Q5
The volume of a liquid flowing out per second from a pipe of length $$ l $$ and radius $$ r $$ is written by a student as $$ V=\dfrac{\pi P r^{4}}{8 \eta l} $$ where $$ P $$ is the pressure difference between two ends of pipe and $$ \eta $$ is coefficient of viscosity of the liquid having dimensional formula$$ \left[\mathrm{ML}^{-1} \mathrm{T}^{-1}\right] . $$ Check whether the equation is dimensionally correct or not.
$$\mathrm{Main}$$ $$\mathrm{Concept}$$ $$\mathrm{used:}$$ Principle of homogeneity, for dimensionally correct equation the dimensions of each term in the both sides of the equation should be same.