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Question

What is the power required by the pump to lift 1000 kg of water per minute from a 20 m deep well and eject it with the speed of 20 m/s?

A
3666.7 W
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B
4666.7 W
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C
6666.7 W
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D
5666.7 W
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Solution

The correct option is C 6666.7 W
Given:
Depth of well, h=20 m
Speed of water, v=20 m/s
Mass of water lifted per minute, m=1000 kg
We know that, power
P=ΔEΔt ...............(1)
where ΔE is change in mechanical energy and Δt is time taken
Now, change in mechanical energy,
ΔE=mgh+12mv2
ΔE=1000×10×20+12×1000×202
ΔE=4×105 J .............(2)
Also,
Time taken,
Δt=1 minute [ given ]
Δt=60 s ...........(3)
On putting (2) and (3) in (1)
P=4×10560=6666.7 W
Hence option (c) is correct.

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