Dimensional Analysis and Intelligent Experimentation Book

Chapter 1 Introduction 1

1.1 Motivation: how to get something for nothing 1

1.2 Pythagoras' theorem 3

References 9

Chapter 2 Numbers and Units in Engineering and Physics 10

2.1 Introduction 10

2.2 Labels 11

2.3 Scales 11

2.4 Measurement with units 12

2.5 Standardized units 13

2.6 Converting from one unit to another 14

2.7 Problems 17

References 19

Chapter 3 Dimensions, Dimensionless Groups, and Variables 20

3.1 The concept of dimension 20

3.2 Dimensional consistency 22

3.3 Empirical relationships that are not dimensionally consistent 24

3.4 Dimensionless groups 26

3.5 Variables 28

3.6 Problems 30

References 37

Chapter 4 Dimensional Analysis 38

4.1 Relations between dimensionless groups 38

4.2 Proof of Pi theorem 42

4.3 Revisiting the example of Sec. 4.2, starting from the Pi theorem 46

4.4 Choosing the dimensionless groups and fundamental dimensions in a different way 48

4.5 Resistance of ships 50

4.6 Heat transfer from pipelines 59

4.7 Problems 62

References 72

Chapter 5 Similarity and Intelligent Experimentation 74

5.1 Similarity 74

5.2 Pressure drops in pipes 75

5.3 Plows in clay 82

5.4 Problems 88

References 91

Chapter 6 Equations in Nondimensional Form 92

6.1 Motivation 92

6.2 Mass-spring systems 92

6.3 Laying underwater pipelines 101

6.4 Partial differential equations describing fluid flow 106

6.5 Problems 108

References 110

Chapter 7 Physical Models 112

7.1 Introduction 112

7.2 Structural models 115

7.3 Aerodynamic models 120

7.4 Hydraulic models 123

7.5 Geotechnical models 128

7.6 Problems 130

References 132

Chapter 8 Solutions to Problems 135

8.1 Introduction 135

8.2Solutions to problems in Chapter 2 135

8.3 Solutions to problems in Chapter 3 137

8.4 Solutions to problems in Chapter 4 139

8.5 Solutions to problems in Chapter 5 147

8.6 Solutions to problems in Chapter 6 148

8.7 Solutions to problems in Chapter 7 151

References 154