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Here's how the hydraulic ram pump actually works, step-by-step:

(1) Water (blue
arrows)
starts flowing through the drive pipe and out of the "waste" valve (#4),
which is open initially. Water flows faster and faster through the pipe
and out of the valve.
(2) At some point, water is moving so quickly through the brass swing
check "waste" valve (#4) that it grabs the swing check's flapper,
pulling it up and slamming it shut. The water in the pipe is moving
quickly and doesn't want to stop. All that water weight and momentum is
stopped, though, by the valve slamming shut. That makes a high pressure
spike (red
arrows)
at the closed valve. The high pressure spike forces some water (blue
arrows)
through the spring check valve (#5) and into the pressure chamber. This
increases the pressure in that chamber slightly. The pressure "spike"
the pipe has nowhere else to go, so it begins moving away from the waste
valve and back up the pipe (red
arrows).
It actually generates a very small velocity *backward* in the pipe.

(3) As the pressure wave or spike (red
arrows)
moves back up the pipe, it creates a lower pressure situation (green
arrows)
at the waste valve. The spring-loaded check valve (#5) closes as the
pressure drops, retaining the pressure in the pressure chamber.

(4) At some point this pressure (green
arrows)
becomes low enough that the flapper in the waste valve (#4) falls back
down, opening the waste valve again.

(5) Most of the water hammer high pressure shock wave (red
arrows)
will release at the drive pipe inlet, which is open to the source water
body. Some small portion may travel back down the drive pipe,
but in any case after the shock wave has released, pressure begins to
build again at the waste valve (#4) simply due to the elevation of the
source water above the ram, and water begins to flow toward the
hydraulic ram again.
(6) Water begins to flow out of the waste valve (#4), and the process
starts over once again.
Click here to view the video of a Ram Pump
in action
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