OH MIGHTY UNCA CECIL!
I posted this a few years back, & the question decended into quibbling, with no good, convincing answer.
So now, I submit it to you, Oh Font Of Universal Wisdom and Part-Time Yo-Yo Demonstrator.
To whit: If I am washing out a glass bottle or narrow-mouthed jar, what is the best way to dry it?
Upside down, for the water to trickle out?
Or, right side up, and let evaporation work?
Towels just leave traces of moisture.
Which way does it dry the fastest?
This is very good.
This is a first world question that merits a precise answer.
As a corollary;
Which method is the fastest to dry shirts on a clothes line?
The collar (and sleeves) at the top or collar hanging at the bottom?
Clearly upside down if there is an appreciable amount of water that could drain out instead of that water sitting at the bottom when it’s right side up. Things dry faster when you remove the bulk of the water, after that is when evaporation begins to matter.
It would seem that upside down on a table would be not as good for evaporation, because the opening would be blocked.
So, it might be the best of both methods to place it upside down, but either
You don’t really get the best of both worlds. Evaporation is going to work better with the hole at the top, because moist air is less dense than dry air.
I would think @TriPolar’s strategy is best - invert for a few minutes until any substantial bulk of water has drained out, then turn it right-way-up for evaporation to take care of the rest.
FWIW, for my French press coffee pot, when I leave it to dry overnight in a dish rack upside down, there is sometimes a drop or two of water on the bottom, unless angled where the drops are more likely to run to and down the side. When emptied and put rightside up on the counter, it’s dry by morning, so I’ll go with evaporation.
My wife dries everything right-side up. I see them drying that way and flip them over.
Not because of speed, but due to the hard-water residue that results if any significant amount of water evaporates…
I’m in a hard water area, if I tried the evaporation method you’d see white marks where the droplets had sat.
If I need to dry out something quick I invert it over the cold air return duct on my heater/AC. The little water left drips down and evaporates and the turbulence in the air flow dries out said something.
Lucky you! Coincidentally I have been researching this for the past few weeks.
My finding shows to achieve the best drying is to invert the bottle in a rack for just several minutes after washing so it can drain.
C. Stand it small opening up. By morning it generally is dry inside and out. Sometimes I have noticed they were even thoroughly dry by late evening.
Whenever I left the bottles inverted, they would still be wet inside the next morning.
I dry wine bottles on a tree, upside down.
Brewers I can understand but why would one need to dry 90 wine bottles at once?
This seems counterintuitive to me. Can you provide an explanation?
When I make a six gallon carboy of wine, I prefer to bottle and age it. I have an Italian floor corker. One of my nephews makes a carboy of wine for parties and dispenses it directly form the carboy. Six gallons of fresh wine is too much IMO.
Ah. New wine in old bottles, then. Classic. 
Actually, even if you use brand new bottles you need to sanitize them before use.
First, the same volume of any gas at a given temperature and pressure has the same number of molecules.
Avogadro's law - Wikipedia
So when water vapor becomes part of the gas mixture its mass is not added, it’s better to think of it as displacing a proportion of the other gases.
Atomic masses are
O=16
N=14
H=1
So water molecules (H2O=18) are significantly lighter than nitrogen (N2=28) and oxygen (O2=32) molecules.
Ah, yes, partial pressures.
So, is this important for the drying-out process? That is, is convection significant?
The molecular mass of water, 18, is much less than nitrogen, 28, and oxygen, 32, the main constituents of air.
Sorry, i failed to see the earlier reply.