Stokes Settling Calculator Formula

Understand the math behind the stokes settling calculator. Each variable explained with a worked example.

Use the Stokes Settling Calculator

Formulas Used

Settling Velocity

settling_velocity = 2 * (particle_density - fluid_density) * 9.80665 * pow(particle_radius, 2) / (9 * viscosity)

Settling Rate (mm/hr)

settling_mmhr = 2 * (particle_density - fluid_density) * 9.80665 * pow(particle_radius, 2) / (9 * viscosity) * 3600000

Variables

VariableDescriptionDefault
particle_densityParticle Density(kg/m3)2650
fluid_densityFluid Density(kg/m3)1000
particle_radiusParticle Radius(m)0.00005
viscosityDynamic Viscosity(Pa s)0.001

How It Works

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.

    Worked Example

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

    particle_density = 2650fluid_density = 1000particle_radius = 0.00005viscosity = 0.001
    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

    Ready to run the numbers?

    Open Stokes Settling Calculator