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Terminal Settling Velocity (Stokes) Calculator

Work out terminal settling velocity (stokes) instantly with clear inputs, formula shown and shareable results.

About Terminal Settling Velocity (Stokes) Calculator

Stokes' law balances weight, buoyancy and viscous drag on a small sphere, giving v = (rho(p) - rho(f)) g d^2 / (18 mu). Because diameter is squared, a fine particle settles dramatically more slowly: 100 micron sand in water falls about 9 mm/s, while 10 micron silt takes a hundred times longer. The law only holds while the Reynolds number stays below about one.

Formulas

Stokes settling velocity

v = (rho(p) - rho(f)) g d^2 / (18 mu)

Validity check

Re = rho(f) v d / mu must be below about 1

Worked example

With the default values below, Terminal Settling Velocity (Stokes) Calculator returns Terminal Settling Velocity of 8.98943 × 10⁻³. Change any input above and every figure here is recalculated in your browser.

Inputs used

Particle diameterminimum 0 m
0.0001 m
Particle densityminimum 0 kg/m3
2,650 kg/m3
Fluid densityminimum 0 kg/m3
1,000 kg/m3
Dynamic viscosity of the fluidminimum 0 Pa s
0.001 Pa s

Results

Terminal Settling Velocity
8.98943 × 10⁻³ m/s
Particle Reynolds Number
8.9894 × 10⁻¹
Time To Settle One Metre
111.2 s
Same Velocity In mm/s
8.98943

Step by step

  1. 1Values used
  2. 2Stokes settling velocity
  3. 3Validity check
  4. 4Terminal Settling Velocity= 0.00899 m/s
  5. 5Particle Reynolds Number= 0.8989
  6. 6Time To Settle One Metre= 111.2 s
  7. 7Same Velocity In mm/s= 8.98943

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What if the Reynolds number is above one?

Stokes' law overpredicts. Use an intermediate or Newton drag regime correlation instead, which grows more slowly with diameter.

Can the velocity be negative?

Yes, when the particle is lighter than the fluid. It then rises at the same rate, which is how creaming and flotation are analysed.

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Terminal Settling Velocity (Stokes) Calculator | Calcrivo