A hydroelectric power station is generating 200MW of electrical power. The water falls a distance of 80m between the lake level behind the dam and the river level below the dam,
Calculate the rate(in cubic metres per second) at which water is flowing through the power station. Assume 100% efficiency.
Please help me solve this fluid mechcanics problem!!!?
2009-06-07 10:04 pm
回答 (1)
2009-06-08 4:19 am
✔ 最佳答案
The power output of the plant is given as P=200MW.The density d of water is d = 1g/cm^3 = 1kg/l.
The force of gravity is g = 9.8m/s^2.
So the work w done per 1m^3 of water falling through 80m under the force of gravity is
w = (1 kg/l)*(1000 l/m^3)*(9.8m/s^2)*(80m)
= 1000*9.8*80 (kg*m^2/s^2)/m^3 = 7.84*10^5 J/m^3.
If r is the rate of flow in m^3/s, then
rw = P = 200MW = 200*10^6 J/s, so
r = P/w = (200*10^6 J/s)/(7.84*10^5 J/m^3)
= 255.1 m^3/s.
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