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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
 
 
 
© Keith Gibbs 2013