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X and Y are two capillary tubes with lengths l_x and l_y and with radii r_x and r_y respectively. When a pressure difference P is maintained between the ends of X, the rate of flow of water through X is 10 cc/sec. X and Y are now connected in series and the same pressure difference P is maintained across the combination. If l_x = 2 l_y and r_x = r_y , rate of flow of water through the combination will be:

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3 cc/sec

$\frac{52}{7} cc / \sec$

$\frac{20}{3} cc / \sec$

$\frac{9}{4} s e c / c c$

answer is C.

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Detailed Solution

The length of the composite tube $= \frac{3}{2} l$
Rate of flow $= \frac{{πPr}^{3}}{8 η (\frac{3}{2} l)} = \frac{2}{3} \times (\frac{{πPr}^{4}}{8 ηl}) = \frac{2}{3} \times 10 = \frac{20}{3} cc / \sec$

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