Granted, this chart assumes the Tank is just standing there taking the abuse. Still, a Steam user found that 10 frying pan hits kill a Tank in nine seconds, compared to 30 blasts from a combat shotgun in 26 seconds.
The forum user, Urik, found that It's not just the frying pan, any melee weapon is a 10-hit kill on a Tank, expert difficulty. You can go all honky-tonk man on him with 10 whacks from the git-tar if you like, which sounds even more absurd (and less durable) than the cookware. I've never done this, probably would never try to do it except as a last resort. I'm betting Tanky-poo, in actuality, makes it take longer than 9 seconds, though.
Left 4 Dead 2: Weapon Effectiveness vs Tank [Hellforge]