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A pipe having an internal diameter D is connected to another pipe of same size. Water flows into the second pipe through ‘n ’ holes each of diameter ‘d ’. If the water in the first pipe has speed V, the speed of water leaving the second pipe is

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$\frac{d^{2} V}{{nD}^{2}}$

$\frac{D^{2} V}{{nd}^{2}}$

$\frac{{nd}^{2} V}{D^{2}}$

$\frac{{nD}^{2} V}{d^{2}}$

answer is A.

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Detailed Solution

From equation of continuity

$A_{1} V_{1} = A_{2} V_{2}$

$π {[\frac{D}{2}]}^{2} V = π {[\frac{d}{2}]}^{2} V^{'} \Rightarrow V^{'} = \frac{D^{2} V}{{nd}^{2}}$

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