Steady state model for a pressurized vessle

[meccard]

I am trying to figure out the relationship between the air pressure inside of an inflated bladder and the diameter of the outlet with a fixed inlet flow rate.

The inlet is fed by a blower which is delivering 600 scfm to the system through a 4" diameter inlet. The bladder is large, it is 120,000 ft^3. I'd like to be able to determine the effect that the cross sectional area of the outlet has on the pressure inside the bladder. The outlet is simply a hole in the bladder with air flow going directly to the atmosphere. The pressure inside is low 2-4 inH2O. I would also like to be able to model the pressure rise over time up to a stead state point?

 

[hunt_mat]

Does the bladder expand and contract? Because if it does then your going to require a constitutive law for the material the bladder is made out of.