A pump draws water from a reservoir and sends it through a horizontal pipe with speed v.Find the relation between…

Q: A pump draws water from a reservoir and sends it through a horizontal pipe with speed v. Find the relation between power of the pump and velocity of liquid.

Sol: From work – energy theorem

$\large P = \frac{K.E(imparted \; to \; water)}{time}$

$\large = \frac{K.E}{volume \; of \; water} \times \frac{volume \; of \; water}{time}$

$\large = (\frac{1}{2}\rho v^2 ) (A v)$