I am having difficulty understanding how to set up a model. The first goal is to find the pressure with respect to time of the outlet, which is unknown.

Initial conditions are as follows:

Transient boundary conditions (dependency) of each of these parameters at the inlet are known, and unknown at the outlet.

It is known that the gas at the outlet is considered high mach number flow.

Does anyone have any suggestions/experience with this sort of situation?

Thanks in advance for any help.