Control Valve Liquid Application Calcs for FL, dP_ch & Pvc

[centaur21]

Maybe I'm missing something but I've gone round and round trying to come up with a way to solve the three (3) equations below.

Let's say I calculate Pvc (pressure at vena contracta, psia) using the formula Pvc = FF * Pv. That's ok but when you insert Pvc into the FL (Liquid Pressure recovery factor) equation, you're still missing the ∆P value because in this case, the ∆P in the FL equation is the ∆P choked value (∆Pch) and not just ∆P (i.e. P1 - P2) which puts me at a dead end.

I realize that control valve manufacturers provide the FL and from there you can solve the other equations, but is the only way to solve for all three equations below is to be given the value for one of the three equations? For these equations, the FL value would have to be the one provided. I would greatly appreciate any input on this question. Thanks!

 

[SPDL310]

Yes the most accurate way to solve those equations is to use the FL value given by the valve manufacturer. The manufacturer determines the FL through physical testing in their validation stage. If the manufacturer doesn't publish an FL value you can use one of the typical FL values from ISA-75.01 based on the type of valve.