Consider the small portion of element dx as shown below.
The mass of the element is, dm=ρdV =ρπr2dx The potential energy of the mass dm is calculated as, dU=(dm)gx dU=gρπr2xdx Integrate the above equation on both sides. U=gρπr2
20
∫
6
xdx Substitute the given values in the above equation. U=10×103×3.14×(2.5)2[
202
2
−
62
2
] =104×3.14×(2.5)2×182 =35.71×106J The time taken by the pump is calculated as, time=