Columnist Dave Barry poked fun at the name \"The Grand Cities,\" adopted by Gran
ID: 1285818 • 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 5.41 m in the amount of 1.97 106 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.
__________ kW
(b) Assume that a continuously operating electric motor with average power 5.90 kW runs the pump. Find its efficiency.
____________ %
Explanation / Answer
(a) use the relation:
Power = Work / Time
Get the amount of work done in 1 day by calculating how much mass is lifted by the given height. Use the formula:
work = mass * g * height, where g = 9.8 m/s^2.
The mass is obtained by multiply volume x density.
Once you have calculated the work, divide it by the amount of time it takes to do this work, namely 1 day, in order to get the power. Note that you must convert "1 day" into seconds, in order to express the power in W or kW.
(b) Divide the answer to (a) by motor's average power of 5.90 kW. Multiply that answer by 100% in order to convert the number to a percentage.