A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference $P$. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is
Medium
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From $\mathrm{V}=\frac{\mathrm{P} \pi \mathrm{r}^{4}}{8 \eta 1} \Rightarrow \mathrm{P}=\frac{\mathrm{V} 8 \mathrm{\eta} 1}{\pi \mathrm{r}^{4}}$
$\Rightarrow \frac{\mathrm{P}_{2}}{\mathrm{P}_{1}}=\frac{\mathrm{V}_{2}}{\mathrm{V}_{1}} \times \frac{1_{2}}{1_{1}} \times\left(\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}\right)^{4}=2 \times 2 \times\left(\frac{1}{2}\right)^{4}=\frac{1}{4}$
$\Rightarrow P_{2}=\frac{P_{1}}{4}=\frac{P}{4}$
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