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 Ht H g g P g gP gH H g A A t o c pc p o pipe surface () (( ) ) =+ ΔΔ ρ κ κρ 2 2 20 2 where 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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Single Phase 02 2 which for constant density gives dH dt v A A pipe surface =
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HW3Prob1 - Pump storage units pump water from a lower to...

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