Question

A 30 m deep well is having water upto 15 m.
An engine evacuates it in one hour. The power
of the engine, if the diameter of the well is 4 m
is​

Answer 1

Answer:7.85kW

Explanation:

Answer 2

Given: A 30 m deep well is having water upto 15 m. An engine evacuates it in one hour. If the diameter of the well is 4 m.

To find: Power of engine

First find the mass of water, $m=v\times \rho$

where, v is volume of water and ρ is density of water.

$\therefore m=\pi\times 2^2\times 15\times 1000$

$m=188495.55\text{ kg}$

Now, find average height of water and well.

$h_{avg}=\dfrac{15+30}{2}=22.5\text{ m}$

Now, find workdone to evacuate water at this height.

$W=mgh$

$W=188495.55\times 22.5\times 9.8$

$W=41563270.8\text{ J}$

Power of engine$,P=\dfrac{W}{t}$

$P=\dfrac{41563270.8}{3600}\times \dfrac{1}{1000}\text{ kW}$

$P=11.55\text{ kW}$

Hence, the power of the engine is 11.55 kW.