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Table of Contents 

TOPIC PAGE 

SI Multiples 1 

Basic Units (distance, area, volume, mass, density) 2 

Mathematical Formulae 5 

Applied Mechanics 10 

Thermodynamics 21 

Fluid Mechanics 28 

Electricity 30 

Periodic Table 34 



Names in the Metric System 



VALUE 


EXPONENT 


SYMBOL 


PREFIX 


1 000 000 000 000 


10 12 


T 


tera 


1 000 000 000 


10 9 


G 


giga 


1 000 000 


10 6 


M 


mega 


1 000 


10 3 


k 


kilo 


100 


10 2 


h 


hecto 


10 


10' 


da 


deca 


0.1 


10" 1 


d 


deci 


0.01 


10" 2 


c 


centi 


0.001 


10" 3 


m 


m i Mi 


0.000 001 


10" 6 


H 


micro 


0.000 000 001 


10" 9 


n 


nano 


0.000 000 000 001 


10 12 


P 


pico 



Conversion Chart for Metric Units 



CD 

> 

O 

O 





To 
Milli- 


To 
Centi- 


To 
Deci- 


To 

Metre, 
Gram, 
Litre 


To 
Deca- 


To 
Hecto- 


To 
Kilo- 


Kilo- 


x10 6 


x10 5 


x10 4 


x10 3 


x10 2 


x10 1 




Hecto- 


x10 5 


x10 4 


x10 3 


x10 2 


x10 1 




x10" 1 


Deca- 


x10 4 


x 10 3 


x10 2 


x10 1 




x10" 1 


x10" 2 


Metre, 
Gram, 
Litre 


x 10 3 


x 10 2 


x10 1 




x10" 1 


x10" 2 


x10" 3 


Deci- 


x 10 2 


x 10 1 




x10" 1 


x10" 2 


x10" 3 


x10 4 


Centi- 


x 10 1 




x10" 1 


x10" 2 


x10" 3 


x10 4 


x10" 5 


Milli- 




x 10" 1 


x10" 2 


x10" 3 


x10 4 


x10" 5 


x10" 6 




Page 1 



BASIC UNITS 



SI 


IMPERIAL 


DISTANCE 




1 metre (1 m) = 10 decimetres (10 dm) 


12 in. = 1 ft 


= 100 centimetres (100 cm) 


3ft = 1yd 


= 1000 millimetres (1000 mm) 


5280 ft = 1 mile 




1760 yd = 1 mile 


1 decametre (1 dam) = 10 m 




1 hectometre (1 hm) = 100 m 




1 kilometre (1 km) = 1000 m 





Conversions: 


lin. 


= 25.4 mm 


1ft 


= 30.48 cm 


mile 


= 1.61km 


1yd 


= 0.914 m 


lm 


= 3.28 ft 



Area 



1 sq metre (lm 2 ) = 10 000 cm 2 

= 1 000 000 mm 2 

1 sq hectometre (1 hm 2 ) = 10 000 m 2 

= 1 hectare (1 ha) 

1 sq km (1 km 2 ) = 1 000 000 m 2 



lft 2 

lyd 2 

1 sq mile 



144 in. 2 
9 ft 2 
640 acre 



1 section 



Conversions: 



lin. 2 

lm 2 

1 acre 

1 sq mile 



6.45 cm 2 
10.8 ft 2 
0.405 ha 
2.59 km 2 



645 mm 




Page 2 



SI 



IMPERIAL 



Volume 








lm' 


= 1 000 000 cm' 
= lxl0 9 mm' 


1ft' 
1yd' 


= 1728 in.' 
= 27 ft 3 


1dm' 

1 litre 

1 mL 

lm' 


= 1 litre 
= 1000 cm' 
= 1 cm' 
= 1000 litres 


1 (liquid) U.S. gallon 

1 U.S. barrel (bbl) 
1 imperial gallon 


= 231 in.' 
= 4 (liquid) quarts 
= 42 U.S. gal. 
= 1.2 U.S. gal. 



Conversions: 




lin.' = 


16.4 cm' 


lm' = 


35.3 ft' 


1 litre = 


61 in.' 


lU.S.gal = 


3.78 litres 


1 U.S. bbl = 


159 litres 


1 litre/s = 


15.9 U.S. gal/min 



Mass and Weight 

1 kilogram (1 kg) 
1000 kg 



1000 grams 
1 tonne 



2000 lb 
1 long ton 



1 ton (short) 
2240 lb 



Density 



Conversions: 



1 kg (on Earth) results in a weight of 2.2 lb 



mass density : 



m fkg 



V m 



mass 
volume 



weight density 



w 

V 



jb 
ft 3 



weight 
volume 



Conversions: 

(on Earth) a mass density of 1 — 3 results in a weight density of 0.0623 — 




Page 3 



SI 



RELATIVE DENSITY 

In SI R.D. is a comparison of mass density 
to a standard. For solids and liquids the 
standard is fresh water, 
water. 



Imperial 



In Imperial the corresponding quantity is 
specific gravity; for solids and liquids a 
comparison of weight density to that of 



Conversions: 

In both systems the same numbers 
hold for R.D. as for S.G. since 
these are equivalent ratios. 



