A hydroelectric power plant draws water from a lake who surface is 55 m above the turbines. It draws the water through pipe with radius 1.2 m. (Patm = 100 kPa, ρwater = 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 m s -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 turbines?
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).