Question

Determine the power required by the pump to raise the \( 2 m^{3} / m i n \) of water of a reservoir at a height of \( 10 m \) if its efficiency is \( 80 \% \)

Answer 1

Given \((\frac{dV}{dt})=2m^3/min\)

h = 10 m

n = 80%

We know that, P = \(\frac{dW}{dt}\)

P = \(\frac{d}{dt}(mgh)\)

P = \(\frac{d}{dt}(mgh)\) \(\because\) m = \(\rho\).V

P = \(\frac{d}{dt}(\rho. vgh)\) 

P = \((\frac{dV}{dt})\rho\,gh\) 

P = \((\frac{dV}{dt})\rho\,gh\)

P = 2 x 1000 x 10 x 10

P_input = 2 x 10⁵ Watt

Output power  = n x input power

 = 0.80 x 2 x 10⁵

P_out = 16 x 10⁴ Watt