Settling Velocity Calculator: v = g (rho_p - rho) d^2 / (18 mu)

How fast a small particle falls through water or another fluid.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • v_s = \frac{g\,\Delta\rho\,d^2}{18\mu}
  • d = \sqrt{\frac{18\mu v_s}{g\,\Delta\rho}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the settling velocity: settling velocity = (g / 18 x density difference between the particle and the fluid x diameter of the particle^2) / (dynamic viscosity of the fluid)
  2. Put the values in (every value in its SI unit): settling velocity = (g / 18 x 1650 x 0.0001^2) / (0.001)
  3. The answer: settling velocity: 0.00898943 m/s
  4. The same answer in other units: 8.98943 mm/s; 32.3619 m/h

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Diameter of the particle; Settling velocity (leave it as it is if this is what you are finding) 0.0089894 m/s; Density difference between the particle and the fluid (leave it as it is if this is what you are finding) 1650 kg/m3; Dynamic viscosity of the fluid (leave it as it is if this is what you are finding) 0.001 Pa s.

  1. The formula, arranged to find the diameter of the particle: diameter of the particle = square root of ((settling velocity x dynamic viscosity of the fluid) / (g / 18 x density difference between the particle and the fluid))
  2. Put the values in (every value in its SI unit): diameter of the particle = square root of ((0.0089894 x 0.001) / (g / 18 x 1650))
  3. The answer: diameter of the particle: 9.99998e-5 m
  4. The same answer in other units: 0.0999998 mm; 99.9998 micrometres

Common questions

What is Stokes' law for settling?

The speed of a small sphere falling through a fluid is proportional to the square of its diameter and the density difference, and inversely proportional to the viscosity.

Why does a bigger particle settle faster?

The speed goes with the square of the diameter, so doubling the size makes it settle four times faster.

When does the law fail?

For particles bigger than about 0.1 mm in water, where the flow around the particle is no longer smooth.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics or water treatment text (Stokes' law and sedimentation).

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