Columnist Dave Barry poked fun at the name \"The Grand Cities,\" adopted by Gran
ID: 2054714 • Letter: C
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 5.73 m in the amount of 2.01 106 liters each day. With a density of 1,050 kg/m3, the waste enters and leaves the pump at atmospheric pressure through pipes of equal diameter.(a) Find the output power of the lift station.
(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 %