Write down the expression for the Stoke's force and explain the symbols involved in it.

Explanation

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
(iii) efficient of viscosity `eta` hour of the liquid
Therefore, `F prop eta^(x)r^(y)v^z implies F = k eta^x r^y v^z` , where k is a dimensionless constant.
Using dimensions, the above equation can be written as
`[MLT^(-2)] = k [ML^(-1)T^(-1)]^(x) xx [L]^(y) xx [LT^(-1)]^(z)`
On solving , we get `x = 1, y = 1 and z = 1`. Therefore, `F = k eta e v`
Experimentally, Stoke found that the value of `k = 6 pi`
`F = 6 pi eta r v` This relation is known as Stoke.s law.