Time till the air pressure is gone

[zach_wildmind]

Hello, I have a 8 gram cartridge of N2O meant for kitchens. Long story short from what I understand it has 10 cm cube of N2O inside. I also know it has 900 psi / 60 bar of pressure inside. The cylinder is exactly like this image.

I am trying to find out how much time it would take if I puncture a hole of 1 mm (millimeter) in the bottom to be completely empty. Basically I am trying to find a way to calculate the time needed for the cyclinder to be empty. Any help is appreciated.

Thank you!

 

[mfb]

Order of magnitude estimate: A 60 bar = 6 MJ/m³ pressure difference can accelerate something with 100 kg/m^(3) (your gas inside) with 60 kJ/kg, enough to make it reach close to the speed of sound where this approximation becomes bad. Anyway, at that speed you have an initial loss of 350 m/s * 1mm² = 350,000 mm³/s = 350 cm³/s. As some gas escapes pressure and temperature inside drop, slowing the escape, but the timescale is still fractions of a second. After a second or two your interior pressure will be nearly identical to the exterior pressure. You still have N2O inside, probably quite cold now. As it warms up to room temperature again a bit more of it will escape. Over much longer timescales random air motion and diffusion will let air in and the remaining N2O out.

 

[zach_wildmind]

wow, that helped a lot. Given the speeds I can now approximate the time. Thank you

 

[boneh3ad]

This can be solved analytically with some relatively simple and well-justified assumptions.

I'll also note that your numbers don't seem to add up. If you have 8 g of N₂O occupying 10 cm³, then that implies its density is 800 kg/m³. At the same time, if you take the initial pressure you gave and assume room temperature, then the ideal gas law would imply that the density is only 115 kg/m³.

 

[DaveC426913]

If you have 8 g of N₂O

Is that 8g of gas, or 8g of cylinder?
No. it must be gas only. The cylinder will weigh considerably more than 8g.

 

[mfb]

A bit of googling suggests these containers have 8 grams of N2O with a total mass of about 30 grams.

The density of liquid N2O is 1.3 g/cm³ by the way. It becomes liquid at room temperature at ~50 bar, so maybe it has a combination of gas and liquid? Then it could take longer to empty these containers.

 

[dRic2]

I attended some lectures last year on safety/industrial accidents and this kind of even (possible outflow from a container) was studied carefully although, for the sake of simplicity, the phase was assumed to remain constant.

If you have to take into account the phase transition during the outflow, this might be a little pain to solve analytically. I would like to know how you take this scenario into account.

 

[zach_wildmind]

I attended some lectures last year on safety/industrial accidents and this kind of even (possible outflow from a container) was studied carefully although, for the sake of simplicity, the phase was assumed to remain constant.

If you have to take into account the phase transition during the outflow, this might be a little pain to solve analytically. I would like to know how you take this scenario into account.

I will simply assume that remains constant as all I need is an approximation of time. Thank you very much!

 

[cjl]

This can be solved analytically with some relatively simple and well-justified assumptions.

I'll also note that your numbers don't seem to add up. If you have 8 g of N₂O occupying 10 cm³, then that implies its density is 800 kg/m³. At the same time, if you take the initial pressure you gave and assume room temperature, then the ideal gas law would imply that the density is only 115 kg/m³.

The seeming discrepancy here is solved because pressurized containers of N2O are a liquid below 97F (if above about 700-1000 psi, depending on temperature - the critical point is about 1000psi at 97F), so the ideal gas law does not apply.