Answer to Question #100612 in Classical Mechanics for Brighton

Question

When a small sphere moves at a low speed through a fluid, the viscous force F opposing the motion is found experimentally to depend on the radius r, velocity v, and the coefficient of viscosity n of the fluid. Find the force dimension of the force F

Answer 1

$F=r^av^b\eta^c$

$\dim [F]=(\dim [r])^a(\dim [v])^b(\dim [\eta])^c$

$MLT^{-2}=(L)^a(LT^{-1})^b(ML^{-1}T^{-1})^c$

$c=1$

$-2=-b-1\to b=1$

$1=a+1-1\to a=1$

Thus,

$F=\eta rv$