| 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 |
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