Question

A pump is used to pump a liquid of density $\rho$ continuously through a pipe of cross-sectional area $A$. If the liquid is flowing with a speed $v$, find the power of the pump.

Answer 1

Mass of liquid pumped per second = Density $\times$ Volume per second
$=Density\times Cross-sectionalarea\times Velocity$
$=\rho Av$
$\therefore Power=\frac{1}{2}\left(\rho Av\right).v^2=\frac{\rho A{v}^3}{2}$