RELATIVE DENSITY (SPECIFIC GRAVITY) OF VARIOUS SUBSTANCES 



Water (fresh) 1.00 

Water (sea average) .... 1.03 

Aluminum 2.56 

Antimony 6.70 

Bismuth 9.80 

Brass 8.40 

Brick 2.1 

Calcium 1.58 

Carbon (diamond) 3.4 

Carbon (graphite) 2.3 

Carbon (charcoal) 1.8 

Chromium 6.5 

Clay 1.9 

Coal 1.36-1.4 

Cobalt 8.6 

Copper 8.77 

Cork 0.24 

Glass (crown) 2.5 

Glass (flint) 3.5 

Gold 19.3 

Iron(cast) 7.21 

Iron (wrought) 7.78 

Lead 11.4 

Magnesium 1.74 

Manganese 8.0 

Mercury 13.6 



Mica 2.9 

Nickel 8.6 

Oil (linseed) 0.94 

Oil (olive) 0.92 

Oil (petroleum) 0.76-0.86 

Oil (turpentine) 0.87 

Paraffin 0.86 

Platinum 21.5 

Sand (dry) 1.42 

Silicon 2.6 

Silver 10.57 

Slate 2.1-2.8 

Sodium 0.97 

Steel (mild) 7.87 

Sulphur 2.07 

Tin 7.3 

Tungsten 19.1 

Wood (ash) 0.75 

Wood (beech) 0.7-0.8 

Wood (ebony) 1.1-1.2 

Wood (elm) 0.66 

Wood (lignum-vitae) ..1.3 

Wood(oak) 0.7-1.0 

Wood (pine) 0.56 

Wood (teak) 0.8 

Zinc 7.0 




Page 4 



Greek Alphabet 


Alpha 


a 


Beta 


P 


Gamma 


Y 


Delta 


A 


Epsilon 


s 


Zeta 


c 


Eta 


Tl 


Theta 


e 



Iota 


i 


Kappa 


K 


Lambda 


X 


Mu 


n 


Nu 


V 


Xi 


S 


Omicron 





Pi 


71 



Rho 


P 


Sigma 


I, a 


Tau 


X 


Upsilon 


u 


Phi 


®A 


Kai 


i 


Psi 


V 


Omega 


Q, co 



MATHEMATICAL FORMULAE 

Algebra 

1. Expansion Formulae 



(x + y) = x + 2xy + y 



(x - y) = x - 2xy + y 
x 2 -y 2 = (x-y) (x + y) 



(x + y) = x + 3x y + 3xy + y 
x + y = (x + y) (x - xy + y ) 



(x-y) = x" - 3x y + 3xy - y 
x 3 -y 3 = (x - y) (x 2 + xy + y 2 ) 



2. Quadratic Equation 

Ifax 2 + bx + c = 0, 



Then x 



■b±Vb 2 -4ac 



2a 




Page 5 



Trigonometry 



1. Basic Ratios 



Sin A = — , cos A = — 



tan A: 



y 




2. Pythagoras' Law 



2,2 i 2 

x +y = n 



3. Trigonometric Function Values 

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

4. Solution of Triangles 
a. Sine Law 



Sin A Sin B Sin C 



b. Cosine Law 



a 2 + b 2 - 2 ab Cos C 



b 2 + c 2 - 2 be Cos A 



a 2 + c 2 - 2 ac Cos B 





Page 6 



Geometry 

1. Areas of Triangles 

a. All Triangles 

base x perpendicular height 



Area: 



Area 



be Sin A ab Sin C ac Sin B 



and, 



Area = ^J s (s - a) (s - b) (s - c) 




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



a + b + c 



b. Equilateral Triangles 



Area = 0.433 x side 2 



2. Circumference of a Circle 



C = 7id 



3. Area of a Circle 



A = TOf 



circumference x r % 



d 2 =0.7854d 2 



4. Area of a Sector of a Circle 



arcxr 



A = — — x 71 r 2 (9 = angle in degrees) 



A : 



360 



9°r 2 



(9 = angle in radians) 





Page 7 



5. Area of a Segment of a Circle 

A = area of sector - area of triangle 



Also approximate area = — h 2 J— - 0.608 



6. Ellipse 



A=*Dd 



Approx. circumference = it 



(D + d) 



t 
d 




Triangle 



Segment 




7. Area of Trapezoid 



H a — H 



A : 



a + b' 




-H 



8. Area of Hexagon 

A = 2.6s 2 where s is the length of one side 



9. Area of Octagon 

A = 4.83s 2 where s is the length of one side 



10. Sphere 



Total surface area A =4tuc 



Surface area of segment A s = 7tdh 



4 3 
Volume V= — 7ir 
3 



Volume of segment 
V s = ^(3r-h) 

V. = -^-(h 2 + 3a 2 ) where a = radius of segment base 






Page 8 



11. Volume of a Cylinder 



V = — d 2 L where L is cylinder length 



12. Pyramid 

Volume 

V = - base area x perpendicular height 
Volume of frustum 




Frustum 



V F = — (A + a + v Aa) where h is the perpendicular height, A and a are areas as shown 



13. Cone 



Area of curved surface of cone: 



A : 



7i DL 




Area of curved surface of frustum 



A F 



7c (D + d)L 



Volume of cone: 

_ base area x perpendicular height 




Volume of frustum: 

_ perpendicular height x tt (R 2 + r 2 + Rr) 




Page 9 



APPLIED MECHANICS 

Scalar - a property described by a magnitude only 

Vector - a property described by a magnitude and a direction 

, T , mjL , A displacement 
Velocity - vector property equal to — —. 

