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Stokes' law
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Viscous drag on a small sphere at low speed.
F = 6πηrvFor a small sphere moving slowly through a viscous fluid, the drag is F = 6πηrv, proportional to speed. It governs the settling of fine particles and oil drops in Millikan's experiment.
A 1 mm steel ball in glycerol quickly reaches a steady slow speed.
It holds only for low Reynolds number (smooth flow).
In more detail
Stokes' law gives the drag on a small sphere moving slowly through a viscous fluid as F = 6πηrv, where η is viscosity, r is radius and v is speed.
Real-world uses
- Measuring the viscosity of oils using falling spheres.
- Modelling the motion of tiny particles in liquids, such as droplets in paint.
- Tiny droplets and dust particles in the air fall slowly and steadily, which is well described by Stokes' law.
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Frequently asked questions
When does Stokes' law apply?
For small spheres at low speeds in viscous fluids, where the flow is smooth.
Why does radius matter so much?
Drag grows with radius, which is why small particles settle slowly.
When does Stokes' law apply?
At low speeds and small sizes, where the flow around the object is smooth. At higher speeds, the quadratic drag law is more appropriate.
Related topics in Newton's Laws & Forces
Centrifugal force · Pseudo forces · Drag force · Terminal velocity of a sphere · Spring force · Springs in series and parallel