Question

Find the power used in pumping $3425m^3$ of water per hour from a well $8m$ deep to the surface, supposing $40$ of the hour's power during pumping is wasted. What is the horsepower of the engine?

Answer 1

Given-

Power , $P=\frac{V}{t}=3425m^3/hr=0.9514m^3/s$

$h=8m$

Power lost $=40\text{\%}$

Output power required here is-

Power = Work done/time

$P_o=\frac{mgh}{t}$

$P_o=\frac{V\times \rho \times g\times h}{t}$

$P_o=0.9514\times 1000\times 10\times 8$

$Po=76112W=76.112kW$

Input power is given by

$P_i=\frac{P_o}{\eta }$

$P_i=\frac{76112}{60\text{\%}}$

$P_i=126853W$

Required horsepower is

$P=\frac{P_i}{746}$

$P=\frac{126853}{746}$

$P=170hp$

Horsepower of the engine is $170hp.$