Question

An engine pump is used to pump a liquid of density $\rho$ continuously through a pipe of area of cross-section $A$. If the speed with which the liquid passes the pipe is $V$, then the rate at which kinetic energy is being imparted to the liquid is:

• A. $\frac{1}{2}A\rho V^3$
• B. $\frac{1}{2}A\rho V^2$
• C. $\frac{1}{2}A\rho V$
• D. $A\rho V^2$

Answer 1

The correct option is A $\frac{1}{2}A\rho V^3$

$\frac{d}{dt}\left(\frac{1}{2}m{V}^2\right)$

Volume flow in time $dt$ is $=AVdt$
$dm=dAVdt$

$=\frac{1}{2}{V}^2\frac{dm}{dt}$
$=\frac{1}{2}{V}^2\frac{\left(AVdtd\right)}{dt}=\frac{1}{2}{V}^{3}Ad$