Stokes Law Settling Velocity Calculator
Calculate Stokes drag force and settling velocity for a spherical particle in a viscous fluid.
Used for sedimentation, aerosol settling, and filtration analysis.
George Stokes derived the drag force on a small sphere moving slowly through a viscous fluid in 1851. The result was elegant: drag is proportional to radius, velocity, and viscosity — and nothing else.
Stokes drag force
F_drag = 6 pi eta r v
Where eta is dynamic viscosity (Pa·s), r is sphere radius (m), and v is velocity (m/s).
Terminal (settling) velocity
At terminal velocity, drag equals buoyant-weight:
v_t = 2 r^2 (rho_p - rho_f) g / (9 eta)
Where rho_p is particle density, rho_f is fluid density, and g = 9.81 m/s^2.
When Stokes law applies
The formula is valid when the Reynolds number Re = rho_f v r / eta is much less than 1. This means small, slow, or in very viscous fluid. For particles above ~100 micrometers settling in air, or above ~1 mm in water, Re exceeds 1 and the quadratic drag law (used in the terminal velocity calculator) is more appropriate.
Practical examples
Dust particles (2 micrometers, density 2500 kg/m^3) settling in air: v_t ≈ 0.001 mm/s. They take hours to settle from 1 meter height — explaining why fine dust stays airborne so long.
Sand grains (200 micrometers, density 2650 kg/m^3) settling in water: v_t ≈ 25 mm/s. This is within Stokes range only marginally.
Red blood cells (diameter ~8 micrometers, density ~1100 kg/m^3) in blood plasma (eta ≈ 0.0027 Pa·s): v_t ≈ 0.1 mm/hr — which matches the measured erythrocyte sedimentation rate (ESR) used as a medical test.
Millikan oil drop experiment
Robert Millikan used Stokes law in 1909 to measure the charge of individual electrons by balancing gravity against an electric field on tiny oil droplets. The experiment earned him the 1923 Nobel Prize.