The magnitude of velocity may be referred to as speed 
In SI the basic unit is ™, in Imperial ^ 

Other common units are ^H, ^ 

h h 

^ . , m . _„ ft 

Conversions: 1 — = 3.28 — 



, km „ ^„, mi 

1 = 0.621 — 

h h 



Speed of sound in dry air is 33 1 ^ at 0°C and increases by about 0.61 ^ for each °C 



s 
rise 



Speed of light in vacuum equals 3 x 10 8 m 



Acceleration - vector property equal to 



s 

change in velocity 
time 



In SI the basic unit is — -, in Imperial — - 

s s 



-. . , m _ _„ ft 

Conversion: 1— = 3.28 — 

s s 



Acceleration due to gravity, symbol "g", is 9.81 — or 32.2 — - 

s s 




Page 10 



LINEAR VELOCITY AND ACCELERATION 



u initial velocity 

v final velocity 

t elapsed time 

s displacement 

a acceleration 



v = u + at 
'v + u 



t 



v 



1 9 

s = ut + y at 

2 - u 2 + 2 as 



Angular Velocity and Acceleration 




9 angular displacement (radians) 

co angular velocity (radians/s); coi = initial, co 2 = final 

a angular acceleration (radians/s 2 ) 



co 2 = coi + at 



9 = coi + co 2 x t 

2 



9 = coit + V^ar 



co 2 2 = coi 2 + 2a9 



linear displacement, s = r 9 

linear velocity, v = r co 

linear, or tangential acceleration, a T = r a 




Page 1 1 



Tangential, Centripetal and Total Acceleration 

Tangential acceleration ax is due to angular acceleration a 



a T = roc 



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



a c = v 2 /r = r co 2 



Total acceleration, a, of a rotating point experiencing angular acceleration is the vector sum 
of a T and a c 

a = ax + a c 
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, defined as a , 

s 

In Imperial the unit of force is the pound lb 

Conversion: 9.81 N = 2.2 lb 
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/s 2 



In Imperial, the mass of an object (rarely used), in slugs, can be calculated from the known 
weight in pounds 

Weight ft 

m = — g — § = 32 V 




Page 12 



Newton's Second Law of Motion 

An unbalanced force F will cause an object of mass m to accelerate a, according to: 
F = ma (Imperial F = ^ a, where w is weight) 

Torque Equation 

T = I a where T is the acceleration torque in Nm, I is the moment of inertia in kg m 2 
and a is the angular acceleration in radians/s 2 

Momentum 

Vector quantity, symbol p, 

p = mv (Imperial p = ^ v, where w is weight) 

. „ x . . kg m 
in SI unit is — ^ — 

Work 

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

W = Fs 

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 




Page 13 



Kinetic Energy 

Energy due to motion 
E v = imv 2 



In Imperial this is usually expressed as E k = ^v 2 where w is weight 
Kinetic Energy of Rotation 

E R = — mk 2 (D 2 where k is radius of gyration, co is angular velocity in rad/s 

or 

Ep = — Icd 2 where I = mk 2 is the moment of inertia 

R 2 

CENTRIPETAL (CENTRIFUGAL) FORCE 

F c = where r is the radius 



or 

F c = m co 2 r where co is angular velocity in rad/s 
Potential Energy 

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

E p = m g h 

In Imperial this is usually expressed E p = w h where w is weight, and h is height above some 
specified datum 




Page 14 



Thermal Energy 

In SI the common units of thermal energy are J, and kJ, (and kJ/kg for specific quantities) 

In Imperial, the units of thermal energy are British Thermal Units (Btu) 

Conversions: 1 Btu = 1055 J 

1 Btu = 778 ft-lb 

Electrical Energy 

In SI the units of electrical energy are J, kJ and kilowatt hours kWh. In Imperial, the unit of 
electrical energy is the kWh 

Conversions: 1 kWh = 3600 kJ 

1 kWh = 3412 Btu = 2.66 x 10 6 ft-lb 

Power 

A scalar quantity, equal to the rate of doing work 
In SI the unit is the Watt W (or kW) 

lW=l| 
In Imperial, the units are: 

Mechanical Power - ~ — , horsepower h.p. 

Thermal Power - =^± 

Electrical Power - W, kW, or h.p. 

Conversions: 746 W = 1 h.p. 



