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

# 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

1. A

$\frac{{\mathrm{D}}^{2}\mathrm{v}}{{\mathrm{nd}}^{2}}$

2. B

$\frac{{\mathrm{nD}}^{2}\mathrm{v}}{{\mathrm{d}}^{2}}$

3. C

$\frac{{\mathrm{nd}}^{2}\mathrm{v}}{{\mathrm{D}}^{2}}$

4. D

$\frac{{\mathrm{d}}^{2}\mathrm{v}}{{\mathrm{nD}}^{2}}$

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### Solution:

Since each pipe receives the same amount of water every pipe,

${\mathrm{A}}_{1}{\mathrm{v}}_{1}={\mathrm{A}}_{2}{\mathrm{v}}_{2}$

$\mathrm{\pi }\frac{{\mathrm{D}}^{2}}{4}\mathrm{v}=\mathrm{n\pi }\frac{{\mathrm{d}}^{2}}{4}\mathrm{v}\text{'}$

thus, $\mathrm{v}\text{'}=\frac{{\mathrm{D}}^{2}}{{\mathrm{nd}}^{2}}\mathrm{v}$

Hence the correct answer is $\frac{{\mathrm{D}}^{2}}{{\mathrm{nd}}^{2}}\mathrm{v}.$

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