The volume of a liquid (v) flowing per second through a cylindrical tube depends upon the pressure gradient (p/l) radius of the tube (r) coefficient of viscosity ( $η$ ) of the liquid by dimensional method the correct formula is

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$V \propto \frac{{Pl}^{4}}{ηr}$

$V \infty \frac{\Pr}{η l^{4}}$

$Vα \frac{\Pr^{4}}{ηl}$

answer is A.

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Detailed Solution

$\begin{array}{l} V = L^{3} T^{- 1} \\ \frac{{pr}^{4}}{ηl} = \frac{{ML}^{- 1} T^{- 2} L^{4}}{{ML}^{- 1} T^{2} L} \end{array}$
DF of $\frac{{πPr}^{4}}{8 η 1} = L^{3} T^{- 1} = DF of V$

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