Define terminal velocity of a small spherical body moving in a viscous medium

When a body falls through a viscous medium (liquid or gas), it drags a layer of the fluid adjacent to it due to adhesion. But fluid layers at a large distance from the body are at rest. As a result, there is relative motion between different distances from the body. But the viscosity of the fluid opposes this relative motion. The opposing force due to viscosity increases with an increase in the velocity of the body.

If the body is small in size, then after an interval of time, the opposing upward force becomes equal to the downward force that causes acceleration of the body. Then the effective force acting on the body becomes zero and the body begins to fall through the medium with a uniform velocity called Terminal Velocity. A graph representing the change in velocity of a falling object with time is shown below figure:

Stokes Law: Stokes proved that if a small sphere of radius r is falling with a terminal velocity v through a medium with a co-efficient of viscosity η, then the opposing force acting on the sphere due to viscosity is

F = 6πηrv …equ(1)

Equ(1) expresses Stoke’s law.

To establish Stoke’s law, the following assumptions are:

i. The fluid medium must be infinite and homogeneous.
ii. The sphere must be rigid with a smooth surface.
iii. The sphere must not slip when falling through the medium.
iv. The fluid motion adjacent to the falling sphere must be streamlined.
v. The sphere must be small in size, but it must be greater than the intermolecular distance of the medium.