Engineering Hand Book
42/42
References
6.1 Periodic Table of El ements
A
1
8A
18
~
r--
1
2
H
2A
3A
4A 5A 6A 7A
He
1.00
2
13
14 15 16
17
4.00
8
3
3 4 5 6 7 8 9 10
U 8e
8 C N
0 F Ne
6.94 9.01
10.8 12.0 14.0 16.0
19.0 20.1
1
2
1
1 1 0 0
8
11
12
13 14 15 16 17
18
Na
Mg 3B 4B 5B
68 78 88 8B 88 1B 2B
AI 51 P
5 CI Ar
22.9 24.3
3
4
5 6 7 8 9 10 11
12 26.9
28.0 30.9
32.0
35.4 39.9
9
1
8
9 7 7 5
5
19
20 21 22 23 24
25 26 27 28 29 30
31 32 33 34
35 36
K
Ca 5e Ti V
Cr Mn Fe Co
Ni
Cu Zn
Ga Ge As
Se Br Kr
39.1
40.0
44.9 47.9
50.9 52.0
54.9 55.8 58.9 58.7
63.5 65.3 69.7 72.5
74.9 78.9 79.9 83.8
0
8 6 0 4 0 4 5
3 0 5 8 2
9 2 6 0
0
37
38 39 40 41 42 43 44
45 46 47 48 49
50 51 52
53 54
Rb
Sr Y Zr Nb
Mo Te Ru Rh Pd Ag
Cd In Sn
Sb
Te
I Xe
85.4 87.6
88.9
91.2
92.9 95.9 97.9
101.
102.
106. 107. 112.
114. 118.
121.
127. 126.
131.
7
2 1 2 1 4 1
9 4 9 4 8
7 8 6 9 3
55
56 57
72
73 74
75 76
77
78
79 80 81 82 83 84
85 86
Cs
Ba
Le Hf Ta
W Re Os lr Pt Au Hg
TI Pb Bi Po
At Rn
132. 137. 138. 178. 180.
183. 186.
190.
192. 195. 197. 200. 204. 207.
209. (209) (210)
(222)
9
3 9 5 9 8
2 2 2 1 0 6 4
2 0
87
88 89
104 105 106
107 108 109
Fr
Ra Ae Rf Db
Sg 8h Hs Mt
(223) 226. 227. (261) (262) (266) (264) (265) (268)
0 0
58
59 60 61 62 63 64
65 66 67 68
69
70 71
Ce
Pr
Nd Pm Sm Eu
Gd Tb Dy Ho Er Tm Yb
Lu
140. 140.
144. (145)
150.
152.
157.
158. 162. 164.
167. 168. 173. 175.
1 9
2
4
0 3 9 5
9 3 9 0 0
90 91
92 93 94 95 96 97
98 99
100 101 102 103
Th Pa
U Np Pu Am
Cm 8k Cf Es Fm Md No Lr
232.
23l.
238. 237. (244) (243)
(247) (247) (251) (252)
(257) (258) (259) (262)
0 0
0 0
- 80 -