Wall thickness

Hi, Just wondering if there is a rule for wall thickness?
I heard about a rule of thirds where the walls must be at least the bore diameter- 1/3wall: 1/3 bore: 1/3 wall, but I can't find a reference for that.

Attached is a sketch of an original 19thC barrel (cast iron). I'm hoping to make an exact copy in bronze. Do you think the bore size should be reduced a little?
It's 36" overall, 2" bore.
Thanks