PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Fluids & Continuum Physics · Quantities, units and the practice of measurement
Measurement and Method, Ch What dimensions decide before you measure anything
Problem
Small spheres, all of the same solid material and density ρs, fall at constant terminal speed v through a viscous fluid. The quantities judged relevant are v, the sphere diameter D, the sphere density ρs, the fluid density ρm, the fluid viscosity η, and g. (a) How many independent dimensionless groups can be formed from these six quantities? (b) An experimenter uses ten different diameters in each of three different fluids (so diameter and fluid vary, while the sphere material, and hence ρs, stays fixed). If the data are plotted using the correct dimensionless groups, onto how many curves do all thirty measurements collapse, and why?