1 h.p. = 550 &^ 



1 kW = 0.948 =^= 




Page 15 



Pressure 

A vector quantity, force per unit area 

In SI the basic units of pressure are pascals Pa and kPa 

lPa=l4 
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 

1 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 equivalencies are: 

1 kPa = 0.294 in. mercury = 7.5 mm mercury 
1 kPa = 4.02 in. water = 102 mm water 
1 psi = 2.03 in. mercury = 51.7 mm mercury 
1 psi = 27.7 in. water = 703 mm water 
1 mH 2 = 9.81 kPa 

Other pressure unit conversions: 

1 bar= 14.5 psi = 100 kPa 

.2 



1 kg/cm =98.1 kPa= 14.2 psi = 0.981 bar 
1 atmosphere (atm) = 101.3 kPa = 14.7 psi 




Page 16 



Simple Harmonic Motion 



Velocity of P = oo a/R 2 -x : 



Acceleration of P = (D xm/s 



m 

s 

2 



2% 



The period or time of a complete oscillation = — seconds 

CO 

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




T = 2jc. 



(displacement 
acceleration 



Simple Pendulum 

T = 2ti / — T = period or time in seconds for a double swing 

V § 

L = length in metres 

The Conical Pendulum 



(elevation) 




force diagram 



R/H = tan 9= F c /W = co 2 R/g 




Page 17 



Lifting Machines 

W = load lifted, 



F = force applied 



MA. 



load 
effort 



W 

F 



V.R. (velocity ratio) 



n 



efficiency 



effort distance 
load distance 



M.A. 



V.R. 



1. Lifting Blocks 

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

2. Wheel & Differential Axle 



Velocity ratio 



2tiR 



27i(r - r, ) 

2 



2R 



r-r, 



2R 



Or, using diameters instead of radii, 

„ . . 2D 

Velocity ratio 



(d-d,) 



3. Inclined Plane 



V.R 



length 
height 



4. Screw Jack 



V.R 



circumference of leverage 
pitch of thread 




Gearing 



S= 






n 



Snatch block 




Pitch 



A 



* 



Effort 
Load 




Page 18 



Indicated Power 

LP. = P m A L N where LP. is power in W, P m is mean or "average" effective pressure in 
Pa, A is piston area in m , L is length of stroke in m and N is number of 
power strokes per second 

Brake Power 

B.P. = Lcd where B.P. is brake power in W, L is torque in Nm and co is angular 
velocity in radian/second 



STRESS, STRAIN and MODULUS OF ELASTICITY 



Direct stress 



Direct strain 



load _ P 
area A 



extension A£ 
original length L 




Modulus of elasticity 

„ direct stress P/A 



PL 



direct strain AiVL AAl 



Shear stress x 



Shear strain 



force 



area under shear 



L 



Modulus of rigidity 

_ shear stress 

(j 

shear strain 



Force 




Force 




x Force 





Page 19 



General Torsion Equation (Shafts of circular cross-section) 



T 
J 



G0 



1. For Solid Shaft 

T % 4 7id 4 
J = — r = 

2 32 

2. For Hollow Shaft 

J = f(r: 4 -r 2 4 ) 



32 



(d 4 -d 4 ) 



T = torque or twisting moment in newton metres 

J = polar second moment of area of cross-section 

about shaft axis, 

x = shear stress at outer fibres in pascals 

r = radius of shaft in metres 

G = modulus of rigidity in pascals 

= angle of twist in radians 

L = length of shaft in metres 

d = diameter of shaft in metres 



Relationship Between Bending Stress and External Bending Moment 



M 
I 



(7 

y 



E 
R 



1. For Rectangle 









D 


- 










BD 3 



M 
I 

c 

y 

E 
R 



external bending moment in newton metres 

second moment of area in m 

bending stress at outer fibres in pascals 

distance from centroid to outer fibres in metres 

modulus of elasticity in pascals 

radius of currative in metres 



12 



2. For Solid Shaft 




7iD 4 

64 




Page 20 



THERMODYNAMICS 



Temperature Scales 



°C = -(°F-32) °F=-°C + 32 

9 5 



°R = °F + 460 (R Rankine) K = °C + 273 (K Kelvin) 
Sensible Heat Equation 

Q = mcAT 

m is mass 

c is specific heat 

AT is temperature change 

Latent Heat 

Latent heat of fusion of ice = 335 kJ/kg 

Latent heat of steam from and at 100°C = 2257 kJ/kg 

1 tonne of refrigeration = 335 000 kJ/day 

= 233 kJ/min 

Gas Laws 

1. Boyle's Law 

When gas temperature is constant 

PV = constant or 

PiV, = P 2 V 2 

where P is absolute pressure and V is volume 

2. Charles' Law 



V 
When gas pressure is constant, — = constant 

or -=i = -=!■ , where V is volume and T is absolute temperature 




Page 21 



3. Gay-Lussac's Law 



When gas volume is constant, — = constant 

T 



P P 

Or — = — , where P is absolute pressure and T is absolute temperature 
lj l 2 



4. General Gas Law 


PiV, _ P 2 V 2 _ 
T, T 2 


= constant 


P V=mRT 


where P 




V 




T 




m 




R 


Also 




PV = nPvoT 


where P 




V 




T 




N 




Ro 



absolute pressure (kPa) 

volume (nr ) 

absolute temp (K) 

mass (kg) 

