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232. assignment (hydroelectric power)

14.7 A hydroelectric power plant draws water from a lake whose surface is 55 m above the turbines. It draws the water through pipe with radius 1.2 m. (Patm = 100 kPa, ro-water = 1000 kg m^-3)

 (a) If, at point A, 55 m below the surface of the lake, the pipe is horizontal and the water is flowing through it at a rate of 9 m s^-1, at what pressure is the water?

(Hint: compare this point to the surface of the lake using Bernoulli's Law.

(b) In order for the turbines to work most efficiently the water should enter them at a speed of 20 ms^-1. In order to achieve this the pipe narrows to what radius just before it enters the turbines?

(c) What is the pressure just before the water enters the tur-bines?

(d) After passing through the turbines the water is now open to the atmosphere again. At what speed is it traveling (assuming that only a negligible fraction of the energy contained in the flow is removed by the turbines).

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