# Calculate Gas Behavior Step-by-Step in Simple Model

• Innovine
In summary, @user wants help calculating rates of change of temperatures and pressures in a gas flow simulation. @user also asks for help understanding a flow rate equation. @user is unfamiliar with differential equations and digital simulation, but would like to try and fake it. @user asks for help specifying the valve/orifice and when that is done, what would be the pressure 1 second later.
JBA said:
That depends upon the size of the hole you drill.
I mentioned the hole size of 0.001m^2 in posts #28, #30 AND #32.

JBA said:
Once again "the reason the user is venting the gas determines whether the flow should be in seconds
No, the reason the user does anything is irrelevant, the nozzle parameters and pressure determines the flow.

JBA said:
if you give me more information about how you are applying your venting program then maybe I can give you a better approximation of an appropriate venting time for that application
.. oh so the PROGRAM I use now determines the venting time??
You are just inventing problems now. If you go all the way back to post #1, you will see I am asking for simplifications, and you constantly drag up new unknowns and new fact1ors. If you would like to help, in an effective way, I suggest you try looking at what I am asking, and try and provide the relevant info, and only the relevant info. Too much information is NOT helpful, it is the exact opposite.To clarify, please answer the following... If I have a 1m^3 tank of O2, pressurized to at 273K, and there is a circular hole, with area 0.001m^2, which is uncorked by a player who intends to empty the tank to atmospheric pressure via said hole, simulated in Unity, for a game which does not require rapid reaction times from the player, and the weather in Shanghai is 30C, humid, and partially overcast, how long to the nearest 10s of seconds does it take for the tank pressure to fall to atmosphere (to within 1000Pa of atmosphere).

Last edited:
It is not the program that selects the flow rate or venting time, it is how you want the venting to interact with the program that determines the flow rate; and, if you don't have any target parameters for that, then just pick one of your above choices because your guess is as good as mine. I am not trying to make things more difficult, it is that without an application goal I have no basis for selecting any orifice size.

As for the orifice coefficient, once you have an orifice size; then, if the flow rate through that orifice size is greater than that you want, you can use the orifice coefficient decimal value below 1.00 to reduce (fine tune) the flow to your desired flow rate; but, if the flow rate for your selected orifice size is less that you want; then, you will need to either increase the orifice size to give exactly your desired rate or increase the orifice size to give just above your desired flow rate and use the orifice coefficient to reduce (fine tune) the flow rate to what you want. It is not that you can't use a coefficient greater than 1.00 to increase your nozzle's flow rate but to do so violates the proper use of the coefficient because that implies your manufactured orifice can flow at a rate greater than the ideal gas laws calculated value and that cannot happen with real life nozzles.

Understood. Did you have a version of the formula with discharge coefficient, for non-choked flows?

And out of morbid curiosity, how complex do things get if I wanted to include heat, in a very, very, very approximate way?

The nozzle coefficient for a nozzle is the same for both critical and subsonic (non-critical) flow; because, it addresses the physical properties of a nozzle such as nozzle entrance shape, bore diameter tolerance variations, nozzle bore surface finish, etc. and not flow properties.

If you have included the temperature adjustment we discussed to reduce the temperature decline rate to a rate that is less than the isentropic P vs T ideal gas law predicts your are already approximating the warming effect due to heat transfer into the tank from the surrounding ambient air and only the below process or a instrumented P vs T test blowdown on an actual tank can result in an accurate determination of an actual tank gas T vs P decline rate.

Just so you understand why I suggest you limit your method to the above, anything beyond that is going to require a full analysis of the heat transfer based upon based upon your tank size and configuration, the tank wall material heat transfer coefficient, area and thickness and the heat transfer coefficient for, assuming your tank is a horizontal cylinder, "an unforced convection flow of air around a horizontal cylinder" and the ΔT between the temperature of the gas inside the tank vs. the air outside the tank. The problem is made even more difficult by the fact that the temperature of the gas inside the tank is constantly reducing by expansion cooling relative to the outside air and, as a result, the ΔT is continuously increasing but at a substantially lower rate than the ideal gas laws predict. Ultimately what comes from this is just a same T vs P as the above original method but with a more accurate T vs P for one specific tank size and configuration.

I was considering sending you the tank cooling rate graph for the depressurization T vs P from my previous project test, but that test is based on a stepped pressure reduction process that took 1 hour to complete, and it was then that I realized that another factor involved in the gas temperature decline during venting is the rate of depressurization of the tank. The tank's gas cooling rate will be exactly equal to the tank depressurization rate; but, the increase in heat transfer rate into the tank from the surrounding air is limited; so, for rapid depressurizations due to high gas venting rates, the heat input from the surrounding air will not be able to proportionally rise with the rapid gas cooling rate.
It is similar to the what happens when a chilled container is removed from a refrigerator freezer, first condensation and then ice forms on its surface and then slowly melts. It is possible to determine this effect by a detailed heat transfer analysis; but, apart from that, I have no idea how to estimate that gas cooling rate variable.

Ok, thanks. I have T constant for the moment. It looks like my valve simulation is working, I can see the mass move, and the pressure stabilizes to the same values in two linked tanks, taking longer to stabilize as the pressure differental decreases. No idea if its realistic or not, but neither will anyone else so that's mission accomplished for now!
Next up is mixed gasses, and then maybe I'll look into temperature :)

Congratulations on a well earned accomplishment when starting with very little knowledge of the subject!

Innovine
Thanks for helping me out and putting up with my frustrations!

JBA
I should have also included your unfailing determination to find a solution in my above post statement.

Innovine

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