A motor pump of power 1 H.P is discharging water with a velocity of 10ms^–1. In order to discharge water with a velocity of 20ms^–1, the power of the motor should be

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2 H.P

4 H.P

8 H.P

16 H.P

answer is C.

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Detailed Solution

We know that,

$P = \frac{\frac{1}{2} m v^{2}}{t} = \frac{1}{2} \frac{(v ρ) v^{2}}{t} = \frac{1}{2} A ρ v^{3}$

$\Rightarrow P \propto v^{3}$

$\Rightarrow (\frac{P'}{P}) = {(\frac{V'}{V})}^{3}$

$\Rightarrow \frac{P'}{1 H P} = {(\frac{20}{10})}^{3}$

$\Rightarrow P' = 8 H P$

Hence the correct answer is 8H.P.

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