Dear MoverZ
You say
Since velocity is not directly addressed in the equations given, the formulas in API RP 520 used to calculate reaction forces can give incredible results.
Well, I cannot blame the API formulas. Maybe the people applying API formulas.
API formulas are based on "free jet" approach.
If a free jet is released in atmosphere or in a large volume, the piping system will receive a reactive force.
This is the force that API counts as:
Reactive_Force= [mass flow-rate]*[jet_velocity]+ [p_jet]*[area_jet]
where
- mass flow rate must be the actual value (it is greater than the designed flow rate, because the actual PSV orifice is larger than minimum required!)
- jet_velocity is the critical speed when the jet gas flow has Mach=1 feature (is counted in Fluid Mechanics as jet_velocity= sqrt(2*R*k*T/ ((k+1)*M)), where notations are as in API, R is the universal perfect-gas constant , in SI is R=8314.5 J/kg mol/K.
- p_jet is the gauge pressure in the released jet
- area_jet is the internal area of piping at the point where the jet is released
This is exactly the API formula, where the numerical coefficient is sqrt(2*R), in SI units sqrt(2*8314.5)=129
Obviously, the formula is based on the "choked" condition i.e. Mach=1 and this is taken into consideration by counting jet_velocity= sqrt(2*R*k*T/ ((k+1)*M)
A possible source of errors may be the term [p_jet]*[area_jet], because it seems that "p" in chocked flow is somehow out of common engineering perception and API does not give details on the subject.
I reattach a paper showing a simple way to evaluate pressure in isentropic choked flow (Mach=1). You can see the same result in some articles, but the fluid mechanics model is more complicated there.
My best regards.