Columnist Dave Barry poked fun at the name \"The Grand Cities,\" adopted by Gran

Question

Columnist Dave Barry poked fun at the name "The Grand Cities," adopted by Grand Forks, North Dakota, and East Grand Forks, Minnesota. Residents of the prairie towns then named a sewage pumping station for him. Assume that at the Dave Barry Lift Station No. 16, untreated sewage is raised vertically by 5.94 m in the amount of 1.96X 10^6 liters each day. With a density of 1,050 kg/m^3, the waste enters and leaves the pump at atmospheric pressure through pipes of equal diameter.

(a) Find the output power of the lift station.
= kW

(b) Assume that a continuously operating electric motor with average power 5.90 kW runs the pump. Find its efficiency.

Explanation / Answer

Volume raised = 2.01*106 lts = 2.01*103 m3/day

Density = 1050 kg/m3

Mass = 1050*2.01*103 = 2110.5*103 kg/day

Change in PE = mgH = 2110.5*103*9.8*5.73 = 118513.017 kJ/day.

= 1.372 kW

Output power = 1.372 kW

Efficiency = output / input = 1.372/5.9 = 0.232 or, 23.2 %

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