Question

A sphere or radius moving with velocity through a fluid experiencces a retarding Force given by f=6ry vz nx where n is the viscosity of the liquid.use method of dimension to find value of x,y,z

Answer 1

Gives

$F=6\pi r\eta v_t$

$F=6r^yv^zn^x$

Dimensions

$F=[M^1L^1T^{-2}]$

$r=[L]\\v=[LT^{-1}]$

$\eta=[M^1L^{-1}T^{-1}]$

$$[M^1L^{-1}T^{-2}]=6[L]^x[LT^{-1}]^y[M^1L^{-1}T^{-1}]^z\\x=1,y=1,z=1$$