The volume of a liquid flowing out per second of a pipe of length l a

1.	The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a students as V= \(\frac{\pi}{8}\frac{Pr^4}{nl}\)where P is the pressure difference between the two ends of the pipe and n is coefficient of viscosity of the liquid having dimensional formula [ML-1T-1].Check whether the equation is dimensionally correct.
Answer» The dimensional part in the expression is \(\frac{Pr^4}{nl}\). Therefore, the dimensions of the right-hand side come out to be \(\frac{[ML^{-1}T^2][L^4]}{[ML^{-1}][L][T]}=\frac{[L^3]}{[T]}\), Which is volume upon time. As [V] = \(\frac{L^3}{T}\),the formula is dimensional correct, because LHS = RHS.

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

Answer»

The dimensional part in the expression is \(\frac{Pr^4}{nl}\).

Therefore, the dimensions of the right-hand side come out to be \(\frac{[ML^{-1}T^2][L^4]}{[ML^{-1}][L][T]}=\frac{[L^3]}{[T]}\),

Which is volume upon time. As [V] = \(\frac{L^3}{T}\),the formula is dimensional correct, because LHS = RHS.