# Expansion of a gas in Airbag System.

## Homework Statement

Hello, this is my first post. First of all, excuse my English, its not my native language :).

Im trying to solve a problem for college (I study mechanical engineering, but posted it here since its a physics problem).
I modelized an airbag system as following: A pressure vessel with a compressed gas inside, directly connected to a nylon bag. I took some data from a real pressure vessel from an used airbag.
It says that it uses Argon, the volume of the vessel is 0,5 liters (or around that). The vessel also says that the gas inside is a 350 bar, but I cant use that as a given, I need that pressure to be a result for the objective of the project, that is calculating the tensions in the vessel and specify a welding procedure. The bag has a volume of 50 liters and the final pressure before the person impacts on it, I take it to be 4 bar.
Now, doing some research I found more data: The expansion of the bag has to be in under 0,080 seconds, and it inflates at say, 300 km/h.

The problem is that I dont know how to begin. I take it to be an adiabatic expantion, because of the short time it takes to expand.
So when I use the formula:

P'V'^gamma = P''V''^gamma, with

P' unknown initial pressure in the vessel, V'=0,5 liters , P''= 4 bar, V'' = 50,5 liters, gamma = 1,67 for argon.
P' = 8897,6 bar !!, not even close to the 350 bar it is in reality.

As for the expantion velocity I dont know how to start, since I cant use Bernoullis equation because argon is not uncompressible.

Remember, I can change the variables to some extend, as long as its reasonable, because the problem is not designing an actual airbag but specifying a welding procedure for the pressure vessel.

All help is greatly appreciated :)