(A) The volume flow rate $V$ (Poiseuille's Law) is given by the formula $V = \frac{\pi P r^4}{8 \eta l}$.To verify this dimensionally:Dimensions of $V

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$V = \frac{\pi P r^4}{8 \eta l}$

(A) The volume flow rate $V$ (Poiseuille's Law) is given by the formula $V = \frac{\pi P r^4}{8 \eta l}$.To verify this dimensionally:Dimensions of $V = [L^3 T^{-1}]$.Dimensions of $P = [M L^{-1} T^{-2}]$.Dimensions of $r = [L]$.Dimensions of $\eta = [M L^{-1} T^{-1}]$.Dimensions of $l = [L]$.Substituting these into the $RHS$: $\frac{[M L^{-1} T^{-2}] [L^4]}{[M L^{-1} T^{-1}] [L]} = \frac{[M L^3 T^{-2}]}{[M T^{-1}]} = [L^3 T^{-1}]$.Since the dimensions of $LHS$ and $RHS$ match,the correct relation is $V = \frac{\pi P r^4}{8 \eta l}$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

Medium

$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$,having a pressure difference $P$ across its ends,is:

A
$V = \frac{\pi P r^4}{8 \eta l}$
B
$V = \frac{\pi \eta}{8 P r^4}$
C
$V = \frac{8 P \eta}{\pi r^4}$
D
$V = \frac{\pi P \eta}{8 r^4}$

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

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EasyIIT 2019

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$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$,having a pressure difference $P$ across its ends,is:

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$(P+\frac{a}{V^2})(V-b)=RT$ represents the equation of state of some gases. Where $P$ is the pressure,$V$ is the volume,$T$ is the temperature and $a, b, R$ are the constants. The physical quantity,which has the same dimensional formula as that of $\frac{b^2}{a}$,will be

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