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This type of pump can be used to pump flowing falling water from a lower height to a higher height using only the potential energy in the water. It uses two concepts, a Class 2 Lever, and a Tipping Bucket. The bellows has a cross-sectional area of about 14 inches^2. As configured in the video the ratio of the lever is about 3.5:1 meaning every pound of force on the end of the lever produces 3.5 pounds of force on the air spring bellows which generates .25psi of pressure. A full 5 gallon bucket of water would compress the water to 10.25psi or about 23ft (No these numbers don't match the video)
There are many variable to adjust to achieve different performance profiles. Lever Ratio, Bucket Volume, and Bellows Diameter are the main ones that can be varied to achieve the desired pumping pressure.
Pumps of a similar nature that aren't ram pumps:
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