Stokes' Law

An analytical expression for the viscous drag force F on a small rigid sphere of radius a moving at steady, low-Reynolds-number relative velocity v through an incompressible Newtonian fluid: F = 6π μ a v directed opposite to v, valid under creeping-flow conditions where inertial effects are negligible and the no-slip boundary condition holds on the sphere surface.

An analytic expression for the terminal settling velocity of a small rigid spherical particle in a quiescent Newtonian fluid at low Reynolds number (Re << 1): v = (2/9)(r^2(ρ_p − ρ_f)g)/μ, where r is particle radius, ρ_p and ρ_f are particle and fluid densities, g is gravity and μ is fluid viscosity; valid for isolated spheres, negligible wall effects, and laminar Stokes flow.