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Stokes' Law Calculator

The Stokes' law calculator will help you determine either the viscosity of a fluid or the terminal velocity of a particle in a falling ball viscometer.

Clear
Terminal settling velocity10.1709 mm/ssettling downwards, 10.1709 mm/s
Stokes drag at that speed270.704 µN6πµrv — linear in both radius and velocity, unlike the quadratic drag of fast flow
Net weight (weight less buoyancy)270.704 µNequal to the drag at terminal velocity, by definition
At twice the radius40.6836 mm/sfour times as fast — settling velocity goes as the SQUARE of radius, which is why fine particles stay suspended almost indefinitely
Time to settle 1 metre1.64 minutes
Reynolds number0.0182well under 1, so Stokes' law is valid
Largest sphere Stokes still describes2.397 mmroughly where Reynolds reaches 1 in this fluid
Viscosity used1.412 Pa·s1,412 centipoise

The formula

Stokes F = 6πµrv; Poiseuille Q = πΔPr⁴ ÷ 8µL

Fourth power, and square

Poiseuille's law has flow proportional to the fourth power of radius. Narrowing a tube by 10% cuts the flow by 34%; halving the radius cuts it to a sixteenth. This is why a modest arterial narrowing has such disproportionate consequences, and why pipe sizing dominates every other variable in a laminar system.

Stokes settling goes as the square of radius, which is why fine particles effectively never settle. Halving a particle's diameter quarters its settling speed, so clay-sized material stays suspended for days or years while sand drops out in seconds. It is the basis of sedimentation analysis and of every clarifier design.

Both laws have validity limits worth respecting. Poiseuille assumes laminar flow and fails above a Reynolds number of about 2300. Stokes assumes creeping flow and starts to fail above a Reynolds number of about 1 — a far stricter condition, and one that a 1 mm steel sphere in water already violates badly. Both modes report the Reynolds number so the answer can be judged rather than trusted.

Laminar tube flow has a parabolic velocity profile, so the centreline moves at exactly twice the mean. That factor of two matters whenever a measurement is taken at one point rather than averaged.