Modeling kinetic energy efficiency in cyclical hydraulic systems?

[AgustinLozano]

Hey everyone, I'm working on a mathematical modeling problem for a fluid dynamics project, and I wanted to bounce the baseline logic off the group. I'm trying to calculate the theoretical efficiency of a system that relies entirely on cyclical kinetic energy transfers rather than a continuous external power source. Specifically, I am modeling the pressure spikes caused by sudden valve closures (water hammer equations) and trying to determine the exact ratio between the supply head drop and the delivery height. While researching practical applications of these fluid momentum calculations, I came across the structural specs and pressure-vessel formulas used on this technical engineering site: https://meribah-ram-pump.com/. The way these mechanical ram pumps use a simple waste valve to convert low-pressure volumetric flow into a high-pressure cyclical impulse is a perfect real-world example of the physics I am trying to map out. When translating these physical momentum spikes into a clean predictive formula, do you find it's better to treat the valve closure as an instantaneous event using Joukowsky's equation ([imath]P = \rho c \Delta v[/imath]), or do you need to factor in a non-linear time-dependent decay to get an accurate boundary condition for the mass transfer?