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

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1.Units, Dimensions and Measurement

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 $l$ and having a pressure difference $p$ across its end, is

A

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

B

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

C

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

D

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

Solution

(a) Formula for viscosity $\eta = \frac{{\pi p{r^4}}}{{8Vl}} \Rightarrow V = \frac{{\pi p{r^4}}}{{8\eta l}}$

Standard 11

Physics

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