#Stokes s law
Stokes’s law , mathematical equation that expresses the settling velocities of small spherical particles in a fluid medium. The law, first set forth by the British scientist Sir George G. Stokes in 1851, is derived by consideration of the forces acting on a particular particle as it sinks through a liquid column under the influence of gravity. The force acting in resistance to the fall is equal to 6πrηv, in which r is the radius of the sphere. η is the viscosity of the liquid, and v is the velocity of fall. The force acting downward is equal to 4 /3 πr 3 (d 1 - d 2 )g, in which d 1 is the density of the sphere, d 2 is the density of the liquid, and g is the gravitational constant. At a constant velocity of fall the upward and downward forces are in balance. Equating the two expressions given above and solving for v therefore yields the required velocity, expressed by Stokes’s law as v = 2 /9 (d 1 - d 2 )gr 2 /η .