Field
Regimes and numbers
Reynolds, Mach, Froude, Strouhal. One number decides whether a flow creeps, separates or shocks, and the same shape behaves differently at each.
One number decides which physics applies
A bacterium and a whale both swim, and they are not doing the same thing at different sizes. The ratio of inertia to viscosity separates them, and crossing it changes the rules rather than the magnitudes.
The Reynolds number, and the length in it
The most useful number in fluid mechanics has an arbitrary quantity buried in it, and quoting one without saying which length was used makes it meaningless. That detail is where most misuse comes from.
When air stops being incompressible
Air is a gas and can obviously be squeezed, yet most of aerodynamics treats its density as fixed. The assumption holds until the flow approaches the speed at which pressure information travels — and then everything changes at once.