To pump out water from a mine with a depth of 20 meters, a pump with a capacity of 4.5 kW

To pump out water from a mine with a depth of 20 meters, a pump with a capacity of 4.5 kW was needed, the efficiency of the pump was 80%. How much water will the pump raise in 7 hours of operation?

h = 20 m.

g = 10 m / s2.

Ns = 4.5 kW = 4500 W.

Efficiency = 80%.

t = 7 h = 25200 s.

m -?

For a water pump that raises water, the efficiency is expressed by the formula: Efficiency = Ap * 100% / Az, where Ap is the pump’s useful work, Az is the pump’s work expended when the water rises.

The useful work of the pump Ap will be expressed by the formula: Ap = m * g * h, where m is the mass of the raised water, g is the acceleration of gravity, h is the depth from which the water rises.

The expended work of the pump Az is expressed by the formula: Az = Ns * t, where Ns is the expended power of the pump, t is the operating time of the pump.

Efficiency = m * g * h * 100% / Nc * t.

m = efficiency * Nz * t / g * h * 100%.

m = 80% * 4500 W * 25200 s / 10 m / s2 * 20 m * 100% = 453600 kg.

Answer: the pump from the mine will be able to lift m = 453600 kg of water.