Sorry, I havent read the thread but I have had a cap come off and flap around on its retaining chain. The fuel being sucked out the tank was very obvious and I guess I lost around a quarter of a tank in around 20 minutes or so. I recall landing at RAF Lyneham, stopping on the runway (with permission), hoping out, replacing the cap, and then being asked if I wanted to back track – I reckon I used rather less of the runway that remained to continue on my way.
The video has resurfaced on the internet. It just shows the filler caps flying off at the moment of rotation (one slightly later I think – didn’t look closely). They were just loosely sitting in position, and didn’t have any retaining cord or chain.
So it looks like the pressure differential across the wing was what pulled out the filler caps.
What pulls out the fuel I have no idea but the pressure differential looks like a good candidate – small though it must be. I doubt it is more than a few % of the absolute pressure, because anything more would rip off the upper wing skin.
I have had an occasion where fuel vented out past old O rings on the cap on my Bonanza. Made a big mess and fuel loss was quick.
Try to suck the content out of an upright bottle without a straw…
I can say without any doubt what so ever that with the cap off, the stream of fuel departing the wing is very very evident!
So, we are still looking for the physics behind this 
In a Piper with storm window, or a DA40, if you close the vents and set the static circuit to “Alternate Static”, IOW cabin pressure, what happens to your altimeter and why? If you further open the storm window, what happens to the altimeter, and why?
Now you all have an excuse to go flying.
If one cap comes off that tank will have less internal pressure than the tank on the other side…IF the fuel selector has a Both position, fuel will transfer to the top-less tank and be siphoned out…
Or if the tank in question has a bladder it will be collapsed and squeeze the fuel out…
Otherwise the fuel loss will be due to sloshing (and thus limited to maybe a quarter of a tank) as described in the previous thread on the subject…
I am not sure if I have posted this earlier in this thread but this thing acutally happened to me.
I took off with a Cessna 206 with one of the fuel caps off. This was a skydiving operation, about 2-3 minutes into the flight they started shouting to me that there was fuel leaking from the wing on to the stabilizer. We went back for landing, I put the fuel cap on(attached to a chain thank god), refueled and we went back up again.
I meant to post this in a more timely fashion, (it came up at the Cambridge dinner last year), but I forgot.
I think we can exclude evaporation as a major factor if a fuel cap is left off.
Looking at this document
Fig 22 shows the specific heat of AvGas to be 2.25 kJ/kgK at 20 deg C
Fig 27 (extrapolated) shows the Heat of Vaporisation as 390 kJ/kg at 20 deg C
So as a “thought experiment” let us assume one third of the fuel somehow manages to evaporate quickly at 20 degrees C, which means there is only time for the heat of evaporation to come from the remaining two thirds of the fuel.
The temperature drop would 390 / (2 × 2.25) = 86 deg C, which is ridiculous – all evaporation would have stopped well before :-)
