Water is pumped at 250 m^3/min from a lake into a tank 65.0 m above the lake. What is the power required in kW and horsepower. What is the increase in potential energy of the water.
Water is pumped at the rate of 250 m^3 per minute from a lake into a tank that is 65 m above the lake. The density of water is 1000 kg/m^3, this gives the mass of 250 m^3 as 250*10^3 kg.
The water is raised at the rate of 250*10^3 kg per minute or 4167 kg/second. The work to be done in raising 1 kg of water by 1 m is equal to 9.8 J. Raising 4167 kg by 65 m requires 4167*9.8*65 2654379 J. The power required is equal to 2654 kW.
The power consumed in increasing the height of the water and storing it in the tank is equal to the increase in potential energy. As the power of the pump is 2654 kW the increase in potential energy is also at the rate of 2654 kW.
1 kilowatt is equal to1.3410 horsepower. 2654 kW in terms of horsepower is 3.487*10^6 hp.