1. An engine pumps 2000kgs of water in 1 minute to an average height of 10m.Calculate the power of the engine if 30% of the energy is wasted in the process.

2. A water pump of power 1.5KW draws water through a mean height of 10m to fill a tank 4m x 3m x 4m. Calculate the time taken to fill the tank

1.

Here,

Work done in the process of lifting water, W = mgh = (2000)(9.8)(10) = 19600 J

Let, X be the power of the engine. Work done per second by the engine is X.

Energy lost per second in the process is 30%, which is (30X)/100.

Therefore, X = W + (30X)/100

=> X = 19600 + (30X)/100

=> X = 19600×100/70

=> X = 28000 J

This is the energy provided by the engine per second. So, power of the engine is 28000 W = 28 kW.

2.

Power of water pump = 1.5 kW

Work done by the pump per second, W = 1500 J

Volume of water to be filled, V = 4×3×4 = 48 m³

Mass of water to be filled, m = (volume)(density) = 48×1000 = 48000 kg

Work to be done to fill the tank, W^/ = mgh = (48000)(9.8)(10) = 4704000 J

So, time taken by the pump to do this work is, t  =W^//W = 4704000/1500 = 3136 s

Or, t = 52.27 min