Stokes' Law Calculator

It applies to small spherical particles settling slowly through a viscous fluid in smooth, laminar flow, such as fine silt in water. It breaks down for larger or faster particles.

A negative terminal velocity means the particle is less dense than the fluid and rises rather than sinks, like an air bubble in water or a foam bead in oil. The magnitude of the velocity is the same in both directions - only the sign flips. In practice, Stokes' Law applies only at low Reynolds numbers (Re < 1); for larger particles or faster flows, drag becomes non-linear and the Stokes formula underestimates drag, giving an overestimate of terminal velocity.

The settling velocity is proportional to the square of the radius, so halving the particle radius cuts the speed to one quarter. That is why fine clay can stay suspended in water for hours or days while sand drops out almost at once.

The falling-ball (or falling-sphere) viscometer is the classic application: a sphere of known radius and density is dropped through a fluid and timed over a fixed distance once it has reached terminal velocity. Rearranging Stokes' law for viscosity gives &eta; = 2r&sup2;(&rho;_p &minus; &rho;_f)g &divide; (9v), so the measured settling speed yields the fluid's viscosity. The same principle governs sedimentation in geology, where it predicts how quickly mineral grains drop out of still water, magma, or a settling tank.