Question

An engine pump is used to pump a liquid of density $\rho$ 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:

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

Answer 1

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

Kinetic energy $\frac{1}{2}m{v}^2$

Energy supplied to liquid per second by the pump

$P=\frac{1}{2}\frac{m{v}^2}{t}$

$P=\frac{1}{2}\frac{Vp{v}^2}{t}$

$P=\frac{1}{2}A\times \left(\frac{l}{t}\right)\times p\times v^2$

putting $[\frac{l}{t}=v]$

$P=\frac{1}{2}A\times v\times p\times v^2=\frac{1}{2}Ap{v}^3$