The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as v=\frac{\pi}{8}\times \frac{Pr^{4}}{\eta l} where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML^{-1}T^{-1}. Check whether the equation is dimensionally correct.
The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as v=\frac{\pi}{8}\times \frac{Pr^{4}}{\eta l} where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML^{-1}T^{-1}. Check whether the equation is dimensionally correct.

Dimension of the given physical quantity is as follows,

[V] = dimension of volume/dimension of time

=[L^{3}]/[T]

=[M^{-1}T^{-2}]

LHS =[L^{3}T^{-1}]

RHS =[L^{3}T^{-1}]

LHS = RHS

Hence, the equation is correct.