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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 / and 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
$V=\frac{\pi P \eta}{8 r^4}$
Solution
(a)
On checking the dimensionality the correct relation is
$V=\frac{\pi P r^4}{8 \eta l}$
Standard 11
Physics
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