characteristic constant (kJ/kgK) 



absolute pressure (kPa) 

volume (m 3 ) 

absolute temperature K 

the number of kmoles of gas 

the universal gas constant 8.314 kJ/kmol/K 



SPECIFIC HEATS OF GASES 





Specific Heat at 


Specific Heat at 


Ratio of Specific 




Constant Pressure 


Constant Volume 


Heats 




kJ/kgK 


kJ/kgK 


T = C p /C v 


GAS 


or 


or 






kJ/kg °C 


kJ/kg °C 




Air 


1.005 


0.718 


1.40 


Ammonia 


2.060 


1.561 


1.32 


Carbon Dioxide 


0.825 


0.630 


1.31 


Carbon Monoxide 


1.051 


0.751 


1.40 


Helium 


5.234 


3.153 


1.66 


Hydrogen 


14.235 


10.096 


1.41 


Hydrogen Sulphide 


1.105 


0.85 


1.30 


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 




Page 22 



Efficiency of Heat Engines 

T - T 

Carnot Cycle r\ = —^-= — - where Ti and T 2 are absolute temperatures of heat source and 
lj 

sink 

Air Standard Efficiencies 

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

1 . . cylinder volume 

T| = 1 - — — — where r v = compression ratio = 

r; Y " } v clearance volume 

specific heat (constant pressure) 

y ~ 

specific heat (constant volume) 

2. Diesel Cycle 

(R Y — V) 

n = 1 — ^ — where r = ratio of compression 

r v T y(R-l) 

R = ratio of cut-off volume to clearance volume 

3. High Speed Diesel (Dual-Combustion) Cycle 

kp y -l 



n = l- 



where r v 



k 



rr[(k-l) + yk(P-l)] 
cylinder volume 



P 



clearance volume 

absolute pressue at end of constant V heating (combustion) 
absolute pressue at beginning of constant V combustion 

volume at end of constant P heating (combustion) 



clearance volume 
4. Gas Turbines (Constant Pressure or Brayton Cycle) 

1 



r, = l- 




Page 23 



where r p = pressure ratio 



compressor discharge pressure 
compressor intake pressure 



W 

o 
a* 

o 



a 

© 

O 

u 

si 
O 

&o 
O 
<| 

c 

a 

u 



< 

Q 
O 



4=WCo-^ 


K Ik 

60 

,0 

£ 


cH ~ 
K |K 

.£ 
a. 

£ 


.0 

OS 
£ 





^k~ 

a 

£ 




K" 

5 


E-T 
ft. 

£ 





ft. 

£ 


K- 

CL 

£ 


Change In 
Internal 
Energy 


K? 

5 


E-T 

£ 





E-T 
K* 

5 


£ 


Work Done 

1W2 
kJ 





a. 


K 
a; 
£ 


2* 

E-T 

Cj 

£ 


k" 

k" 


-a 

cd ^ 
cu 


k" 

K 

5 


K~" 

ft. 


-2 

K 

£ 





c 

£ 


a. 

2 

CO 

c 

+^ 

CD 

K. 

I 

1 

Is 


1 
f-1 






tl 






II 

eC Is" 


V 

II 

^|k" 


0, 
1 


a, lo, 
11 

EC Ik" 










n<C|^ 
11 
kIk* 


II 
kIk" 


1 
0, 












* vc£5 

II 


11 


O 

1 


8 





- 


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s: 


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8 

E 2 

Z 1 ^ 


C <u C 
03 C © 
-t-J C r \ 


+■* 

S " ° 

CQ CO 

g 8 11 


13 ■»-** 


* 

.— co 

g 11 


CO 

E° 

a 11 



o 
c 



> 



t3 



O 
* 



50 



o 

o 

+ 

rn 

I! 

3 



a, (2jj 

B (Dm 

^ £h ? 

„ ^ s i J 

O [§ < ^ 



_ 

^ ■ — . 
a -3 

+_> 
S3 

o 
o 



60 

M 

to 



•> s 



^MHD> S 



to 






3 





^ 


-.. 


D 


O 


kl 




J3 


3 


ra 







T3 


rf> 


Q. 










c 


a 


<U 


m 


■* 


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eft 


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o 
o 

Oh 



Cl, 



a. 



S3 C8 t-w 

■Js 13 "Es *n 

i> a> i> M 

nJLuBt f^«q p*i«l ^^ 

o o o q^ 

O O O ^3 

u w a> ±3 

& 0, a, c 

C/5 &0 C<0 ttj 



S a 

5 o 

X « ^ 

w w a, 

o ,y ^ 

a ^ <d 

o P ^ 

c J= 3 

+-> 5- to 

R J » 

W c I- 1 

~h Ph cu 







Page 24 



Heat Transfer by Conduction 

n= AAtAT 
V d 

where Q = heat transferred in joules 

A, = thermal conductivity or coeficient of heat 



transfer in 



J x m 



or 



W 



m 2 x s x °C m x °C 



A = area in m 2 
t = time in seconds 
AT = temperature difference between surfaces in °C 
d = thickness of layer in m 



