Drew;
My knowledge of this is somewhat limited, but my understanding is that Barlow's formula is for high Pressure tubing under a constant load. Firing a shotgun does not produce that constant load, but only very briefly reaches its peak pressure. It is my understanding it takes a considerably higher pressure to bulge or burst a barrel than that indicated by Barlow's formula. This is what I was hoping some of our engineering Friends would chime in on, as to just what formula is most applicable for this purpose.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra