Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be 0.03 m3/s, determine mechanical power that is converted to thermal energy during this process due to frictional effects.

Question

Physics

Gary

8 May, 05:20

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be 0.03 m3/s, determine mechanical power that is converted to thermal energy during this process due to frictional effects.

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Answers (1)

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Jonathan Hanna · Answer 1

6.5 kW

Explanation:

Input power = 20 kW = 20000 W

h = 45 m

Volume flow per second = 0.03 m^3 / s

mass flow per second = volume flow per second x density of water

= 0.03 x 1000 = 30 kg/s

Output power = m g h / t = 30 x 10 x 45 = 13500 W

Power converted in form of heat = Input power - Output power

= 20000 - 13500 = 6500 W = 6.5 kW

Thus, mechanical power converted into heat is 6.5 kW.