A water pump that consumes 2 kW of electric power when operating is claimed to take in water from a lake and pump it to a pool whose free surface is 30 m above the free surface of the lake at a rate of 50 L/s. Determine if this claim is reasonable.

Question

Alivia Hobbs

Physics

11 April, 23:27

A water pump that consumes 2 kW of electric power when operating is claimed to take in water from a lake and pump it to a pool whose free surface is 30 m above the free surface of the lake at a rate of 50 L/s. Determine if this claim is reasonable.

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Answers (1)

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Fernando Fleming · Answer 1

This claim is not reasonable.

Explanation:

In order to calculate the power required by the pump assuming 100% efficiency we use formula:

P = Qρgh

where,

P = power

Q = volume flow rate = 50 L/s = 0.05 m³/s

ρ = density of water = 1000 kg/m³

g = 9.8 m/s²

h = height = 30 m

Therefore,

P = (0.05 m³/s) (1000 kg/m³) (9.8 m/s²) (30 m)

P = 14700 W = 14.7 KW

Since, the power required by the the pump in case of 100% efficiency is 14.7 KW. It must require more power than this in actual, because the efficiency can never be 100%, due to losses.

Therefore, this claim is not at all reasonable, that the pump of 2 KW can perform this task.