A Student's Guide to Dimensional Analysis by Lemons, Don S. -- Read -- Imperial Library of Trantor

Index

Half title Title page Imprints page Contents Preface Acknowledgments 1 Introduction

1.1 Dimensional Homogeneity

Symmetry under Change of Units

1.2 Dimensionless Products

Dimensional Analysis

1.3 Dimensional Formulae 1.4 The Rayleigh Algorithm

A Marble on the Interior Surface of a Cone Rayleigh’s Algorithm The Rayleigh Algorithm Modified

1.5 The Buckingham ππ Theorem 1.6 The Number of Dimensions 1.7 The Number of Dimensionless Products 1.8 Example: Pressure of an Ideal Gas 1.9 A Mistake to Avoid

Essential Ideas Problems

2 Mechanics

2.1 Kinematics and Dynamics 2.2 Effective Dimensions

The Number of Effective Dimensions

2.3 Imposed Dimensions 2.4 Example: Hanging Spring-Mass System 2.5 Example: Hanging, Stretched Cable 2.6 Asymptotic Behavior 2.7 Example: Speed of Sound 2.8 Example: Side Window Buffeting 2.9 Example: Two-Body Orbits Essential Ideas Problems

3 Hydrodynamics

3.1 Fluid Variables 3.2 Example: Water Waves 3.3 Surface Tension

Capillary Waves

3.4 Example: Largest Water Drop 3.5 Viscosity

Terminal Speed Stokes’ Law

3.6 Example: Hydraulic Jump

Reynolds Number

3.7 Example: Equilibrium Pipe Flow 3.8 Example: Non-Equilibrium Pipe Flow 3.9 Scale Models Essential Ideas Problems

4 Temperature and Heat

4.1 Heat Transfer 4.2 The Dimensions of Temperature and Heat 4.3 Conduction and Convection 4.4 Example: Cooking a Turkey 4.5 Diffusion 4.6 Making the Equations Dimensionless 4.7 Example: Growth of Arctic Ice 4.8 Example: Stack Effect Essential Ideas Problems

5 Electrodynamics and Plasma Physics

5.1 Maxwell’s Equations 5.2 Example: Oscillations of a Compass Needle 5.3 Example: Radiation from an Accelerating Charge 5.4 Example: Child’s Law 5.5 Plasma Physics 5.6 Example: Plasma Oscillations 5.7 Example: Pinch Effect Essential Ideas Problems

6 Quantum Physics

6.1 Planck’s Constant 6.2 Example: Blackbody Radiation 6.3 Example: Spectral Energy Density of Blackbody Radiation 6.4 Example: Bohr Model 6.5 Atomic Units 6.6 Example: Quantum Ideal Gas 6.7 Example: Quantized Radiation from an Accelerating Charge Essential Ideas Problems

7 Dimensional Cosmology

7.1 The Fundamental Dimensional Constants 7.2 Eddington-Dirac Number 7.3 Example: Gravitational-Electrostatic Mass 7.4 Example: Classical Electron Radius 7.5 Classical Scales 7.6 Fine Structure Constant 7.7 The 15 Scales 7.8 Planck Scale 7.9 Example: Planck Mass 7.10 The 22 Quantities Essential Ideas Problems

Appendix Answers to Problems References Index