Question

State Stokes' law and an expression for the magnitude of the viscous force.

Answer 1

Stokes' law states that the viscous force acting on a sphere when a fluid passes by it or the sphere moves through it is directly proportional to the fluid's coefficient of viscosity η, the sphere's radius r, and the free-stream velocity v₀ at small enough relative speeds `vecv_0` for the flow to be streamlined. The viscous force's magnitude,

f ∝ ηrv₀

∴ f = − 6πηrv₀

where `vecf` is the opposite of `vecv_0`, so the minus sign is included. Theory and experimentation yield the constant 6π