sasklimin,

Because you’ve mentioned the formulas given by Pipe Support Design and Engineering by Smith & Van Laan/ B31.1 "PSV steam case", activating this old thread, I have some remarks addressed to B31.1/ P1 and V1 expressions.

First, it is clear that B31.1/ Appendix II considers that not all stagnation enthalpy (h0) can be transformed to a state based on chocked parameters, so there is a correction as "h0-a" instead of "h0". Here I can speculate that this difference is because steam is not a "perfect gas", so to the domain of lower temperatures/ pressures we may have steam/water mixture or water and the idea is PSV can "consume" a quantity of enthalpy up to such fluid state; maybe this approach is not conservative, but I don’t need to comment it too much; just consider "h0-a" as the enthalpy that is transformed.

It is interesting that, excepting the above mentioned deviation, the B31.1 model is still based on the "perfect gas" model and there is equivalence between the "b" factor of B31.1 and "k"- the specific heat ratio (or "adiabatic index").
The corresponding formula is k=b/(b-1); I guess this info was lost from the original work (unknown for me), but this is evident checking the values of "k" versus "b" factors given in B31.1. i.e. k=11/(11-1)=1.10 for "wet steam" and k=4.33/(4.33-1)=1.30 for both saturated steam "> 90% quality" and "Superheated steam".

With these remarks, one can compare directly the results (between the paper with "perfect gas" model and B31.1 model) because (k-1)/(k+1)=1/(2b-1) appears in B31.1/"V1" expression and 1/k=(b-1)/b appears in "P1" expression.

More specific, following the paper I attached some time ago, in SI units we obtain h0-a=(1/2)*(k+1)/(k-1)*V1^2=(1/2)*(2b-1)*V1^2 that would lead to a SI correspondent of B31.1/(A.2) expression; also P1=(W/A)*(1/k)*V1 =(W/A)*((b-1)/b)*V1 i.e. you obtain the SI correspondent of (A.1) expression.

You may note that "gc" and "J" appears there because B31.1 is based on US Customary Units, while the "SI formulas" coefficients in Smith &Van Laan’s book must be "2" (from theory) instead 2.0085 and 1.995 (from units conversions). But this is a secondary remark and anyway the results are quite accurate vs. the assumptions made; more interesting is that "the perfect gas model" of "P1" pressure gets results in-line with B31.1.

What I try to say is that P=(W/A)*(1/k)*V (where P and V are characteristic to isentropic choked status) is confirmed indirectly by B31.1 and obviously it is a more general formula. In fact, this long discussion was just intended to clarify which pressure "p" must be considered as the design pressures in the end of PSV discharge piping and vent pipe, for open discharge installation; the goal is to check the reaction force there.

My best regards.