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=\frac{\pi }{8}\frac{Pr^{4}}{\eta l}
where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML^{-1}T^{-1}. Check whether the equation is dimensionally correct.

Answers (1)

Let us write dimensions of -

Volume per second (V)=\frac{V}{T}

                                        =[L^{3}T^{-1}]

P=\frac{F}{A}=[ML^{-1}T^{-2}]

\gamma =[L]

\eta =[ML^{-1}T^{-1}]

l =[L]

Now, Dimensions of L.H.S.=[M^{0}L^{3}T^{-1}]

& dimensions of R.H.S. =[M^{0}L^{3}T^{-1}]

The equation is dimensionally correct since the dimensions of both sides are equal.

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