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Question: A 30 m deep well is having water up to 15 m. An engine evacuates it in one hour. The power of the en...

A 30 m deep well is having water up to 15 m. An engine evacuates it in one hour. The power of the engine, if the diameter of the well is 4 m is:

A

11.55 kW

B

1155 kW

C

23.10 kW

D

2310 kW

Answer

11.55 kW

Explanation

Solution

Mass of water, m = volume ×density =

πr2l×ρ=π(2)2×15×1000kg\pi r^{2}l \times \rho = \pi(2)^{2} \times 15 \times 1000kg

h=30+152=22.5mh = \frac{30 + 15}{2} = 22.5m

p=Wt=mght=π(2)2×15×1000×9.8×22.53600p = \frac{W}{t} = \frac{mgh}{t} = \frac{\pi(2)^{2} \times 15 \times 1000 \times 9.8 \times 22.5}{3600}

=11.55 KW