How Fast Does Air Escape from a Pressurized Suit into Space?

[Carlos PdL SdT]

I have a weird question here. At what speed does air flow from a pressurized container at one atm into vacuum (rupture in ISS for example).
I was watching the Martian and I wanted to see how much deltaV Mark Wattney can get by puncturing his suit, so I did my homework and saw that the spacesuit held two liters of liquid nitrogen and one liter of liquid oxigen (about 2.6kg total propellant mass). The mass of a person with a spacesuit is 100kg as estimated by NASA in the bok, so I only needed to know the specific impulse, or the exit velocity. I applied Bernoulli and came to an answer of about 400m/s which is way more than Mach 0.3 so Bernoulli doesn't work.
How do I get the air escape speed if it is above Mach 0.3?

 

[boneh3ad]

It depends on what the internal pressure and temperature are. In most cases, the flow will also be choked (it will always be choked if the external pressure is vacuum), so it will be moving exactly Mach 1.

Are you at all familiar with compressible flows?

 

[Carlos PdL SdT]

It depends on what the internal pressure and temperature are. In most cases, the flow will also be choked (it will always be choked if the external pressure is vacuum), so it will be moving exactly Mach 1.

Are you at all familiar with compressible flows?

Not much. Till now I've only seen incompressible flow in class. But then I guess I'd only have to plug in sqrt(1'4*R*T) and make a relation between T and the amount of air that remains within the suit. Or assume it's always the same which is easier to do.

 

[boneh3ad]

It will be a poor approximation if you assume the amount of air is not changing in the suit. The air will be escaping fairly rapidly and the suit doesn't have that much volume. I'd suggest doing a Google search for choked flow (though I am not a huge fan of the Wikipedia entry, the NASA article on it is pretty good). That will hopefully give you a sense of what you are dealing with here. You can then probably move on from there to calculate the mass flow rate and/or velocity or whatever else you need. Just keep in mind that the temperature is going to change as the flow accelerates so you have to account for that.

 

[Carlos PdL SdT]

It will be a poor approximation if you assume the amount of air is not changing in the suit. The air will be escaping fairly rapidly and the suit doesn't have that much volume. I'd suggest doing a Google search for choked flow (though I am not a huge fan of the Wikipedia entry, the NASA article on it is pretty good). That will hopefully give you a sense of what you are dealing with here. You can then probably move on from there to calculate the mass flow rate and/or velocity or whatever else you need. Just keep in mind that the temperature is going to change as the flow accelerates so you have to account for that.

Thank you again, but as I understand it in this specific case where the air is held in separate tanks I could assume a constant pressure and temperature. It'd change however if I used my first example of a hole in the ISS. Anyway I looked at the NASA site and I feel like it's going to become one of my best friends for the next years