Fermenter Vent Problem

[Winemaker]

Hello, I work at a winery and I am trying to solve a complicated problem and would really appreciate some help. The question is what is the smallest diameter of vent pipe that can be used, that will allow all of the CO2 continually being produced in a fermentation to escape without building any pressure in the tank. I know from experience that a two foot man-way is more than enough to vent it, but a pin-hole would surely cause the tank to build pressure and bulge. I want to solve this so we can plumb the exhaust from our fermenters, while minimizing capital costs.
Here are the specs:
154,000gal tank
Temp: 100F (311K)
CO2 is being produced at a rate of 1,538.4mol CO2/hr or 39.26 m³ /hr @311K
Psi inside of tank cannot exceed 1, preferably 0
Atmospheric pressure at the outlet of the pipe is standard.
All materials are stainless steel.
Assume that the effects of gravity and bends in the pipe are negligible.
I would like to be able to learn how to solve this for varying lengths of the pipe.

Any help on this would be greatly appreciated, let me know if there are any missing variables I can fill in or if I am under/over thinking it. Thank you!

 

[stapel]

Hello, I work at a winery and I am trying to solve a complicated problem and would really appreciate some help. The question is what is the smallest diameter of vent pipe that can be used, that will allow all of the CO2 continually being produced in a fermentation to escape without building any pressure in the tank. I know from experience that a two foot man-way is more than enough to vent it, but a pin-hole would surely cause the tank to build pressure and bulge. I want to solve this so we can plumb the exhaust from our fermenters, while minimizing capital costs.
Here are the specs:
154,000gal tank
Temp: 100F (311K)
CO2 is being produced at a rate of 1,538.4mol CO2/hr or 39.26 m³ /hr @311K
Psi inside of tank cannot exceed 1, preferably 0
Atmospheric pressure at the outlet of the pipe is standard.
All materials are stainless steel.
Assume that the effects of gravity and bends in the pipe are negligible.
I would like to be able to learn how to solve this for varying lengths of the pipe.

Any help on this would be greatly appreciated, let me know if there are any missing variables I can fill in or if I am under/over thinking it. Thank you!

Is the CO₂ being produced at a continuous rate, or (which seems more reasonable) does it vary? What formula(s) have you been given for this exercise? Also, how do you account for the fact that CO₂ is heavier than "normal" atmosphere, so it tends to sink? (We can help you with the math, but you'll need to provide whatever are the math- or physics-class simplifications, or else the industry-specific parameters and formulae.) Thank you!