How to calculate reservoir capacity and hydropower output?
If you aren’t at least a junior in civil engineering, your “teacher” (especially if you’re a high school student) is showing signs of sadism and needs to be spanked with a vintage Pickett Log-Log Trig-Trig slide rule. The way you phrased your question I doubt you know what a “maxima/minima” problem is, much less a “Lagrangian” Professional engineers currently do this hydropower stuff with software. If he wants “real world” answers, you have been set a series of complicated calculus problems I won’t go into deeply here, except to note that the real guys have to know the river flow in, flow out through the penstocks and turbines (a totally separate series of fluid dynamics calculations), what accumulation of water in the reservoir that gives you over time with a given dam height, efficiency of the turbine/generator set, leakage to groundwater through the reservoir walls, evaporation losses. and so on.. I’m going to assume that you’re in a high school physics honors course (or something s
