Is all more complex than poor laymen types like me can understand by just trying to extrapolate what "should" happen. So thats why I'm running a few little tests... I am interested in what actually happens - why it happens is a minor (but interesting) part of it. I'll think about theory and see what explanations I can come up with after I observe the real behavior.
First (moving straight into a contradiction of what I just said I was going to do) - the Pressure Argument. The lid I am using is a round plastic take-away container lid. It weighs 6g and has a radius of 5.5cms. convert that into pressure needed to lift it and you have about - 0.0009psi. Now using a chart I found on engineeringtoolbox.com, you need an extra 0.31psi to raise the boiling point of water from 100C to 101C. So the pressure this lid could apply at best is 3/100ths of that needed to raise the boiling point by 1 degree C. AND - in the combination of this lid and the beakers being used, you can see on the photos there is a gap left at the spout of about 1cm square. So its not even going to be that amount of pressure. This increase might be enough to visibly change the behavior of the boil, but I don't think so. And I also don't think pressure would significantly change the nature of the boil even if it were higher, it would just change the temperature at which things happen.
Second - in these experiments I took into account what Pat had mentioned about the amount of headspace and the surface to volume ratios. So I looked at my brew kettle, which is a decent example of the situations I am trying to address. ie: its a little big for my batch size and I either get too low a boil or too high an evaporation rate using it as it is.
So i worked out how much liquid in the beakers, would give the same wort depth to width (diameter) ratio as I get in my kettle. This was about 400-500 ml in the slightly more than 1L beakers. This results in wort that is about twice as wide as it is deep. I used 400-500ml as the starting volume for all the following tests. This left slightly more than 50% headspace in the beakers.
SOME STUFF ABOUT LIDS
(almost all the way on - means lid slightly ajar, perhaps 5 or 6 mm from the outside edge of the lid to the edge of the beaker)
Lid "almost" all the way on - vs - Lid 2/3rds on... adjust boil vigor
Beakers filled to 500ml, brought to hard boil and heat off. adjusted back to 500ml with boiling water from kettle. Lids on, flame back on - boil vigor adjusted visually to the same level. boil till one of the beakers hits 200ml.
Result - small but definite difference in boil vigor. Final difference in amount boiled off was a small but noticeable decrease for the beaker with the lid mostly on. On the order of 40ml
Lid 'almost' all the way on - vs - lid 2/3rds on. Equal amounts of heat applied
Beakers filled to 500ml, brought to hard boil and heat off. Adjusted back to 500ml with boiling water from the kettle. Lids on, flame back on. Beakers swapped from burner to burner every 5 minutes for a total boil time of 30 mins.
Result - Medium increase in boil vigor for beaker with lid on. Virtually no difference in amount boiled off.
Lid 'almost' all the way on - vs - No Lid at all. Equal amounts of heat applied.
Beakers filled to 500ml, brought to hard boil and heat off. Adjusted back to 500ml with boiling water from the kettle. Lid on one beaker most of the way, flame back on. Beakers swapped from burner to burner every 5 minutes for a total boil time of 30 mins.
Result - distinct increase in boil vigor in beaker with lid. Virtually no difference in amount boiled off.
Lid "fully" on - vs - No lid at all. Equal amounts of heat.
Beakers filled to 500ml, brought to hard boil and heat off. Adjusted back to 500ml with boiling water from the kettle. Lid fully on one beaker, flame back on. Beakers swapped from burner to burner every 5 minutes for a total boil time of 30 mins.
Result - A small but noticeable difference in the amount of liquid boiled off. On the order of about 25-35ml
Result summary - In all the cases but one, where the heat applied was the same, the amount of liquid lost was near enough to the same. The exception was the case where the lid was completely on, where a small decrease in boil off was observed.
There was an observable increase in boil intensity in all cases where a lid was on to any extent at all, with a larger increase where the lid was closer to being fully on.
In the case where the boil intensity was "matched", the lid being more "closed" resulted in the amount of liquid lost being reduced by an observable, but with the precision of the scale used, not very measurable amount.
Conclusions - (or speculations really) Any decrease in evaporation that might be brought about by placing a lid on a boiling vessel, will be (roughly) balanced by the increase in vaporization brought about by an increase in boil intensity when the lid is placed on the vessel. So unless an effort is made to balance the vigor of the boil in the vessel, putting a lid on will not decrease the amount of liquid lost during the boil. Although a reduction might be seen if the lid completely closes the pot, this may present other brewing problems.
If however the boil intensity in a vessel with a lid (even less than fully on) is reduced to match in intensity the boil before the lid was put on... then a reduction in the amount of liquid lost will be observed.