This subject was discussed in
Unfortunately that thread got a bit messy with some irrelevant side-issues causing a bit of bickering and hair-splitting.
Basically the situation is that the diameter of the column and the size of the pot are determined by different factors, so there is no fixed ratio between them.
The column diameter is mainly determined by the vapor velocity up the column. In a small R&D column of around 2" diameter the vapor velocity will be in the region of 6 to 10 inches per second, but on a large vodka column of say 10 ft diameter you can get vapor velocities of 6 to 10 feet per second. So the column diameter is determined by the rate at which you want to run.
In a pot still the pot size is determined by the heating method and the size of the batch you are working with. Let us imagine your fermenters produce 100 gallons per batch. You will probably want a pot of around 150 gallons to be able to boil this safely. If you want to process this in 12 hours you will need a column roughly double the diameter (4 x the area) than if you want to process it in 48 hours. And of course you need to put heat into the pot at 4x the rate for the 12 hour scenario.
Distillers generally want to be able to process a batch in 8 to 12 hours (one shift) so it turns out that in practice there is an approximately consistent ratio between the pot size and the column diameter (or more correctly the column cross sectional area) but this is a coincidence - as explained above there are different drivers in determining the pot and column sizes.