Stokes' law

Advanced

Drag on a small sphere in viscous fluid.

Key relationF = 6πηrv

A sphere moving slowly in a viscous fluid feels F = 6πηrv. It lets you measure viscosity from a falling-ball experiment.

Worked example

Used by Millikan to find oil-drop radius.

Common mistake

Fails if flow becomes turbulent.

In more detail

Stokes' law gives the drag on a small sphere moving slowly through a viscous fluid, F = 6πηrv. It applies at low Reynolds numbers.

Measuring viscosity by timing falling spheres in a fluid.
Modelling the motion of pollen and particles in air or water.
Tiny droplets of fog or dust particles fall slowly through air, which Stokes' law describes well at low speed.

What is the condition for Stokes' law?

Low speeds and small spheres, so the flow is smooth around the sphere.

Does the drag depend on speed?

Yes, in direct proportion, for low speeds.

When does Stokes' law fail?

At higher speeds or larger sizes, when the flow around the sphere becomes turbulent and the drag is no longer linear in speed.