Question

A pump on the ground floor of a building can pump up water to fill a tank of volume $30{m^3}$ in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30% , how much electric power is consumed by the pump?

Answer 1

here we first use the relation between work, mass and height to find the work. Further we will use this work to find out the power by using the given efficiency of the pump. Also, we will study the basics of work and power for better understanding.
Formula used
$W = mgh$
$P = \dfrac{W}{t}$

Complete step by step solution:
Here, we know that volume of the tank is 30, and mass of the water m is given by:
$m = 30 \times 1000 = 30000kg$
Now, time t is given as 900 seconds, height h is 40m. so the work done is given as:
\eqalign{ & W = mgh \cr & \Rightarrow W = 30000 \times 9.8 \times 40 \cr & \therefore W = 11760000J \cr}
Further, power is given as:
\eqalign{ & P = \dfrac{W}{t} = \dfrac{{11760000}}{{900}} \cr & \therefore P = 13066.67watt \cr}
Efficiency e is given as:
\eqalign{ & e = 30\% = \dfrac{3}{{10}} \cr & \Rightarrow P = 13033.67 \times \dfrac{{10}}{3} \cr & \therefore P = 43.56kW \cr}
Therefore, we get the required electric power consumed by the pump given by P.

Additional information:
As we know the power. It is the amount of energy transferred or converted per unit time. In the International System or S.I Unit of power is the watt. The S.I unit of power can also be written as one joule per second. Power is a scalar quantity, which means it has only magnitude not direction.
Further, the energy is defined as the ability to do work. Energy can be found in many things and can take different forms, like-kinetic energy is the energy of motion, and potential energy is energy due to an object's position or structure. Total energy of a system is given by the sum of kinetic energy and potential energy.
We also know that, according to the law of conservation of energy, energy can neither be created nor be destroyed; rather it can only be transferred from one form to another. Here, in this question electrical energy is transferred to heat energy.

Note:
Here we should remember that work is also defined as a product of force and displacement. If there is no displacement there is no work done. Work is measured in Joule. Also, efficiency can never be greater than one.