Stokes Settling Calculator

Calculate the settling velocity of a small sphere in a viscous fluid: v_s = 2 * (rho_p - rho_f) * g * r^2 / (9 * mu).

kg/m3
kg/m3
m
Pa s

Settling Velocity

0.00898943 m/s

Settling Rate (mm/hr)32,361.9450 mm/hr

Settling Velocity vs Particle Density

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Formula

## Stokes Settling (Low Reynolds Number) Very small particles settle through a fluid at a terminal velocity governed by Stokes' law. ### Formula **v_s = 2 (rho_p - rho_f) g r^2 / (9 mu)** - *rho_p* = particle density - *rho_f* = fluid density - *r* = particle radius - *mu* = dynamic viscosity This applies when Re < 1 (creeping flow regime). Larger particles settle faster because velocity scales as r^2.

Esempio Risolto

Sand grain (r = 50 um, rho = 2650 kg/m3) in water.

  1. 01v_s = 2 * (2650 - 1000) * 9.807 * (5e-5)^2 / (9 * 0.001)
  2. 02delta_rho = 1650
  3. 03r^2 = 2.5e-9
  4. 04v_s = 2 * 1650 * 9.807 * 2.5e-9 / 0.009
  5. 05v_s = 8.09e-5 / 0.009 = 0.00899 m/s