COEFFICIENTS OF THERMAL CONDUCTIVITY 



Material 


Coefficient of 




Thermal Conductivity 




W/m °C 


Air 


0.025 


Aluminum 


206 


Brass 


104 


Brick 


0.6 


Concrete 


0.85 


Copper 


380 


Cork 


0.043 


Felt 


0.038 


Glass 


1.0 


Glass, fibre 


0.04 


Iron, cast 


70 


Plastic, cellular 


0.04 


Steel 


60 


Wood 


0.15 


Wallboard, paper 


0.076 




Page 25 



Thermal Expansion of Solids 



Increase in length 

where L 

a 

(T 2 - Ti ) 



L a (T 2 - Ti ) 

original length 

coefficient of linear expansion 

rise in temperature 



Increase in volume 
Where V 

P 
(T 2 - T, ) 



V P (T 2 - Ti ) 

original volume 

coefficient of volumetric expansion 

rise in temperature 



coefficient of volumetric expansion 

P 



coefficient of linear expansion x 3 

3a 



SPECIFIC HEAT and LINEAR EXPANSION OF SOLIDS 





Mean 


Coefficient 




Mean 


Coefficient 




Specific Heat 


of 




Specific Heat 


of 




between 0°C 


Linear Expansion 




between 0°C 


Linear Expansion 


Solid 


and 100°C 


between 0°C and 


Solid 


and 100°C 


between 0°C and 




kJ/kgK or 


100°C 
(Multiply by 10" 6 ) 




kJ/kgK or 


100°C 
(Multiply by 10" 6 ) 




kJ/kg°C 




kJ/kg°C 


Aluminum 


0.909 


23.8 


Iron (cast) 


0.544 


10.4 


Antimony 


0.209 


17.5 


Iron (wrought) 


0.465 


12.0 


Bismuth 


0.125 


12.4 


Lead 


0.131 


29.0 


Brass 


0.383 


18.4 


Nickel 


0.452 


13.0 


Carbon 


0.795 


7.9 


Platinum 


0.134 


8.6 


Cobalt 


0.402 


12.3 


Silicon 


0.741 


7.8 


Copper 


0.388 


16.5 


Silver 


0.235 


19.5 


Glass 


0.896 


9.0 


Steel (mild) 


0.494 


12.0 


Gold. 


0.130 


14.2 


Tin 


0.230 


26.7 


Ice 


2.135 


50.4 


Zinc 


0.389 


16.5 


(between -20°C 












and 0°C) 















SPECIFIC HEAT and VOLUME EXPANSION FOR LIQUIDS 




Liquid 


Specific Heat 

(at20°C) 

kJ/kgKorkJ/kg°C 


Coefficient of 
Volume Expansion 
(Multiply by 10" 4 ) 


Liquid 


Specific Heat 

(at 20°) 

kJ/kgKorkJ/kg°C 


Coefficient of 
Volume Expansion 
(Multiply by 10-4) 


Alcohol (ethyl) 


2.470 


11.0 


Olive Oil 


1.633 




Ammonia 


0.473 




Petroleum 


2.135 




Benzine 


1.738 


12.4 


Gasoline 


2.093 


12.0 


Carbon Dioxide 


3.643 


1.82 


Turpentine 


1.800 


9.4 


Mercury 


0.139 


1.80 


Water 


4.183 


3.7 




Page 26 



Chemical Heating Value of a Fuel 

Chemical Heating Value MJ per kg of fuel = 33.7 C + 144 (h 2 - ^) + 9.3 S 

8 

C is the mass of carbon per kg of fuel 

H 2 is the mass of hydrogen per kg of fuel 

O2 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 

Air (kg per kg of fuel) = [-C + 8 (h 2 - ^_) + s] 



100 

23 



Air Supplied from Analysis of Flue Gases 

Air in kg per kg of fuel = 33 (C( ^ 2 + CQ) x C 

C is the percentage of carbon in fuel by mass 

N 2 is the percentage of nitrogen in flue gas by volume 

C0 2 is the percentage of carbon dioxide in flue gas by volume 

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

Boiler Formulae 

m,(h!-h 2 ) 



Equivalent evaporation 
Factor of evaporation = 
Boiler efficiency 



2257 kJ/kg 

2257 kJ/kg 
m s( h i- h 2 ) 



m f x calorific value of fuel 



where rh s = mass flow rate of steam 

hi = enthalpy of steam produced in boiler 

h 2 = enthalpy of feedwater to boiler 

rh, = mass flow rate of fuel 




Page 27 



FLUID MECHANICS 



Discharge from an Orifice 



Let A 

and A c 
then A c 

or C c 



cross-sectional area of the orifice = (7t/4)d 

cross-sectional area of the jet at the vena conrtacta = ((tt/4) d ^ 

C C A 

A 



where C c is the coefficient of contraction 





Vena contracta 

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

Q = area of the jet at the vena contracta x actual velocity 
= A c v 
or Q = C C AC V s/^gli 

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

C d 

i.e. (^j — ^A^„ 



and Q = C d A ^/^gh 
Typically, values for Cd vary between 0.6 and 0.65 
Circular orifice: Q = 0.62 A y/2gh 
Where Q = flow (m 3 /s) A = area (m 2 ) h = head (m) 
Rectangular notch: Q = 0.62 (B x H) ^sfl$\ 

