Question: Consider a turbine extracting energy from a penstock in a dam, as in the figure. For turbulent flow (Chap. 6) the friction head loss is

Consider a turbine extracting energy from a penstock in a dam, as in the figure. For turbulent flow (Chap. 6) the friction head loss is hf = CQ2, where the constant C depends upon penstock dimensions and water physical properties. Show that, for a given penstock and river flow Q, the maximum turbine power possible is Pmax = 2ρgHQ/3 and occurs when Q = (H/3C)1/2.

Consider a turbine extracting energy

Turbine

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