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

Question #163001

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?



1
Expert's answer
2021-02-15T00:57:05-0500

The pump motor power can be found as follows:


P=Qρghηt,P=\dfrac{Q\rho gh}{\eta_t},

here, QQ is the flow rate of the pump, ρ\rho is the density of the water, gg is acceleration due to gravity, hh is the head of the pump, ηt\eta_t is the pump efficiency.

Then, we get:


P=500 Lmin1 min60 s103 m31 L1000 kgm39.8 ms220 m0.6=2722 W.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.

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