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Sedimentation & Stokes Settling Velocity Calculator

Sir George Gabriel Stokes formulated the terminal settling velocity equation in 1851 for spherical particles sinking through viscous fluids.

Diameter of suspended spherical particle in microns (fine sand/silt ≈ 20 - 100 µm; clay floc ≈ 5 - 20 µm).

Density of mineral particle (quartz sand ≈ 2,650 kg/m³; biological sludge floc ≈ 1,020 - 1,050 kg/m³).

Fluid density (Water ≈ 1,000 kg/m³).

Water dynamic viscosity (Water at 20°C ≈ 0.001002 Pa·s).

Calculated Result
2.243 mm/s

Stokes Settling Velocity

Settling Velocity (v_t)

2.243 mm/s (8.07 m/h)

Particle Diameter (d)

50 µm (0.050 mm)

Particle / Fluid Density

2650 kg/m³ / 1000 kg/m³

Particle Reynolds Number (Re_p)

0.1119 (Laminar Stokes Flow)

Calculation Breakdown

  1. 1. Unit Conversionsd = 50 µm = 5.00e-5 m, Δρ = 2650 - 1000 = 1650 kg/m³, μ = 0.001002 Pa·s
  2. 2. Stokes Settling Law Formulationv_t = [g · d² · (ρ_p - ρ_f)] / [18 · μ] = [9.81 · (5.00e-5)² · 1650] / [18 · 0.001002] = 2.243 mm/s
  3. 3. Surface Overflow Rate EquivalenceA settling velocity of 8.07 m/h corresponds to the design overflow rate of a clarifier tank required to capture 100% of particles ≥ 50 µm.

Settling Velocity vs Particle Diameter (Quartz Sand)

Interactive visualization based on your current inputs

v_t (mm/s)
0.02.24.56.79.020 µm40 µm50 µm80 µm100 µmDiameter (µm)Velocity (mm/s)

What Is the Sedimentation & Stokes Settling Velocity Calculator?

Stokes settling velocity defines the constant terminal downward speed of a particle suspended in a fluid when gravity and drag forces achieve equilibrium.

How Does the Sedimentation & Stokes Settling Velocity Calculator Work?

Derived from the low Reynolds number Navier-Stokes equations where viscous shear forces dominate inertial turbulent eddies.

Sedimentation & Stokes Settling Velocity Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

v_t = \frac{g \cdot d^2 (\rho_p - \rho_f)}{18 \mu}, \quad Re_p = \frac{\rho_f v_t d}{\mu}

Terminal velocity balances gravity, buoyancy, and viscous drag. Valid for particle Reynolds numbers in the laminar regime (Re < 1.0).

How to Use the Sedimentation & Stokes Settling Velocity Calculator

  1. Enter particle diameter in microns (µm).
  2. Provide solid particle density.
  3. Optionally customize fluid density and dynamic viscosity for temperature.

Step-by-Step Example Calculation

50 µm Fine Sand in Water (20°C)

Input Values:

particleDiameterMicrons:50
particleDensityKgM3:2650
fluidDensityKgM3:1000
dynamicViscosityPaS:0.001002
Worked Steps: Particle sinks at 2.24 mm/s (8.07 m/h) with Re_p = 0.11 (strictly laminar Stokes flow), requiring a clarifier surface overflow rate ≤ 8.07 m/h.

Understanding Your Result

Settling Velocity (mm/s / m/h): Downward fall velocity.

Particle Reynolds Number: Confirms laminar Stokes regime validity (Re < 1.0).

Clarifier Loading Rate: Maximum allowable basin overflow flux.

Factors That Affect the Result

  • Particle diameter has quadratic impact (d²); doubling particle diameter quadruples settling speed.

When Should You Use This Calculator?

  • Water purification sedimentation basin sizing, stormwater retention ponds, and mineral slurry thickeners.

Assumptions & Limitations

  • Assumes rigid spherical particle in unhindered infinite fluid (particle volumetric concentration < 1%).

Frequently Asked Questions

Calculation Accuracy & Reference Note

Exact analytical Stokes creeping flow solution.

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