drag

Drag is what a fluid does to a solid that is trying to move through it. Unlike contact friction between two solid surfaces, drag depends on speed — and the dependence comes in two flavours. At low velocities, where the fluid flows smoothly around the object without tearing into eddies, drag is linear in velocity and set by the fluid's viscosity: F = b · v. This is the Stokes regime, and it is what governs the motion of dust motes in air or ball-bearings in honey. At high velocities, where the object has to shove fluid mass out of the way and leaves a turbulent wake behind it, drag is quadratic: F = ½ · ρ · C_d · A · v². This is the Newtonian regime, and it is what governs cars, aircraft, baseballs, cyclists, and falling skydivers.

The crossover between the two regimes is controlled by a dimensionless number — the Reynolds number Re = ρ·v·L / η, which measures the ratio of inertial to viscous effects. Below Re ≈ 1 the linear regime rules; above it the quadratic regime takes over. Most macroscopic objects in everyday air or water are firmly in the quadratic regime, while microscopic objects (cells, dust, aerosols) are firmly in the linear one.

Drag has a characteristic consequence that plain friction does not: because the drag force grows with speed, a body falling under gravity in a fluid reaches a terminal velocity at which drag exactly balances gravity, and from that moment on it falls at constant speed. The approach to terminal velocity is exponential in the linear regime and slightly different in the quadratic, but in both cases it is the signature that distinguishes drag from contact friction.