Answer to Question #308524 in Mechanics | Relativity for Trooye

Question

What is the theoretical horsepower required to pump water at 6.30liters/second from a large reservoir to the surface of another reservoir 120m higher?

Answer 1

Explanations & Calculations

$\qquad\qquad \begin{aligned} \small 1 W&=\small 0.00134\,hp\\ \\ \small Energy&=\small mgh\\ \small power(W)&=\small \frac{mgh}{t}=\frac{V\rho.gh}{t}=\Big(\frac{V}{t}\Big).\rho gh\\ &=\small 0.0063\,m^3s^{-1}\times1000\,kgm^{-3}\times9.8\,ms^{-2}\times120\,m\\ &=\small 7408.8\,W\\ &=\small 7408.8\,W\times0.00134\,hp\,W^{-1}\\ &=\small 9.93\,hp \end{aligned}$