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 = kr
xη
yv
z We have MLT
-2 =
L
x(ML
-1T
-1)
y(LT
-
1)
zSolving this gives x = 1, y = 1 and z = 1.
By other methods k
can be shown to be 6π.
Thus giving:
F =
6πηrv
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