Answer to Question #163001 in Mechanics | Relativity for Sage Topaz

Question

We want to pump water from a well 20 m deep at the rate of 500 L/min. Assuming 60 % pump efficiency, how powerful should the pump motor be?

Answer 1

The pump motor power can be found as follows:

$$P=\dfrac{Q\rho gh}{\eta_t},$$

here, $Q$ is the flow rate of the pump, $\rho$ is the density of the water, $g$ is acceleration due to gravity, $h$ is the head of the pump, $\eta_t$ is the pump efficiency.

Then, we get:

$$P=\dfrac{500\ \dfrac{L}{min}\cdot\dfrac{1\ min}{60\ s}\cdot\dfrac{10^{-3}\ m^3}{1\ L}\cdot1000\ \dfrac{kg}{m^3}\cdot9.8\ \dfrac{m}{s^2}\cdot20\ m}{0.6}=2722\ W.$$