Stokes' Law Calculator - Terminal Velocity and Settling

Your details

Choose which quantity to compute. Supply all other values and the selected output replaces the terminal velocity in the results.
SI uses metres and kilograms; CGS uses centimetres and grams (Poise for viscosity).
Diameter of the spherical particle. In SI: metres. In CGS: centimetres.
m
Density of the particle material. Quartz sand ~ 2650 kg/m³. In CGS: g/cm³.
kg/m³
Density of the surrounding fluid. Water at 20 °C ~ 998 kg/m³. In CGS: g/cm³.
kg/m³
Dynamic viscosity of the fluid. Water at 20 °C ~ 0.001 Pa·s (1 mPa·s). In CGS: Poise (1 P = 0.1 Pa·s).
Pa·s
Height the particle must fall through the fluid - used to compute settling time.
m
Terminal velocityOseen regime (approximate)
0.008989m/s

Steady-state velocity the particle reaches as gravity balances drag

Stokes drag force0N
Reynolds number0.8989
Settling time111.24s
Flow regimeLow-inertia regime (0.1 to 1) - slight over-estimate
0.8989
Stokes regime<0.1Oseen regime0.1-1Transitional1+

Terminal velocity is 0.008989 m/s (Re = 0.8989).

  • The Reynolds number is 0.899, just above 0.1. Stokes' law slightly over-estimates velocity here; the Oseen correction (multiplying by 1 + 3Re/16) improves accuracy.
  • The Stokes drag force on the particle at terminal velocity is 8.472e-9 N.
  • At this velocity, the particle takes about 111.24 s to settle through the specified distance.

Next stepConsider using the intermediate drag law or a CFD approach for particles this large relative to the fluid viscosity.

 = Powered by OnlyCalculators