An electric motor of 1hp is used to run the water pump.

Question

An electric motor of 1hp is used to run the water pump. The water pump takes 10 minutes to fill an overhead tank. The tank has a capacity of 800 liters and a height of 15 m. Find the actual work done by the electric motor to fill the tank. Also, find the efficiency of the system. (Density of water = 1000 $kgm^{-3}$ )
(Mass of 1 liter of water = 1 kg) (447600 J, 26.8%)

Accepted Answer

Solution:

Power = P = 1 hp = 746 W

Time = t = 10 min = $10 imes 60$ s = 600 s

$\frac{Capacity}{volume}$ = V = 800 liters

Height = h = 15 m

Work done = W = ?

Efficiency = E = ?

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

P =$\frac{w}{t}$

Or W = $P imes t$

W = $746 imes 600$

W = 447600 J

Since the work done by the electric pump to fill the tank is 447600 J. It is equal to the input.

Hence input = actual work doe = W = 447600 J

Output = P.E = mgh

Since 1 litre = 1kg, therefore 800 litres = 800 kg

Output = P.E = $800 imes 10 imes 15$ = 120000J

% Efficiency = $\frac{Output}{Input }×100$

% Efficiency = $\frac{120000}{447600}×100$

Efficiency = 26. 8 %