With all pressure boundaries the mass flow becomes part of the solution. Given the density is also varying we get a fairly nasty problem in a numerical sense. Ie if density alters because of local pressure, the flow velocity changes as does the mass flow: which variable is the one to mess with to get the defined pressure drop.
What you plan is OK, but be aware of the potential for a stiff solution. Nozzles tend to be OK, but adding in shocks can complicate things. If you have LDA so know the velocity, can you use a velocity inlet then compare the pressure drops?
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