Trompes are very simple devices. A vertical pipe or shaft goes down to a separation chamber, a pipe coming away from that chamber allows the water to exit at a lower level, and another pipe coming from the chamber allows the compressed air to exit as needed.
Water rushing down the vertical pipe falls through a constriction. The constriction produces a lower pressure because of the venturi effect, and an external port allows air to be sucked in. The air forms bubbles in the pipe. As the bubbles go down the pipe they are pressurized proportionally to the hydraulic head, which is the height of the column of water in the pipe. The compressed air rises to the top of the separation chamber. The separation chamber has a compressed-air takeoff pipe, and the compressed air can be used as a power source.
The energy of the falling water entrains the air into the water. The air is compressed by surrounding water pressure (which increases under a column due to the discharge to atmospheric pressure). The pressure of the air delivered cannot exceed the hydraulic head of the discharge pipe of the separation chamber.
Large trompes were often situated at high waterfalls so that ample head was available. (However, trompes can raise the water, via siphon-effect, nearly to 70% of its initial elevation.) The Ragged Chute plant on the Montreal River near the town of Cobalt, Ontario, is a trompe and tourist attraction. It is now owned by Canadian Hydro and exists beside a modern hydroelectric plant.
Compressed air from a trompe is at the temperature of the water, and its partial pressure of water vapor is that of the dewpoint of the water's temperature. If the water is cool, the compressed air can be made very dry by passing it through pipes that are warmer than the water. Often, ordinary outside air can warm the pipes enough to produce dry, cool compressed air.
Today, trompes constructed of plastic pipe are being used to provide aeration for mine drainage treatment. In this application, mine water is used to drive the trompe and the compressed air that is generated is used to oxygenate the mine water and to drive off excess dissolved carbon dioxide that may be present thus raising the pH of the water being treated.
https://en.wikipedia.org/wiki/Trompe