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


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-


3/42


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 -


[ 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 -


4/42


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-


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 -


5/42

I

. .


Multiply

By To obtain

I

Fathom

1.8288'

meter(m)


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


q/crns

Ns/m'

0.1000 10

Meter

0.0006213712 mile(USstatute)


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 -

.. :. ..


6/42


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


- 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 -


7/42


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


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 -


8/42


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 -


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 -


9/42


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 -


To Convert

To

Multiply By

Milligrams 1000

Grams

Hundredweights, Long

Long Tons

0.05


Metric Tons

0.050802345


Short Tons

0.056


Kilograms

50.802345


Avoirdupois Pounds

112

Hundredweights, Short

Long Tons

0.04464286


Metric Tons

0.045359237


Short Tons

0.05


Kilograms

45.359237


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 -


10/42


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 -


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)


22.4


Kilograms

1016.04691


Avoirdupois Pounds 2240


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


22.04623

Tons, Metric

Kilograms 1000

Tons, Metric

Avoirdupois Pounds

2204.623

Tons, Metric

Troy Ounces

32150.75

- 17 -


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


Grams/cu cm 0.001


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-


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 -



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 -


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 -


13/42


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 -


[ 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 -


14/42


ul tply Into

Into Into

Into Into Into Into

I

bv

Milli Centi

Oeci

MGL* Oeca Hecto

Kilo

To


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


15/42


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 -



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

.:


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

+


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


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


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~



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 -



25/42


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-



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 -


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 -


power dissipation


27/42


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


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 -

/


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 -


PhysicalQuantity


29/42


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


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-

/


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


,--


31/42


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 -


Conversion:


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 -


~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


A scalar quantity, equa l to the rate of doing work

In SI the unit is the Watt W (or kW)


33/42


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 -


01 atmosphere (atm) 10 1.3 kPa 14.7 psi


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-


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


35/42


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-


5.3.14 Elastic Deformation

.P= F A

.y

= FL

o

A6L


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 -

/


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


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


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 -


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


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

.. .


39/42


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


40/42

C I l

c

o

C])

>

c:

o

(J

0

c:

I l

..

: :J

E

&


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-


. -

Nominal

Outside

Inside

Wall

pipe size

diameter

diameter

thickness

Flow area

(in)

(mm)

(mm)

(mm)

(m')


41/42


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 -

. .


I J


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 -

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