Air Cannon Physics: Pot. Energy & Barrel Depth

[physicsisrad]

Homework Statement

Hey guys, I'm currently working on an air cannon for my physics assignment. We are attempting to determine the effects of chamber pressure, barrel length and the depth of the projectile into the barrel on the muzzle velocity of the fired object. Now I'm not asking for a solution, but I am struggling to find the relevant equations that I require in order to do some pre-testing calculations. If somebody could help me out in regards to the equation for the potential energy held by a volume of compressed air and also if somebody could offer some background theory in regards to the depth of the object into the barrel this would also be appreciated.
Cheers,
physicsisrad

Homework Equations

The Attempt at a Solution

 

[Coto]

Why not deal with this problem using pressures? In particular, the pressure of the air inside the barrel versus the pressure outside the barrel (atmospheric). This will determine the amount of force the air will exert on the object, dependent upon of course the objects exposed surface area.