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After studying the artist's conception drawing, it appears non, or poorly functional. The drain F must start at the bottom of tank D and be higher than the input to the stack E. The input to the stack E must be such that it extends below the water level, yet as pressure builds becomes uncovered so pressurized air can enter the stack G. The way it is drawn would work if the tube F is bent up so the output is much higher.
That causes an oscillatory action that puts slugs of air and water into the stack G, allowing the pressure to push the water out. If the output of F is lower, as drawn, the water, air , and pressure would just flow out the bottom.
I suppose there could be a precise restriction in pipe F, potentially adding precision, complexity, and adjustment to the more simpler approach.
https://en.m.wikipedia.org/wiki/Trompe
It appears as if the first two images in that Wikipedia page have the same flaw. The third, for the Taylor Hydraulic Trompe, is most likely correct. It certainly shows everything better.

- Tayler Trompe
- Taylor_trompe_sketch.svg.png (99.33 KiB) Viewed 630 times
The height of the riser shaft should dictate how much air pressure can be built up in the blast pipe, or how high the water can be pushed. Maybe. Height may also be related to the slugs of water verses slugs of air in the 'stack' G. Probably.
The blowoff pipe is the pulser pump, but designed to maximize air pressure.
The operating head plus the maximum flow would dictate the horse power available.
Apparently the action of the blowoff pipe can be quite dramatic on larger Trompes.
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