I am trying to develop a method for calculting the rate of pressure loss from a small hole in a pressurized vessel full of water (small air pocket likely at top of vessel).
I've found a formula for calculting the flow rate of a liquid through a small hole (link), but I don't know how to relate this to a rate of pressure decay as it is kind of a cyclical process. As water leaves the vessel, the water pressure would decrease, thus also decreasing the flow rate. This would probably happen until surface tension stopped the leak.
My thought is that, assuming a rigid vessel, pressure would decrease as a function of the volume of water in the vessel, and the pressure and the flow rate as some sort of differential equation perhaps, but I'm not sure how to go about deriving that.
The application in question is the hydrostatic testing of plate heat exchangers. When completing unbalanced tests, water is pumped into one side of the heat exchanger and held at this pressure for a period of time. My thinking is that given a leak, the pressure should drop quite quickly thus indicating a failure. Alternatively, the rate at which the pressure drops should allow us to back calculate the rate of water leakage and maybe even hole size.
Any help or direction would be super appreciated.