First slide

Power

Question

An engine pump is used to pump a liquid of density $ρ$ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is

Moderate

A

$\frac{1}{2} {Aρv}^{3}$
B

$\frac{1}{2} {Aρv}^{2}$
C

$\frac{1}{2} Aρv$
D

$Aρv$

Solution

Energy supplied to liquid per second by the pump
$= \frac{1}{2} \frac{{mv}^{2}}{t} = \frac{1}{2} \frac{{Vρv}^{2}}{t} = \frac{1}{2} A \times (\frac{l}{t}) \times ρ \times v^{2} [\frac{l}{t} = v]$
$= \frac{1}{2} A \times v \times ρ \times v^{2} = \frac{1}{2} {Aρv}^{3}$

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