Serway & Jewett — Fluid Mechanics: Problem 21

Water falls over a dam of height \(h\) with a mass flow rate of \(I_V\), in units of kilograms per second. (a) Show that the power available from the water is \(P = I_V gh\) where \(g\) is the free-fall acceleration. (b) Each hydroelectric unit at the Grand Coulee Dam takes in water at a rate of \(8.50 \times 10^5 \text{ kg/s}\) from a height of \(87.0 \text{ m}\). The power developed by the falling water is converted to electric power with an efficiency of \(85.0\%\). How much electric power does each hydroelectric unit produce?