Question

A water pump that consumes 2 kW of electric power when operating is claimed to take in water from a lake and pump it to a pool whose free surface is 30 m above the free surface of the lake at a rate of 53 L/s. Determine if this claim is reasonable. (Round the final answer to one decimal place.)

Answer 1

Answer:

The claim is not reasonable

Explanation:

From the question we are told that

The power consumed is $P = 2kW = 2*10^3 W$

The height of the pool's free surface is $h = 30 \ m$

The rate is $Q = 53\ L /s$

Given that the rate is 53 liters in 1 second , let say the 1 liter is equivalent to 1 kg so 50 liter = 50 kg

So the workdone by the pump is mathematically represented as

$W = m * g * h$

=>     $W = 50 * 9.8 * 30$

=>      $W =14700 \ J$

So what this value is telling us is that 14700 J of work is done in one  second

and generally power is workdone per time thus the power consumed to move water at the given rate is 14.7 kW which is far greater than the power stated in the question so the claim is not reasonable