Sarthaks Test
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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 = πPr4/8ηl

where 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.

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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.

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