Question

An electric pump has 2kW power. How much water will the pump lift every minute to a height of 10m?

Answer 1

In the above question the power of the pump is given to us as 2kW. This pump will do work in order to lift the water at a particular rate. First we will define power for the above pump system and then accordingly estimate how much water does it pump to a height of 10m every minute.

Formula used:
$W=mgh$
$P=\dfrac{W}{t}$

Complete step by step answer:
To begin with let us first obtain the expression for work done in lifting a body to a particular height under the action of gravitational force. If the body has mass ‘m’ and is to be lifted at height h with respect to the initial position, then the work done (W )or the energy required to do so is given by,
$W=mgh$
The rate at which work is done is defined as the power of that mechanical system. If the above water pump, lifts the water to a height h in time t, the power P of the pump is given by,
$P=\dfrac{W}{t}=\dfrac{mgh}{t}$
The pump has a power of 2kW and we wish to determine the amount of water it lifts to a height of 10m in 1min. hence from the above expression we get the mass of the water as,
$\begin{aligned} & P=\dfrac{mgh}{t} \\\ & 2kW=\dfrac{m\times 10m{{s}^{-2}}\times 10m}{60\sec }\because 1\min =60\sec \\\ & \Rightarrow m=\dfrac{2\times {{10}^{3}}\times 60}{100}kg \\\ & \Rightarrow m=1200kg \\\ \end{aligned}$

Density of water is equal to $1000kg/{{m}^{3}}$, hence we get the volume of the water lifted in 1 min to a height of 10m is equal to $1.2{{m}^{3}}$ which is equal to 1200 liters of water.

Note: Density of any substance is defined as the ratio of mass to its volume. It is to be noted that we have expressed the amount of water in terms of its volume as it is more convenient. 1 kg of water is equivalent to 1 liter of water.