Contents


A General information 1

B Mathematics and computing 5
B.1 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
B.1.1 Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
B.1.2 Quadratic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
B.1.3 Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
B.1.4 Vector algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
B.1.5 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
B.1.6 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
B.1.7 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
B.1.8 Analytic geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
B.1.9 Solid geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
B.1.10 Dierential calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
B.1.11 Standard Dierentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
B.1.12 Dierential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
B.2 Integral calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
B.3 Laplace transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
B.4 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
B.4.1 Approximate solution of an algebraic equation . . . . . . . . . . . . . . . 15
B.4.2 Numerical integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
B.4.3 Richardson’s error estimation formula for use with Simpson’s rule . . . . . 16
B.4.4 Fourier series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
B.5 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
B.6 Probabilities for events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
B.6.1 Distribution, expectation and variance . . . . . . . . . . . . . . . . . . . . 17
B.6.2 Probability distributions for a continuous random variable . . . . . . . . . 18
B.6.3 Discrete probability distributions . . . . . . . . . . . . . . . . . . . . . . . 18
B.6.4 Continuous probability distributions . . . . . . . . . . . . . . . . . . . . . . 19
B.6.5 System reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
B.7 Bias, standard error and mean square error . . . . . . . . . . . . . . . . . . . . . 19
B.7.1 Central limit property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
B.7.2 Confidence intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

C Mechatronics and control 21
C.1 Charge, current, voltage and power . . . . . . . . . . . . . . . . . . . . . . . . . . 21
C.2 Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
C.3 Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
C.4 AC networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
C.4.1 Average and root mean square values . . . . . . . . . . . . . . . . . . . . 23
C.4.2 Phasors and complex impedance . . . . . . . . . . . . . . . . . . . . . . . 24
C.4.3 Balanced 3 phase a.c supply . . . . . . . . . . . . . . . . . . . . . . . . . 24
C.4.4 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
C.4.5 DC machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
C.4.6 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
C.5 Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
C.6 Step function response and frequency response . . . . . . . . . . . . . . . . . . 26
C.6.1 First-order systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
C.6.2 Second-order systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
C.7 Operational amplifier stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

D Solid Mechanics 33
D.1 Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
D.1.1 Square screw threads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
D.1.2 Flat clutches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
D.1.3 Kinematics of particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
D.1.4 Mass flow problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
D.1.5 Kinematics of rigid bodies with sliding contacts . . . . . . . . . . . . . . . 34
D.1.6 Mass moments of inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
D.2 Stress analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
D.2.1 Elastic constants of materials . . . . . . . . . . . . . . . . . . . . . . . . . 35
D.2.2 Beam theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
D.2.3 Elastic torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
D.2.4 Thin walled pressure vessels . . . . . . . . . . . . . . . . . . . . . . . . . 39
D.3 Two-dimensional stress transformation . . . . . . . . . . . . . . . . . . . . . . . . 39
D.4 Yield criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
D.5 Two-dimensional strain transformation . . . . . . . . . . . . . . . . . . . . . . . . 40
D.6 Elastic stress-strain relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
D.7 Thick-walled cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

E Thermofluids 43
E.1 Cross-references to table numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 43
E.2 Dimensionless groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
E.3 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
E.4 Continuity and equation of motion . . . . . . . . . . . . . . . . . . . . . . . . . . 46
E.4.1 Cylindrical polar coordinates . . . . . . . . . . . . . . . . . . . . . . . . . 46
E.4.2 Rectangular Cartesian coordinates . . . . . . . . . . . . . . . . . . . . . . 46
E.4.3 Vector form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
E.5 Equations for compressible flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
E.6 Friction factor for flow in circular pipes (Moody diagram) . . . . . . . . . . . . . . 48
E.7 Perfect gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
E.8 Heating (or calorific) values of fuels . . . . . . . . . . . . . . . . . . . . . . . . . . 54
E.9 Properties of R134a refrigerant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
E.10 Transport properties of air, water and steam . . . . . . . . . . . . . . . . . . . . . 62
E.11 Approximate physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
E.12 Thermodynamic property tables for water/steam (IAPWS-IF97 formulation) . . . 67

List of Tables

A.1 SI Units and abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
A.2 Conversion factors from Imperial to SI units . . . . . . . . . . . . . . . . . . . . . 2
A.3 Decimal prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
A.4 Physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3



