Dear all,

Anindya has sent me two articles about the subject. They are valuable, no doubt. However, the author has developed a quite complex system – eight equations, all based on the assumptions of perfect fluid in steady-state, adiabatic, frictionless and isentropic flow.

If the goal is to evaluate the choked sonic speed and choked fluid pressure, a serious simplification can be applied. There is a p_choked formula that supplements API formula being developed in the same way as that leading to the choked sonic speed expression. I have no idea why API does not detail the reaction force formula with p_choked expression.

I attach my interpretation. The result is identical with the articles’ conclusion and is- in fact- exactly what Anindya has posted previously.
So my contribution was just to simplify everything to "one page" presentation. In addition it is not subject to copyright.

This discussion is not about where the choked flow and reaction force may appear. The formulas are evaluating the sonic speed and choked pressure in isentropic choked flow section- they are not showing where is that point.
About this aspect, I think the reaction force must be count just where there is "the free jet" effect- at the end of open discharge piping and in that point there is a "choked" flow in many cases.
It may be a long discussion about this aspect- anyway is what I am thinking.

The formulas are not counting friction effects.
Are interesting also the remarks I found in the articles "As mentioned before, the relief valve body has a very complex geometry. This complex geometry causes the relieving fluid to have a complex flow pattern. The fluid must change direction several times and there are certainly some frictional effects within the relief valve body. However, by making these assumptions, analytical expressions can be developed and these expressions yield interesting information and valuable insight about a rather complex problem. More complicated methods can certainly be utilized to analyze the body of the relief valve. However, these added complexities will certainly require a more detailed description of the geometry within the relief valve body and will almost certainly require numerical methods for computations."

I second this interpretation, the formulas are just what we can do analytically and this fluid mechanics model is just one possible. The fact API has accepted this way is encouraging.

Thank you, Anindya for your help.

Best regards.