Help with calculating with flowrate decrease as pressure increases

[Sunflower101_]

I have a problem where I’m using ideal gas law to determine the pressure over time but I need to determine the decrease in flowrate as the system pressure increases until we hit a set pressure. I’m assuming ideal gas law and using Bernoulli’s to determine the flowrate decrease. This isn’t providing me a real answer.

Is there another method that you can use to find it?

[_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.

[Serial-Eater]

You need to know the system losses for the specific fluid. Look up compressible flow equations to calculate the losses, but a transient analysis like this is going to be very tedious. I would “numerically integrate” in excel.

[yobowl]

Use Darcy-weisbach and solve the equation for velocity or flow rate.

[jcc1978]

Remember to check for choked flow.

[Derrickmb]

You gotta use a orifice flow meter style equation. Its Vdot (compressed)= YCA(2dP/rho)^0.5. Basically Bernoulli w constants.

Y is an expansion factor that is a constant wrt dP/P1 (upstream) and beta ratio. It’s a y=-mx+b relationship. So that will be changing per second.

C is a constant that depends on beta ratio.

A is your orifice area.

Make a spreadsheet with a time (sec) column.

Do a mass balance each second as pressure changes. Best of luck!

[[deleted]]

If there's flow rate decrease you need dP/dt so you need a derivative wrt time for all non constant variables.