Stokes Settling Calculator Formula
Understand the math behind the stokes settling calculator. Each variable explained with a worked example.
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) * 3600000Variables
| Variable | Description | Default |
|---|---|---|
particle_density | Particle Density(kg/m3) | 2650 |
fluid_density | Fluid Density(kg/m3) | 1000 |
particle_radius | Particle Radius(m) | 0.00005 |
viscosity | Dynamic 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)
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.
- 01v_s = 2 * (2650 - 1000) * 9.807 * (5e-5)^2 / (9 * 0.001)
- 02delta_rho = 1650
- 03r^2 = 2.5e-9
- 04v_s = 2 * 1650 * 9.807 * 2.5e-9 / 0.009
- 05v_s = 8.09e-5 / 0.009 = 0.00899 m/s
Frequently Asked Questions
When does Stokes law fail?
When the particle Reynolds number exceeds about 1, inertial effects become important and the drag coefficient no longer scales linearly with velocity.
How does this apply to sedimentation?
Stokes settling governs sedimentation in lakes, blood cell separation in centrifuges, and paint settling in cans.
What about non-spherical particles?
An equivalent-sphere correction factor is applied. Flatter or more irregular particles settle slower than spheres of the same mass.
Ready to run the numbers?
Open Stokes Settling Calculator