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 litres 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 litre of water = 1 kg) Ans. (447600 J, 26.8 %)


Given:  

Power of the motor = P =  I hP = 746 watt
Mass of 800 liters of water to be lifted when (1 liter = 1 Kg)  = m = 800 kg
Time taken  = t = 10 min  = 600 sec 
Height of the tank = h = 15 m
gravitational acceleration = g = 10 m s⁻²



To Find:

Work done by the motor = W = ? J
The efficiency of the system = ?


Solution:  


As Power is defined as the rate of doing work. So,

P = `\frac {W}{t}`

Or 

W = P ｘ t

Putting values 

W = 746 watt ï½˜ 600 s

W = 447,600 Ws

or 

W = 447,600 J
This is the total input energy of the Machine to do work.

Now to find the Efficiency of the system we will also need to find the Output of the Machine, that is the work done on lifting the water to a height h  So, 

The output of the machine = W' = mgh    (W= F ｘ S  and F = weight = W = mg, and S = h). So, putting values 

W' = 800 kg ï½˜ 15 m  ï½˜ 10 ms⁻² 

W' = 120,000 Kgm²s⁻² 

or

W' = 120,000 J
this is the output of the machine

Now 


and


By putting values we have

% Efficiency = `\frac {120,000 J}{447,600 J}` ｘ 100

by simplifying we get 

% Efficiency = 26.8 %
the efficiency of the machine is 26.8 %

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