A dimensionally consistent relation for volume V of a liquid of coefficient of viscosity ' eta &

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1.Units, Dimensions and Measurement

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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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