The rate of steady volume flow of water though a capillary tube of length 'l ' and radius 'r ' under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow though them under same pressure difference across the combination is

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$\frac{V}{17}$

$\frac{V}{16}$

$\frac{16 V}{17}$

$\frac{17 V}{16}$

answer is B.

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Detailed Solution

Rate of flow of liquid V = P / R

here , R (liquid resistance) $= \frac{8 ηl}{{πr}^{4}}$
Another tube liquid resistance $R^{1} = \frac{8 ηl}{π {(\frac{r}{2})}^{4}} = 16 R$
For series combination $V_{new} = \frac{P}{R + R^{1}} = \frac{P}{17 R} = \frac{V}{17}$

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