Question

Derivation of Stokes law from dimension method

Answer 1

Answer:

Dimensional analysis proof of Stokes' Law

Suppose that the sphere has radius r and falls through a fluid of viscosity η. Let the terminal velocity be v (Figure 1).  

We can calculate the viscous drag F on the sphere by dimensional analysis.  

If

F = krxηyvz  

We have MLT-2 = Lx(ML-1T-1)y(LT- 1)z

Solving this gives x = 1, y = 1 and z = 1.  

By other methods k can be shown to be 6π.

Thus giving:

F = 6πηrv