HW3Prob1 - Pump storage units pump water from a lower to...

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Single Phase 02 1 Pump 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 t H g g P g g P g H H g A A t o c p c p o pipe surface ( ) ( ( ) ) = + Δ Δ ρ κ κρ κ κ 2 2 2 0 2 where κ = + K overall 1 . For the given initial conditions determine the time required to raise the level in the upper reservoir one foot. Air 80 ft 200 ft Pump Atmosphere 60 ft 100 ft H o Problem Data Pump Δ P 100 psia Pipe Diameter 6 ft Upper Reservoir Surface Area 4.356 x 10 7 ft 2 Overall loss coefficient (including friction) 6 Fluid Temperature 60 F Solution A mass balance on the upper reservoir gives dM dt m = ±
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