I would just assume the loss of fuel (actual or imagined) to be part of POH numbers 
If we do the maths it is the ratio of the hole surface to fuel surface should appear somewhere in the “hydraulic transmitted force”, regid tanks will do the rest…
I’ve just noticed this. I suspect that the low pressure on the upper surface of the wing is a bit of a red herring.
The lift force is generated over the whole wing area to counteract the aircraft’s weight. Fuel fillers are not large in comparison. A back of the fag packet calculation for my aircraft shows a (very rough and over simplified) figure of about 0.1 kg. Lifting liquids by vacuum / lower air pressure is not easy at all unless you have effectively the straw in the drink itself as it’s always easier to extract air in preference to the liquid.
Given a rigid fuel tank I strongly suspect that the biggest factor in fuel loss is fuel sloshing and perturbations to the liquid caused by movements in the aircraft.
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 :-)
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.
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…
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.
So, we are still looking for the physics behind this
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!
Try to suck the content out of an upright bottle without a straw…
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.