Where B = breadth (m) H = head (m above sill) 
Triangular Right Angled Notch: Q = 2.635 H 5/2 
Where H = head (m above sill) 




Page 28 



Bernoulli's Theory 



H 

H 

h 

P 



w 2g 
total head (metres) 
height above datum level (metres) 
pressure (N/m 2 or Pa) 



w 

V 



force of gravity on 1 m of fluid (N) 
velocity of water (metres per second) 



Loss of Head in Pipes Due to Friction 

Loss of head in metres = f- 



?L v 2 



L 

d 
pipes 



length in metres 
diameter in metres 



d 2g 

v = 
f = 



velocity of flow in metres per second 

constant value of 0.01 in large pipes to 0.02 in small 



Note: This equation is expressed in some textbooks as 

T v 2 
Loss = 4f=^ ^— where the f values range from 0.0025 to 0.005 
d 2g ° 



Actual Pipe Dimensions 

Scheduled (SI Units) 



Nominal 

Pipe Size 

(in) 


Outside 
Diameter 

(mm) 


Inside 

Diameter 

(mm) 


Wall 

Thickness 

(mm) 


Flow 
Area 
(m 1 ) 


l 
s 


10.3 


6.8 


1.73 


3.660 x 10 ~* 


i 

4 


13.7 


9.2 


2.24 


6.717 x 10" 5 


1 
8 


17.1 


12.5 


2.31 


1.236 x 10"* 


1 
2 


21.3 


15.8 


2.77 


1.960 x KT 4 


1 

4 


26.7 


20.9 


2.87 


3.437 x 10"* 


1 


33.4 


26.6 


3.38 


5.574 x 10 " 4 


li 


42.2 


35.1 


3.56 


9.653 x 10 ~* 


ii 


48.3 


40.9 


3.68 


1.314 x 10" 3 


2 


60.3 


52.5 


3.91 


2.168 x 10" 3 


2i 


73.0 


62.7 


5.16 


3.090 x 10" 3 


3 


88.9 


77.9 


5.49 


4.768 x 10" 3 


8} 


101.6 


90.1 


5.74 


6.381 x 10 " 3 


4 


114.3 


102.3 


6.02 


8.213 x 10 -3 


5 


141.3 


128.2 


6.55 


1.291 x 10 -2 


6 


168.3 


154.1 


7.11 


1.864 x KT 2 


8 


219.1 


202.7 


8.18 


3.226 x 10 -2 


10 


273.1 


254.5 


9.27 


5.090 x 10 " 2 


12 


323.9 


303.2 


10.31 


7.219 x 10" 2 


14 


355.6 


333.4 


11.10 


8.729 x 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 


17.45 


0.2594 




Page 29 



ELECTRICITY 



Ohm's Law 



or h 

where I 
E 
R 



E 
R 

IR 

current (amperes) 
electromotive force (volts) 
resistance (ohms) 



Conductor Resistivity 

a 
where p = specific resistance (or resistivity) (ohm metres, Q-m) 
L = length (metres) 
a = area of cross-section (square metres) 

Temperature correction 

R t = Ro (1 + at) 

where R, = resistance at 0°C (Q) 
R t = resistance at t°C (Q) 
a = temperature coefficient which has an average value for copper of 0.004 28 

(Q/Q°C) 

R 2 = Rl (l±^il 
(1 + atJ 

where Ri = resistance at ti (Q) 
R2 = resistance at t2 (Q) 



a Values 



Q/Q°C 



copper 

platinum 

nickel 

tungsten 

aluminum 



0.00428 

0.00385 

0.00672 

0.0045 

0.0040 




Page 30 



Dynamo Formulae 

Average e.m.f. generated in each conductor = — rr r 

° 60c 

where Z = total number of armature conductors 

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

O = useful flux per pole (webers), entering or leaving the armature 
p = number of pairs of poles 
N = speed (revolutions per minute) 

Generator Terminal volts = E G - I a R a 

Motor Terminal volts = E B + I a R a 

where E G = generated e.m.f. 

E B = generated back e.m.f. 

I a = armature current 

R a = armature resistance 

Alternating Current 

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

Mean value of sine curve = 0.637 maximum value 

., , R.M.S. value 0.707 1 „ 

Form factor of sinusoidal = = = 1.11 

Mean value 0.637 

pN 
Frequency of alternator = cycles per second 

Where p = number of pairs of poles 
N = rotational speed in r/min 




Page 31 



Slip of Induction Motor 

Slip speed of field - speed of rotor , nn 

— - — xlOO 

Speed of field 

Inductive Reactance 

Reactance of AC circuit (X) = 27ifL ohms 
where L = inductance of circuit (henries) 



Inductance of an iron cored solenoid = — ; — henries 

LxlO 8 



where T = turns on coil 

[i = magnetic permeablility of core 

A = area of core (square centimetres) 

L = length (centimetres) 

