Great, sounds like we are indeed getting somewhere. As you've said, A_inner,internal = A_inner,external is the key requirement for it to work using the original syphon system. Unfortunately that means that the walls of the inner container need to have zero thickness - impossible.


However, I did a quick check and actually it's not as bad as it looks. An old margarine container or something similar as the inner container gives you a wall thickness under 0.5mm. Say A_inner,internal = 100x100mm = 10,000mm². Then A_inner,external is 10,100.25mm² (assuming 0.5mm wall thickness). The resulting equation looks like:
Code:
h_print = V_transfer * 0.000001 + h_constant
If you transfer 1L of water between the containers (V_transfer = 100*100*100 = 1000,000mm³) then the print height changes by a whole 1mm. In the mean time, the bottom of the container has fallen 100mm, so you've printed a 100mm high object. The focus change with a 1mm change in height isn't worth worrying about.




The new idea is intruiging. I hadn't thought about using different density water in the containers. I think that'll definitely work, although getting the right densities could be rather painful (measuring density to high accuracy is difficult if you can't measure volume perfectly).

For avoiding waves from the droplets, maybe what you need is a sort of Z-bend near the end of the pipe. That way, if a drop is falling freely down the middle of the pipe, it now gets attached to the wall and slides down there at a reasonably low speed.