Columnist Dave Barry poked fun at the name \"The Grand Cities\" adopted by Grand
ID: 1968736 • 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 their next municipal building for him. At the Dave Barry Lift Station No. 16, untreated sewage is raised vertically by 5.49 m, at the rate of 1 890 000 liters each day. The waste, of density 1 050 kg/m3, enters and leaves the pump at atmospheric pressure, through pipes of equal diameter.(a) Find the output mechanical power of the lift station.
(b) Assume an electric motor continuously operating with average power 5.55 kW runs the pump. Find its efficiency (as a number between 0 and 1).
Explanation / Answer
Given that Volume of sewage = 1 890000*10-3m3 Height of sewage h = 5.49 m Density of waste = 1050 kg/m3 Time taken = 1 day = 24hrs = 24*60*60 s = 86400s----------------------------------------------------------------------------------------------- work done = mgh = Vgh = 1050* 1 890 000*10-3*9.8* 5.49
= 106770069 J
(a) Power = W/t
= 106770069/86400
=1235.76 W
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(b) power delivered = 1235.76W
Actual power of pump = 5.85 kW = 5850W
Therefore efficiency = power delivered/actual power of pump
= 1235.76 W/5850W
= 0.2112 or 21.12% Time taken = 1 day = 24hrs = 24*60*60 s = 86400s
Time taken = 1 day = 24hrs = 24*60*60 s = 86400s
----------------------------------------------------------------------------------------------- work done = mgh = Vgh = 1050* 1 890 000*10-3*9.8* 5.49
= 106770069 J
(a) Power = W/t
= 106770069/86400
=1235.76 W
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(b) power delivered = 1235.76W
Actual power of pump = 5.85 kW = 5850W
Therefore efficiency = power delivered/actual power of pump
= 1235.76 W/5850W
= 0.2112 or 21.12%