Capacitance Reactance 



Capacitance reactance of AC circuit = ohms 

2jrfC 



where C = capacitance (farads) 



r 



Total reactance 



27ifL ohms 

2ti fC J 



Impedence (Z) = -^/(resistance) 2 + (reactance) 2 



R 2 + (2tc fL - — *— ) 2 ohms 
I 27tfC 



Current in AC Circuit 

impressed volts 



Current ■ 



impedance 




Page 32 



Power Factor 



p.f. 



true watts 
volts x amperes 



also p.f. = cos O, where O is the angle of lag or lead 
Three Phase Alternators 



Star connected 
Line voltage 
Line current 

Delta connected 
Line voltage 

Line current 



V3 x phase voltage 
phase current 



phase voltage 

V3 x phase current 



Three phase power 

P = V3 E l I l cosO 
E l = line voltage 
II = line current 
cos O = power factor 





\ E 2 


P 






\ R 


E 


E \ 


/ E I 






R \ 


/ I 2 R 


1 P 


I 


\ R 


E 

\ I 


\ R 


E 


/ VPR / 


\y^ E 


2 \^^ 












I R ^ / 


\ P 










/ P 


p 






/ I 2 


i 






Page 33 



Noble Gases 



< 

oo = 




00 


m 


o 


co 








o 




CO 


o Jg d 


cn 
co >; cri 


00 

8£8 


■<t a> co 


CM 


CO 


m 


§^S 


i- > 


<N X 


»- 2 cj 


7- < co 


in X t- 


CD 


S J^ 
















E 
c 
o 








CO 

&co 


o 


in 


o 


o> 




o 




< 


o 5^ 


o 


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cn 

in^oi 


CD 
CO CM 


8<i& 




Of N 


8^8. 


i- > 


cd ^t 


O) U. i- 


T-On 


CO CO |-~ 


m — f- 


A, 


r» >- t- 




1 












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t-- 


CD 


co 




4, 


cn 




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o 
co .„ c\i 


S^fS 


CM .CD CM 

m H i- 


S£S 


CO 

Q 

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C CO 

cn t co 

co H t- 


CO 

IIS 






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OO 


00 


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co 




m < 




o 


cn 
in „ d 


cn 
co <J ■* 


■^ £ CM 


cn 
C ~ ° 




co ,*-, CD 


§ E te 


T- > 




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co < r- 


in c/) t- 


CO CO CM 




(D 111 i- 






en 


cn 




CM 


cn 




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o 
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in 
cm .9 c\i 


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CM XI O 




S O CD 


8?£S 




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co O r-. 


in CO -^ 


CO CL CM 




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m CO i- 


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CO -= CD 
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coSS 


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cm m 






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CD 

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feall 










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CD 1- -^ 




m 


cn 


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co 


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CD 
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co p o 


iri 
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co 

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cn > 


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cn 


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m 

CO > 


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1- 
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CD 

c 
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CO 


in 

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co .cd in 
cm u. in 


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CM 
CD "> § 

h- O T- 


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Stl 




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m £ -* 
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CD Z i- 


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Page 34 



ION NAMES AND FORMULAE 



MONATOMIC 



POLYATOMIC 



Ag + 


silver ion 


B0 3 3 " 


borate ion 


Al 3+ 


aluminum ion 


C2H3O2 


acetate ion 


Au + and Au 2+ 


gold ion 


CIO" 


hypochlorite ion 


Be 2+ 


beryllium ion 


C10 2 " 


chlorite ion 


Ca 2+ 


calcium ion 


CIO3- 


chlorate ion 


Co 2+ and Co 3+ 


cobalt ion 


CIO4" 


perchlorate ion 


Cr 2+ and Cr 3+ 


chromium ion 


CN" 


cyanide ion 


Cu + and Cu 2+ 


copper ion 


CO3 2 " 


carbonate ion 


Fe 2+ and Fe 3+ 


iron ion 


C2O4 2 " 


oxalate ion 


K + 


potassium ion 


Cr0 4 2 " 


chromate ion 


Li + 


lithium ion 


Cr 2 7 2 " 


dichromate ion 


Mg 2+ 


magnesium ion 


HCO3" 


hydrogen carbonate or bicarbonate ion 


Na + 


sodium ion 


H 3 + 


hydronium ion 


Zn 2+ 


zinc ion 


HPO4 2 " 


hydrogen phosphate ion 






H2PO4" 


dihydrogen phosphate ion 






HSO3" 


hydrogen sulphite or bisulphite ion 






HSO4" 


hydrogen sulphate or bisulphate ion 






Mn0 4 " 


permanganate ion 






N 3 " 


azide ion 






NH 4 + 


ammonium ion 






N0 2 " 


nitrite ion 






N0 3 " 


nitrate ion 






2 2 - 


peroxide ion 






OCN" 


cyanate ion 






OH" 


hydroxide ion 






P0 3 3 " 


phosphite ion 






P0 4 3 " 


phosphate ion 






SCN" 


thiocyanate ion 






SO3 2 " 


sulphite ion 






S0 4 2 " 


sulphate ion 






S2O3 2 " 


thiosulphate ion 




Page 35 




power engineering 

TRAINING SYSTEMS 



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