Gas Flow (Help with Physics needed)

[IKE]

Fluid dynamics is generally a 2nd or 3rd year ME course which many find difficult. The real difficulty in what you are asking is that the volumes, transitions, and connections are extremely important to get an accurate answer. While your desire for 10% accuracy may seem relatively low, many fluid dynamics problems using values from test data will only claim to get you within 30% or so.

Check out introduction to fluid dynamics by Fox and MacDonald. They have a ton of great examples in that book and you may find one that will work well for you. If the pressure differential is relatively low, you could probably use something like bernoulli equations of "incompressible" fluid theory (even though it is clearly compressed). If it is relatively high pressure differential, then you would need to use a completely different set of equation.