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

Hint: 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.