A pump installed on ground takes 15 minutes to fill a water tank of 30m3 volume placed at a height of 50 m. If the efficiency of pump is 30%, the power consumed by the pump will be:
Hello,
Density of water is = 1000 kg/m3
Volume of water filled = 30 m3
Therefore, mass of water filled in the tank = (1000 kg/m3)(30 m3) = 30000 kg
Height to which the water is raised = 50 m
Acceleration due to gravity = 9.8 m/s2
So, rise in potential energy of the water = (30000 kg)(9.8 m/s2)(50 m) = 1.47 X 107 J
The work is done by the pump in 15 min = 900 s
Power of the pump = (1.47 X 107 J)/(900 s) = 16300 Watt
Let, x be the electrical power given to the pump, since the efficiency of the pump is 30%
Therefore,
x(30/100) = 16300
=> x = 54333.3 Watt
So, the power consumed by the pump is 54333.3 Watt.