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> Hang on a sec, you're assuming that the water is smoothly accelerating at 9.81ms^2 for the entire 2km way down.

No, that's the raw potential energy calculation.

For power, you use the basic relationship that P=FV (force times velocity). The system would operate in a steady state for any given rate of power input/output, but that potential energy calculation governs how long it would take to charge/discharge.

The acceleration due to gravity only matters if you're trying to discharge all of the energy of a parcel of water on impact at the bottom (via smashing it into something). A potential energy storage system would instead want to charge and discharge close to steady state, with very little acceleration throughout.

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