Everyone here seems to be missing 1 very important factor, and a possibly important second factor.
The first, and likely insignificant factor is that air in this situation may not behave as an ideal gas. The temperature and pressure ranges are too wide to be sure that the air won't exhibit some deviation from the accepted ideal gas laws. It probably will, but it would be worth checking. I don't have the proper reference material here to check.
The more important factor: You are most likely dealing with flow approaching supersonic speeds. This will cause the fluid to behave far differently than an incompressible fluid. (Yes, for most fluids, even gases, you can use incompressible assumption; compressibility for flow is usually a function of Mach, although heat transfer during the flow can affect this a great deal.) I don't have the time (or the info handy) to do the calcs, but I bet you will have choked flow for at least part of the time, where the Mach number stays at 1 at the tightest constriction (Mach 1 = speed of sound, and speed of sound goes up with pressure (usually), so constant Mach number is not constant speed) Once you hit choked flow, increasing the pressure gradient were have
far less effect on the flow that when in unchoked flow.
I just have to resist the urge to measure my tank valve and calculate this out.
Must...fight...the...geekiness