My answer to the original question is an over-simplification in that it does not address the fact that pressure is not constant but diminishes with time and space, so it will vary with powders of different burn rates. If pressure could be kept constant in magnitude and duration (not the case with internal ballistics), a lower pressure would be required in a 12-gauge barrel than in a 20-gauge barrel to accelerate the same mass (1 ounce) to the same velocity (1150 fps).
The consideration of duration of the applied force explains how slower burning powders like Longshot produce higher velocity with lower peak pressure.
Still, I think that Pascal's law (Force = Pressure x Area) explains, at least in part, why SAAMI specifications allow higher pressure in the smaller gauges.
Disclaimer: I do not hold a degree in engineering or physics, but I did enjoy my introductory physics class, and I occasionally sleep in a Holiday Inn, although not last night.
