a pump on the ground floor of a building can pump water to fill tank of volume 30m^3 in 15 minutes.Iftank is 40m above the ground and the effifciency of pump is 30%,how much electric power is consumed by the pump?
a pump on the ground floor of a building can pump water to fill tank of volume 30m^3 in 15 minutes.Iftank is 40m above the ground and the effifciency of pump is 30%,how much electric power is consumed by the pump?
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 = 40 m
Acceleration due to gravity = 9.8 m/s2
So, rise in potential energy of the water = (30000 kg)(9.8 m/s2)(40 m) = 1.17 X 107 J
The work is done by the pump in 15 min = 900 s
Power of the pump = (1.17 X 107 J)/(900 s) = 13000 Watt
Let, x be the electrical power given to the pump, since the efficiency of the pump is 30%
Therefore,
x(30/100) = 13000
=> x = 43333.33 Watt
So, the power consumed by the pump is 43333.3 Watt.
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 = 40 m
Acceleration due to gravity = 9.8 m/s2
So, rise in potential energy of the water = (30000 kg)(9.8 m/s2)(40 m) = 1.17 X 107 J
The work is done by the pump in 15 min = 900 s
Power of the pump = (1.17 X 107 J)/(900 s) = 13000 Watt
Let, x be the electrical power given to the pump, since the efficiency of the pump is 30%
Therefore,
x(30/100) = 13000
=> x = 43333.33 Watt
So, the power consumed by the pump is 43333.3 Watt.
