How does it work?
Initially, the [4] waste valve is open, the [5] delivery valve is closed. The water in the [1] drive pipe starts to flow under the force of gravity and picks up speed and kinetic energy until it forces the waste valve closed. The momentum of the water flow in the supply pipe against the now closed waste valve causes a water hammer, raises the pressure in the pump and opens the delivery valve [5], so some water flows into the delivery pipe [3]. Since this water is being forced uphill through the delivery pipe farther than it is falling downhill from the source, the flow slows down and when it reverses the delivery check valve closes and the waste valve reopens, allowing the process to begin again.
A pressure vessel [6] containing air cushions the hydraulic pressure shock when the waste valve closes, and it also improves the pumping efficiency by allowing a more constant flow through the delivery pipe. Although, in theory, the pump could work without it, the efficiency would drop drastically and the pump would be subject to extraordinary stresses which would shorten its life considerably. This air is under pressure and is gradually dissolved in the water, so to maintain this cushion a small inlet below the delivery valve automatically draws in a bubble of air with each pump cycle. (Source; Wikipedia)