Question: A 1.0 HP motor pumps out water from a well of depth 20 meters and fills a water tank of volume 2238 ...

Question

A 1.0 HP motor pumps out water from a well of depth 20 meters and fills a water tank of volume 2238 liters at the height of 10 meters from the ground. The running time of the motor to fill the empty water tank is: $\left( {g = 10m{s^{ - 2}}} \right)$
A. 5 minutes
B. 10 minutes
C. 15 minutes
D. 20 minutes

Answer 1

Solution

Specific pump power is the measurement of electric power needed to operate a pump, relative to the volume flow rate. Also, $1{\text{ }}hp = 746{\text{ }}Watts$
In this question, the power of the motor is given, which is transferring the water from a well to a water tank. First, find the total potential energy required to transfer the water to 10+20=30m height from the well then find the time required.

Complete step by step answer:
Pump of $1{\text{ }}hp = 746{\text{ }}Watts$ and the depth of the well is 20 meters.
Work done by a motor is equal to the change in the potential energy of water when it is pumped from the well to the overhead tank, where work done is given as, $W = P * t$
Now assume the total time to fill the tank to be $t$ seconds.
The total height the water is pumped is given as: $10 + 20 = 30{\text{ }}m$
Now use the work done formula

W = P \times t \\\ = 746 \times t \\\

The mass of the water, whose density is $1\dfrac{{kg}}{{{m^3}}}$

m = density \times volume \\\ = 1\dfrac{{Kg}}{{{m^3}}} \times 2238{m^3} \\\ = 2238Kg \\\

So the potential energy will be

PE = mgh \\\ = 2238 \times 10 \times 30 \\\ = 671400J \\\

As per energy conservation rule work done by a motor is equal to the change in the potential energy of water; hence we can write

W = PE \\\ 746 \times t = 671400 \\\ t = \dfrac{{671400}}{{745}} \\\ = 900\sec \\\ = 15\min \\\

The total running time of the motor to fill the empty water tank is $15\min$

So, the correct answer is “Option C”.

Note:
The potential energy is the same as the work done in the same way kinetic energy is. Potential energy is a way of storing energy as of virtue of its motion while work is done is the way of changing energy from one form to another.