Question

dimensional analysis of stokes law

Answer 1

Suppose a spherical body of radius r moves at speed v through a fluid of viscosity ƞ ,viscous force F acting on the body depends on r,v and ƞ .
According to the dimensional analysis we can write,

Let F = kravb ƞ​c

Where k is the dimensional less constant.

MLT-2 = kLa(LT-1)b(ML-1 T-1)c

On equating the coefficients of M,L,T on both sides we get :
a,b,c each = 1
hence F = krvƞ,
value of  k = 6π,
hence stokes law becomes,

F = 6πƞrv

This  is the required stokes law