Consider that a static pressure vessel has no recoil. Gas pressure must create momentum to create recoil. Free recoil is completely described by conservation of momentum. Gas pressure creates momentum only in a flow situation. In the case of a gun, the flow is due to increasing volume within the barrel. Momentum can't be found from pressure. Pressure, in and of itself tells you nothing about a dynamic process.
It is easy to visualize the pressure of the powder gas pressing back on the breech and causing recoil. It is also wrong. If the barrel were plugged at the front of the chamber, firing would produce no recoil (if the gun held together). The barrels are locked onto the action and constitute a pressure vessel, but one that has expanding volume.
Momentum of the ejecta is matched by the rearward velocity and mass of the gun. Momentum is transmitted from the barrel/action to the stock and to the shooter. Pressure influences recoil only as it influences momentum of the ejecta.
Free recoil momentum of the gun an d ejecta total momentum are equal.
DDA
