Question

A motor is used to lift water from a well of depth 10 m and to fill water tank of volume 30 m${}^3$ 10 minutes. The tank is at height of 20 m above ground. If 20% of energy is wasted, the power of the motor is (in kW)

Answer 1

$Power=\frac{energy}{time}$

$dP=\frac{dE}{dt}$

$=\frac{dm}{dt}\times g\times h$

As it will be useful power

Volume $=30m^3$

$\frac{mass}{volume}=density$

$mass=1000kg\times 30m^3$

takes $10min$ to fill

$\therefore \frac{dm}{dt}=\frac{30000}{10\times 60}kg/s$

$\therefore \frac{dm}{dt}=50kg/s$

$\therefore P=50\times 10\times 30$

$=15000W=15kw$

$\frac{15}{totalP}\times 100=80$ given by

total power $=\frac{150}{8}kw$ (question efficiency)

$=18.75kw$