It would be interesting to make a barrel without a forcing cone and choke so that the shell case would fit the chamber more like a rifle and the shot charge could enter the barrel unimpeded.
They did that, called it a Chamberless gun, they did though normally have a choke.
M/Lers had no forcing cone & most were cylinder bore. They, of course, did not use a case. They both shot extremely well.
Bore area is proportional to the Square of their diameters, therefore the 12 ga bore has about 40% more area than the 20 & about 75% more than a 28. If you fire for instance an ounce of shot out of each @ 1200 fps, you have indeed applied the same amount of Work. The Pressure to move the load to that level will though be 75% more for the 28 & 40% more for the 20 than for the 12, all figures in PSI or pounds per square inch. PSI is what deforms the shot, NOT total work.
Note also this pressure is NOT meaning the peak pressure but the total pressure applied. Even if by use of a slower burn powder we bring the Peak pressure of the smaller gauge down to a similar level to the 12, that pressure will be maintained for a longer period of time.
"IF" we were talking Static pressure then the applied time would be meaningless, but for the milleseconds involved here it does in fact become meaningful.
