Stokes' law

Stokes' law:

The law states that, “The viscous force (Fv) acting on a small sphere falling through a viscous medium is directly proportional to the radius of the sphere (r), its velocity (v) through the fluid, and the coefficient of viscosity (K) of the fluid”. 

This is the expression for viscous force acting on a spherical object moving through a viscous medium. 

Terminal Velocity:

Consider a spherical object falling through a viscous fluid. Forces experienced by it during its downward motion are,

1. Viscous force (Fv), directed upwards. Its magnitude goes on increasing with increase in its velocity.

2. Gravitational force, or its weight (Fg), directed downwards, and

3. Buoyant force or upthrust (Fu), directed upwards.

Net downward force given by f = Fg - (Fv +Fu), is responsible for initial increase in the velocity. Among the given forces, Fg and Fu are constant while Fv increases with increase in velocity. Thus, a stage is reached when the net force f becomes zero. At this stage, Fg = Fv + Fu . After that, the downward velocity remains constant. This constant downward velocity is called terminal velocity. Obviously, now onwards, the viscous force Fv is also constant. The entire discussion necessarily applies to streamline flow only. 

Consider a spherical object falling under gravity through a viscous medium as shown in the figure. Let the radius of the sphere be r, its mass m and density U. Let the density of the medium be V and its coefficient of viscosity be K. When the sphere attains the terminal velocity, the total downward force acting on the sphere is balanced by the total upward force acting on the sphere. Total downward force = Total upward force weight of sphere (mg) = viscous force + buoyant to due to the medium 

This is the expression for the terminal velocity of the sphere. From the above equation,