Dimensional Analysis

By: J. C. Gibbings

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Hardcover | 21 January 2011

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312 Pages

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22.86 x 15.88 x 1.27

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For experiments, dimensional analysis enables the design, checks the validity, orders the procedure and synthesises the data. Additionally it can provide relationships between variables where standard analysis is not available.

This widely valuable analysis for engineers and scientists is here presented to the student, the teacher and the researcher. It is the first complete modern text that covers developments over the last three decades while closing all outstanding logical gaps. Dimensional Analysis also lists the logical stages of the analysis, so showing clearly the care to be taken in its use while revealing the very few limitations of application. As the conclusion of that logic, it gives the author's original proof of the fundamental and only theorem.

Unlike past texts, Dimensional Analysis includes examples for which the answer does not already exist from standard analysis. It also corrects the many errors present in the existing literature by including accurate solutions.

Dimensional Analysis is written for all branches of engineering and science as a teaching book covering both undergraduate and postgraduate courses, as a guide for the lecturer and as a reference volume for the researcher.

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An Elementary Introduction	p. 1
Notation	p. 1
The Purpose of this Chapter	p. 2
Units and Dimensions	p. 3
Units-conversion Factors	p. 3
Dimensional System	p. 5
Synthesis of Experimental Data	p. 6
Comparison of Results	p. 10
Re-ordered Functions	p. 10
Preliminary General Analysis	p. 13
Fluid-mechanic Force on a Body	p. 16
Benefits of Dimensional Analysis	p. 19
References	p. 23
Concepts, Dimensions and Units	p. 25
Notation	p. 25
Summary of Basic Logic	p. 25
The Definition of Concepts	p. 27
The Definition of Primary Physical Concepts	p. 28
The Definition of Time	p. 29
The Definition of Force	p. 32
The Definition of Quantity	p. 32
Summary of Primary Concepts	p. 32
Constant Relative Magnitude	p. 33
Dimensional Equality	p. 33
Units-conversion factors	p. 34
Products of Concepts	p. 35
Dimensional Equality in Functional Relations	p. 36
Limitation to Functional Operations	p. 36
The Complete Equation	p. 37
Derived Concepts and Their Measure	p. 39
Dimensions of Units-conversion Factors	p. 44
The Inclusion of Units-conversion Factors	p. 47
Formation of Dimensionless Groups from units-conversion Factors	p. 48
Summarising Comments	p. 49
References	p. 53
The Pi-Theroem	p. 55
Notation	p. 55
The Outline from of the Therom	p. 55
The Basic outcome	p. 57
The Generalised Pi-theorem	p. 57
Illustrative Examples	p. 59
Liner Mass Oscillation	p. 61
Non-linear Mass Oscillation	p. 62
Impact of a Jet	p. 63
Electromagnetic Field Energy	p. 64
Heat Exchanger	p. 66
Prior Proofs of the Pi- theorem	p. 67
The Careful Choice of Variables	p. 72
The Necessity for a Units-conversion Factor for Angle	p. 74
General Results from the Pi-theorem	p. 76
Summarising Comments	p. 77
References	p. 81
The Development of Dimensional Analysis	p. 83
Notation	p. 83
The Case for the History of Dimensional Analysis	p. 83
The Onset of Similitude	p. 84
The Onset of Dimensional Analysis	p. 84
The Developing Use of the Pi-theorem	p. 85
The Place of Dimensional Analysis	p. 90
The Reynolds Pipe-Flow Experiment	p. 90
References	p. 92
The Choice of Dimensions	p. 95
Notation	p. 95
Care in Choosing Dimensions	p. 96
The Number of Non-dimensional Groups	p. 96
Mass and Force Dimensions	p. 97
Mass and Volume Dimensions	p. 100
Temperature and Quantity Dimensions	p. 102
Mass and Quantity Dimensions	p. 104
The Angle Dimension	p. 106
Electrical Dimensions	p. 107
Use of Vectorial Dimensions	p. 109
Concluding Comments	p. 113
References	p. 114
Supplementation of Derivations	p. 115
Notation	p. 115
Information from the Physics	p. 116
The Bending of a Beam	p. 116
Planetary Motion	p. 118
Extrapolated Solutions	p. 120
Uncoupled Equations	p. 121
Forced Convention of Thermal Energy	p. 124
Compressible-flow Energy Transfer	p. 124
In Compressible-flow Energy Transfer	p. 131
The Rayleigh-Riabouchinsky Problem	p. 134
Natural Thermal Conversion	p. 139
Summarising Comments	p. 144
References	p. 146
Systematic Experiment	p. 149
Notation	p. 149
The Benefits of Dimensional Analysis	p. 150
Reduction of Variables	p. 151
Further Reduction of Non-dimensional Groups	p. 153
Alternate Dependent Variables	p. 155
Parameter Variation	p. 156
Range of Application	p. 156
Superfluous Variables	p. 157
Missing Variables	p. 157
Influence of Variables	p. 159
Measurement Limitation	p. 162
Effectiveness of Experimental Variables	p. 165
The Validity Criterion	p. 167
Synthesis of Experimental Data
Concluding Comments	p. 174
References	p. 177
Analytical Results	p. 179
Analytical Results from Dimensional Analysis	p. 179
Example I: Flow Turbulence	p. 179
The Complexity of Flow Turbulence	p. 180
The Physics of Turbulence	p. 180
The Turbulent-Power Law	p. 184
Prandtl's Mixing Length	p. 186
The Log-law	p. 188
Jet Flow	p. 190
Table of Contents provided by Ingram. All Rights Reserved.

Dimensional Analysis

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