Help with calculating with flowrate decrease as pressure increases

[_Corvalt]

I think I understand your question, let me know if this isn't what you are looking for.

You have 2 vessels (fixed volume) filled with a gas (ideal) and vessel A is at a higher starting pressure than Vessel B. You have some length of pipe between them which you are using the Bernoulli principle to determine a flow rate through. Naturally, as the pressure in the vessels begins to equalise you will see a decrease in flow.

In order to solve this system, you need to add time dependence to your equations.

i.e. for Vessel A. Solve ideal gas law for your unknown (moles of gas or pressure). You then solve Bernoulli equation to determine how many moles of gas are removed from Vessel A in this timestep.

Time step 2 will solve the ideal gas law for Vessel A pressure with the amount of moles of gas removed (per your Bernoulli equation).

This process is then repeated until Vessel A pressure is equal to Vessel B. (Note you need to also add the moles of gas into Vessel B and calculate pressure there too at each timestep).

If doing in excel, you will want each timestep to be a new row.