What??????????? When a PSV opens to atmosphere with the vessel at 400 psig or 1000 psig (note, you always do PSV calcs in gauge pressure because you are actually doing a dP calculation and P
upstream gauge+P
atm-P
atm=P
upstream gauge) you have sonic velocity through a known orifice size. Perfectly well defined parameter, simply a function of gas composition and temperature. Same speed of sound for all upstream pressures greater then critical pressure (which is about P
atm / 0.6). The mass flow rate is a function of velocity and density upstream of the PSV so you would have a different mass flow rate for every upstream pressure.
The API 521 calculation assumes that you know the required mass flow rate to keep your vessel from exceeding MAWP plus allowable build up pressure (for other than the fire case allowable build up is to 110% of MAWP). If you already have a PSV in place and you are trying to find the flow rate, it is a trivial bit of Algebra to solve the API 521 equation for mass flow rate and you have all of the unknowns in the new equation.
If you are asking about the required flow rate, read API 521 a bit more carefully. It says that you need to investigate the credible scenarios and determine the inflow rate from your system for each credible scenario. Then pick the scenario with the largest inflow rate as the required PSV flow rate. Plug that into the API 521 equation and get the required orifice size.
David Simpson, PE
MuleShoe Engineering
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