Handbook of Formulae and Constants - 2003

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Handbook of
Formulae and
Physical Constants


For The Use Of Students And Examination Candidates




Duplication of this material for student

in-class use or for examination

purposes is permitted without written

approval.


Approved by the Interprovincial Power Engineering
Curriculum Committee and the Provincial Chief
Inspectors' Association's Committee for the
standardization of Power Engineer's Examinations n
Canada.

www.powerengineering.ca
Printed July 2003




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 1012 T
tera
1 000 000 000 109 G
giga
1 000 000 106 M
mega
1 000 103 k
kilo
100 102 h
hecto
10 101 da
deca
0.1 10-1 d
deci
0.01 10-2 c
centi
0.001 10-3 m
milli
0.000 001 10-6

micro
0.000 000 001 10-9 n
nano
0.000 000 000 001 10-12 p
pico



Conversion Chart for Metric Units






To



To
To
To
Metre, To
To
To
Milli-
Centi-
Deci-
Gram,
Deca-
Hecto-
Kilo-
Litre








Kilo-
x 106
x 105
x 104
x 103
x 102
x 101








Hecto-
x 105
x 104
x 103
x 102
x 101
x 10-1








Deca-
x 104
x 103
x 102
x 101
x 10-1
x 10-2
t
er
nv
o
Metre,






C
Gram,
x 103
x 102
x 101
x 10-1
x 10-2
x 10-3
o
T
Litre








Deci-
x 102
x 101
x 10-1
x 10-2
x 10-3
x 10-4








Centi-
x 101
x 10-1
x 10-2
x 10-3
x 10-4
x 10-5








Milli-
x 10-1
x 10-2
x 10-3
x 10-4
x 10-5
x 10-6


Page 1





BASIC UNITS

SI
IMPERIAL

DISTANCE

1 metre (1 m) = 10 decimetres (10 dm)
12 in. = 1 ft
= 100 centimetres (100 cm)
3 ft = 1 yd
= 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:

1
in.
=
25.4
mm

1 ft = 30.48 cm
1
mile
=
1.61
km
1
yd
=
0.914
m
1
m
=
3.28
ft


Area


1 sq metre (1 m2) = 10 000 cm2
1 ft2 = 144 in.2

= 1 000 000 mm2
1 yd2 = 9 ft2

1 sq mile = 640 acre = 1 section
1 sq hectometre (1 hm2) = 10 000 m2

= 1 hectare (1 ha)


1 sq km (1 km2) = 1 000 000 m2


Conversions:


1
in.2 = 6.45 cm2 = 645
mm2
1
m2 = 10.8 ft2

1 acre = 0.405 ha

1 sq mile = 2.59 km2

Page 2




SI

IMPERIAL

Volume

1
m3 = 1 000 000 cm3
1 ft3 = 1728 in.3

= 1 x 109 mm3
1 yd3 = 27 ft3

1
dm3 = 1 litre
1(liquid) U.S. gallon = 231 in.3

1 litre = 1000 cm3
= 4 (liquid) quarts
1
mL
=
1
cm3
1 U.S. barrel (bbl) = 42 U.S. gal.
1
m3 = 1000 litres
1 imperial gallon = 1.2 U.S. gal.


Conversions:

1
in.3 = 16.4 cm3
1
m3 = 35.3 ft3

1 litre = 61 in.3

1 U.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 grams
2000 lb = 1 ton (short)

1000 kg = 1 tonne
1 long ton = 2240 lb


Conversions:


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


Density

mass
weight

density

mass

=

density
weight

=

volume
volume

m kg
w lb

=





=





V 3
m
V 3
ft

Conversions:

kg
(on Earth) a mass density of 1
results in a weight density of 0.0623 lb
m3
ft3

Page 3





SI

Imperial

RELATIVE DENSITY

In SI R.D. is a comparison of mass density
In Imperial the corresponding quantity is
to a standard. For solids and liquids the
specific gravity; for solids and liquids a
standard is fresh water.
comparison of weight density to that of
water.


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
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
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
Iron (cast)....................7.21
Wood (elm).................0.66
Iron (wrought) ............7.78
Wood (lignum-vitae) ..1.3
Lead ..........................11.4 Wood
(oak).................0.7-1.0
Magnesium .................1.74 Wood
(pine)................0.56
Manganese..................8.0 Wood
(teak) ................0.8
Mercury ....................13.6 Zinc.............................7.0


Page 4





Greek Alphabet

Alpha

Iota

Rho

Beta

Kappa

Sigma
,
Gamma

Lambda

Tau

Delta

Mu

Upsilon

Epsilon

Nu

Phi
,
Zeta

Xi

Kai

Eta

Omicron

Psi

Theta
Pi

Omega
,




MATHEMATICAL FORMULAE

Algebra

1. Expansion Formulae


(x + y)2 = x2 + 2xy + y2


(x - y)2 = x2 - 2xy + y2


x2 - y2 = (x - y) (x + y)


(x + y)3 = x3 + 3x2y + 3xy2 + y3


x3 + y3 = (x + y) (x2 - xy + y2)


(x - y)3 = x3 - 3x2y + 3xy2 - y3


x3 - y3 = (x - y) (x2 + xy + y2)

2. Quadratic Equation

If
ax2 + bx + c = 0,

- b
b2 - 4ac
Then

x
=

2a

Page 5





Trigonometry


1. Basic Ratios

y
x
y

A
Sin

= ,
A

cos

= ,
A
tan

=
h
h
x


2. Pythagoras' Law

x2 + y2 = h2


3. Trigonometric Function Values

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

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

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


4. Solution of Triangles


a. Sine Law

a
b
c
=
=


A
Sin
B
Sin
C
Sin


b. Cosine Law


c2 = a2 + b2 - 2 ab Cos C


a2 = b2 + c2 - 2 bc Cos A


b2 = a2 + c2 - 2 ac Cos B


Page 6





Geometry

1. Areas of Triangles

a. All Triangles

height
lar
perpendicu
x
base


Area
=

2

A
Sin

bc
C
Sin

ab
B
Sin

ac
Area


=
=

=

2
2
2
and,

Area
=
(s

s

-
c)
-

(s

b)
-

(s

a)


a +
b
+ c


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

2

b. Equilateral Triangles

Area = 0.433 x side2

2. Circumference of a Circle

C = d

3. Area of a Circle

r
x
nce
circumfere

A = r2 =
=
2
d = 0.7854d2
2
4


4. Area of a Sector of a Circle

r
x
arc
A
=

2


A
=
2
x r

( = angle in degrees)
360

r 2

A
=
( = angle in radians)
2


Page 7


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