# Handbook of Formulae and 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 1 000 000 000 000 1 000 000 000 1 000 000 1 000 100 10 0.1 0.01 0.001 0.000 001 0.000 000 001 0.000 000 000 001 EXPONENT 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 SYMBOL T G M k h da d c m µ n p PREFIX tera giga mega kilo hecto deca deci centi milli micro nano pico

Conversion Chart for Metric Units

To Millix 106

To Centix 105

To Decix 104

To Metre, Gram, Litre x 103

To Decax 102

To Hectox 101

To Kilo-

Kilo-

Hecto-

x 105

x 104

x 103

x 102

x 101

x 10-1

DecaTo Convert

x 104

x 103

x 102

x 101

x 10-1

x 10-2

Metre, Gram, Litre Deci-

x 103

x 102

x 101

x 10-1

x 10-2

x 10-3

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 DISTANCE

1 metre (1 m) = 10 decimetres (10 dm) = 100 centimetres (100 cm) = 1000 millimetres (1000 mm) 1 decametre (1 dam) = 10 m 1 hectometre (1 hm) = 100 m 1 kilometre (1 km) = 1000 m Conversions: 1 in. 1 ft 1 mile 1 yd 1m Area 1 sq metre (1 m2) = 10 000 cm2 = 1 000 000 mm2 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 1 m2 1 acre 1 sq mile = = = = 6.45 cm2 = 645 mm2 10.8 ft2 0.405 ha 2.59 km2 1 ft2 = 144 in.2 1 yd2 = 9 ft2 1 sq mile = 640 acre = 1 section = = = = = 25.4 mm 30.48 cm 1.61 km 0.914 m 3.28 ft 12 in. 3 ft 5280 ft 1760 yd = = = = 1 ft 1 yd 1 mile 1 mile

IMPERIAL

Page 2

SI

Volume 1 m3 = 1 000 000 cm3 = 1 x 109 mm3 1 dm3 1 litre 1 mL 1 m3 = = = = 1 litre 1000 cm3 1 cm3 1000 litres Conversions: 1 in.3 1 m3 1 litre 1 U.S.gal 1 U.S. bbl 1 litre/s Mass and Weight 1 kilogram (1 kg) = 1000 grams 1000 kg = 1 tonne Conversions: = = = = = =

IMPERIAL

1 ft3 = 1728 in.3 1 yd3 = 27 ft3 1(liquid) U.S. gallon = = 1 U.S. barrel (bbl) = 1 imperial gallon = 231 in.3 4 (liquid) quarts 42 U.S. gal. 1.2 U.S. gal.

16.4 cm3 35.3 ft3 61 in.3 3.78 litres 159 litres 15.9 U.S. gal/min

2000 lb = 1 ton (short) 1 long ton = 2240 lb

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

mass density =

m ⎛ kg ⎞ ⎜ ⎟ V ⎝ m3 ⎠

mass volume

weight density =

w ⎛ lb ⎞ ⎜ ⎟ V ⎝ ft 3 ⎠

weight volume

ρ=

ρ=

Conversions:

(on Earth) a mass density of 1

kg results in a weight density of 0.0623 lb m3 ft 3

Page 3

SI

Imperial

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. Conversions:

In Imperial the corresponding quantity is specific gravity; for solids and...

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