Stokes Law of Resistance of a Sphere

a law giving the force of resistance F experienced by a sphere when it undergoes slow translational motion in an unbounded viscous fluid. The law states that F = 6πμrv, where μ, is the viscosity of the fluid, r is the radius of the sphere, and v is the speed of the sphere. This formula was set forth by G. G. Stokes in 1851. The law holds only for small Reynolds numbers Re « 1.

Stokes’ law has applications in colloid chemistry, molecular physics, and meteorology. The law can be used to determine the settling speed of fine fog droplets, colloid particles, silt particles, or other small particles. The terminal velocity v_ter of a small sphere falling through a viscous fluid is

where ρ is the density of the fluid, ρ’ is the density of the sphere, and g is the acceleration of gravity. Stokes’ law is used in viscosi-metry to determine the viscosity of very viscous fluids.