In this lecture we continue our consideration of dimensionality by studying Nondimensional Numbers. These are widely used throughout Fluid Mechanics to define flow regime, let us know what we can exclude in analysis, and help us scale problems.

The nondimensional numbers today are all some Force compared to Inertia: (1) Euler number compares pressure and inertia, common for aerodynamics; (2) Reynolds number compares viscosity and inertia, commonly used for defining laminar and turbulence; (3) Froude number compares weight and inertia, which is most popular in large ship flows; (4) Weber number compares surface tension and inertia, for things like bubbles and droplets; and (5) the Mach number compares gas compression and inertia for supersonic highspeed aerodynamics.