Order-of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies Peter Goldreich, California Institute of Technology Sanjoy Mahajan, University of Cambridge Sterl Phinney, California Institute of Technology Draft of 1 August 1999 c 1999 Send comments to
[email protected] ii Contents 1 Wetting Your Feet 1 1.1 Warmup problems 1 1.2 Scaling analyses 13 1.3 What you have learned 21 2 Dimensional Analysis 23 2.1 Newton’s law 23 2.2 Pendula 27 2.3 Drag in fluids 31 2.4 What you have learned 41 3 Materials I 43 3.1 Sizes 43 3.2 Energies 51 3.3 Elastic properties 53 3.4 Application to white dwarfs 58 3.5 What you have learned 62 4 Materials II 63 4.1 Thermal expansion 63 4.2 Phase changes 65 4.3 Specific heat 73 4.4 Thermal diffusivity of liquids and solids 77 4.5 Diffusivity and viscosity of gases 79 4.6 Thermal conductivity 80 4.7 What you have learned 83 5 Waves 85 5.1 Dispersion relations 85 5.2 Deep water 88 5.3 Shallow water 106 5.4 Combining deep- and shallow-water gravity waves 108 5.5 Combining deep- and shallow-water ripples 108 5.6 Combining all the analyses 109 5.7 What we did 109 Bibliography 110 1 1 Wetting Your Feet Most technical education emphasizes exact answers. If you are a physicist, you solve for the energy levels of the hydrogen atom to six decimal places. If you are a chemist, you measure reaction rates and concentrations to two or three decimal places.