Stoke’s law and its applications
When a body falls through a viscous medium, it drags the layer of the fluid immediately in contact with it. This produces a relative motion between the different layers of the liquid. Stoke performed many experiments on the motion of small spherical bodies in different fluids and concluded that the viscous force F acting on a spherical body of radius r depends directly on
i) radius (r) of the sphere
ii) velocity (v) of the sphere and
ii) coefficient of viscosity η of the liquid
Therefore F ∝ ηx r yvz ⇒ F =kηxr y vz , where k is a dimensionless constant.
Using dimensions, the above equation can be written as
[MLT – 2] = k [ML−1T – 1] x ×[ L]y × [LT−1] z
On solving, we get x=1, y=1, and z=1 Therefore, F=kη rv
Experimentally, Stoke found that the value of k = 6π
F = 6πη rv (7.23)
This relation is known as Stoke’s law
Since the raindrops are smaller in size and their terminal velocities are small, remain suspended in air in the form of clouds. As they grow up in size, their terminal velocities increase and they start falling in the form of rain.
This law explains the following:
a) Floatation of clouds
b) Larger raindrops hurt us more than the smaller ones
c) A man coming down with the help of a parachute acquires constant terminal velocity.