B.1 Some indefinite integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
B.2 Some definite integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
B.3 Standard normal table: values of pdf (y) = f (y) and cdf (y) = F (y). . . . . . . 20
B.4 Student t table: values tm;p of x for which P (jXj > x) = p, when X is tm. . . . . . 20

C.1 Colour codes for resistors etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
C.2 Standard values for components . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
C.3 Operational amplifier signal processing stages . . . . . . . . . . . . . . . . . . . 31

D.1 Second moments of area for simple cross-sections . . . . . . . . . . . . . . . . . 36
D.2 Beams bent about principal axis . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
D.3 Torsion of solid non-circular sections . . . . . . . . . . . . . . . . . . . . . . . . . 38

E.1 Dimensionless groups for Thermofluids . . . . . . . . . . . . . . . . . . . . . . . 44
E.2 Empirical correlations for forced convection . . . . . . . . . . . . . . . . . . . . . 45
E.3 Perfect gases (ideal gases with constant specific heats) . . . . . . . . . . . . . . 50
E.4 Isentropic compressible flow functions for perfect gas with
E.5 Ideal (semi-perfect) gas specific enthalpy h (kJ kg􀀀1, 25 C datum) . . . . . . . . 52
E.6 Molar Enthalpy of Formation h0
f (kJ kmol􀀀1 at 25 C and 1 atmosphere) as gas or
vapour (g), except where indicated as solid (s) or liquid (l). . . . . . . . . . . . . . 53
E.7 Ideal gas molar enthalpy h (kJ kmol􀀀1, 25 C datum) . . . . . . . . . . . . . . . . 53
E.8 Heating (or calorific) values of gas fuels at 25 C. . . . . . . . . . . . . . . . . . . 54
E.9 Heating (or calorific) values of liquid fuels at 25 C. . . . . . . . . . . . . . . . . . 54
E.10 Saturated Refrigerant 134a — Temperature (􀀀60C to critical point) . . . . . . . 56
E.11 Saturated Refrigerant 134a — Pressure (0.2 bar to critical point) . . . . . . . . . 57
E.12 Superheated Refrigerant 134a (0.2 bar to 1 bar) . . . . . . . . . . . . . . . . . . 58
E.13 Superheated Refrigerant 134a (1.5 bar to 4 bar) . . . . . . . . . . . . . . . . . . 59
E.14 Superheated Refrigerant 134a (5 bar to 12 bar) . . . . . . . . . . . . . . . . . . . 60
E.15 Superheated Refrigerant 134a (16 bar to 30 bar) . . . . . . . . . . . . . . . . . . 61
E.16 Transport properties of dry air at atmospheric pressure . . . . . . . . . . . . . . . 63
E.17 Transport properties of saturated water and steam . . . . . . . . . . . . . . . . . 64
E.18 Approximate physical properties at 20 C, 1 bar. . . . . . . . . . . . . . . . . . . . 65
E.19 Saturated water and steam — Temperature (triple point to 100 C) . . . . . . . . 68
E.20 Saturated water and steam — Pressure (triple point to 2 bar) . . . . . . . . . . . 69
E.21 Saturated water and steam — Pressure (triple point to 2 bar) . . . . . . . . . . . 70
E.22 Saturated water and steam — Pressure (triple point to 2 bar) . . . . . . . . . . . 71
E.23 Subcooled water and Superheated Steam (triple point to 0.1 bar) . . . . . . . . . 72
E.24 Subcooled water and Superheated Steam (0.1 bar to 1 atmosphere) . . . . . . . 73
E.25 Subcooled water and Superheated Steam (2 bar to 8 bar) . . . . . . . . . . . . . 74
E.26 Subcooled water and Superheated Steam (10 bar to 40 bar) . . . . . . . . . . . 75
E.27 Subcooled water and Superheated Steam (50 bar to 80 bar) . . . . . . . . . . . 76
E.28 Subcooled water and Superheated Steam (90 bar to 140 bar) . . . . . . . . . . . 77
E.29 Subcooled water and Superheated Steam (160 bar to 220 bar) . . . . . . . . . . 78
E.30 Supercritical steam (250 bar to 500 bar) . . . . . . . . . . . . . . . . . . . . . . . 79
E.31 Supercritical steam (600 bar to 1000 bar) . . . . . . . . . . . . . . . . . . . . . . 80