joists

The hood duct needs to run through kitchen ceiling and vent out in a wall (not roof). My joists are 2 x 8 with the ceiling drywall dating back to the 1950s. What is the max duct diameter I can install in my joists space? Is there any clearance (air gap) consideration between the pipe and joists...

I know there are a ton of threads about this, but I can't seem to find one that fits my situation. The 2x10 floor joists supporting my bathroom span 15' at 16" o.c.. I doubled them up to reduce deflection for tile - glued and screwed them together. I rerouted my toilet and ran 3" pipe across 4...