With a six gallon pot you won't be doing full boils, right?
I don't think your pot diameter has too much to do with it. Well, not at the level we're talking here. Yes, there's evaporation rate to worry about potentially, but that's too advanced. At least for me.
Here's a snippet I found on BTUs:(not my words)
Here is a simple way to see how many BTUs you need for your pot size. Water density is 8.3 lb/gal. To raise 1 gallon of water (1 x 8.3 = 8.3 lbs) from 70 to 212 deg F in 1 hour you will need 8.3 x 142 = 1,178.6 BTUs.
Using this BTU requirement for each gallon of water you can figure out how many BTUs would be required to boil your pot of water in one hour. For example a 30 quart pot (7.5 gallons) (full) would require 7.5 X 1,178.6 BTUs = 8,839.5 BTUs to bring the pot to a boil in one hour, assuming 100% efficiency.