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

1.	The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student asv = πPr4/8ηlwhere P is the pressure difference between the two ends of the pipe and η is coefficent of viscosity of the liquid having dimensional formula ML–1 T–1.Check whether the equation is dimensionally correct.
Answer» The dimensional part in the expression is (ρr⁴/ηl).Therefore, the dimensions of the right hand side comes out to be ([ML^-1 T^-2 ][L⁴ ]/[ML^-1 T^-2 ][L]) = [L³]/[T], which is volume upon time. Hence, the formula 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 asv = πPr4/8ηlwhere P is the pressure difference between the two ends of the pipe and η is coefficent of viscosity of the liquid having dimensional formula ML–1 T–1.Check whether the equation is dimensionally correct.

Answer»

The dimensional part in the expression is (ρr⁴/ηl).Therefore, the dimensions of the right hand side comes out to be

([ML^-1 T^-2 ][L⁴ ]/[ML^-1 T^-2 ][L]) = [L³]/[T], which is volume upon time. Hence, the formula is dimensionally correct.