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I was quite fascinated by the concept of an ancient type of air compressor, called a trompe. It entrains air bubbles into a falling stream of water via the Venturi effect, and extracts the air at a lower level where it is pressurized by the hydraulic head. More details on the Wikipedia page.

Now, the output of such a device in comparison to its size, combined with the fact that you need to have sufficient amounts of water conveniently falling down somewhere, means that this device is not competitive with air compressors we use.

However, I was wondering how it performs on the energy level, and noticed that I'm not quite sure how I should calculate that. If I take the work that the air does when decompressing as my energy output, what would be my energy input? Could I say that it's the work I need to do to overcome the buoyancy of the pressurized air at the lower level?

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