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Single Phase 02 1Pump storage units pump water from a lower to upper reservoir during off peak hours when electricity is cheap, to be released through hydroelectric turbines during peak demand periods. The pumped portion of such a facility is illustrated below. Assuming the lower reservoir height does not change, show that the height of the upper reservoir as a function of time is given by H tHggPggPg HHgAAtocpcpopipesurface( )(( ))=+−−−−⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪ΔΔρκκρκκ22202where κ=+Koverall1. For the given initial conditions determine the time required to raise the level in the upper reservoir one foot. Air80 ft200 ftPumpAtmosphere60 ft100 ftHoProblem DataPump ΔP 100 psia Pipe Diameter 6 ft Upper Reservoir Surface Area 4.356 x 107ft2Overall loss coefficient (including friction) 6 Fluid Temperature 60 F SolutionA mass balance on the upper reservoir gives dMdtm=±
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