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 $\upsilon$, then the rate at which kinetic energy is being imparted to the liquid is

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

Answer 1

Answer: (A)

Volume of liquid flowing per second $A\upsilon$
Mass of liquid flowing per second, $m=A\upsilon \rho$
The rate at which kinetic energy is being imparted to the liquid is
$=\frac{1}{2}m{\upsilon }^2=\frac{1}{2}\left(A\upsilon \rho \right){\upsilon }^2=\frac{1}{2}A\rho {\upsilon }^3$