The impulse resulting from launching the bullet is simply velocity times mass. Pressure and barrel time have no bearing on operating the action. (We are talking strictly recoil operated actions here.)
There is a minor complication in that the cartridge impulse includes both the bullet impulse and the powder impulse. It's difficult to get a handle on the average muzzle velocity of the powder gas so various rules of thumb have been proposed. The one I've been using for the Luger has the average gas muzzle velocity at 1.5 times the bullet velocity. Fortunately the bullet mass dominates so small errors in the gas velocity do not make a great difference.
So cartridge impulse is the bullet mass times muzzle velocity plus 1.5 times the powder mass times the muzzle velocity.
impulse = ( bullet mass + 1.5 * powder mass ) * muzzle velocity.
You have to be careful about using consistent units. The resulting number (around 0.5 lbf*s for the Luger) is the figure of merit for a particular load's ability to operate the action.
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