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I have a passing interest in water desalination projects. One of the challenges of desalination is simply moving the water from the ocean to the desalination plant. Typically the plant is built above the height of sea level, possibly by tens to hundreds of meters.

Is there a highly efficient mechanical method already devised, to use the weight of the waste water returning to the ocean, to lift more supply water to the desalination plant?

Since purified water is removed by the desalination plant, the brackish return water will be slightly lower in volume than the supply, and there will be losses from viscous drag in the pipes, so there's not a huge amount of energy recovery available.

But it seems like some useful percentage of energy saving / energy recovery should be possible, using the stored potential energy of the lifted return water, to offset the energy requirements of lifting the supply water.

Dale Mahalko
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Hydroelectric dams approximate your description.

Look at the below schematic diagram of a hydroelectric power plant. As you can see, the kinetic energy of the water flow spins a turbine which powers a generator to produce electric power. That electric power can be used to (partially) power a pump to pump the water to whatever elevation is required.

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Mowzer
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You can construct two elevator shafts with the cables connected via a pulley. If you fill one elevator with with processed water to go down and fill the other one with fresh sea water, then you just need a small electric engine to offset the weight difference. This will be as efficient as you can get it in terms of wasted energy. But the capital costs and the low throughput make it rather unpractical.

You may find this a contrived example, but the losses of viscous drag that you mention yourself can be reduced to an arbitrarily low value by choosing a sufficiently large pipe diameter. It will cost a lot, though.

So, you need to specify what the capital cost is allowed to be for a given throughput.