By the end of August, I intend to build a working Hero's Fountain. I made my first attempt the other day. It didn't work, but I identified a number of ways I can improve it for my next attempt. Below is the test apparatus. It uses a plastic bowl and two milk jugs for the water vessels. The nozzles are pieces of copper tubing and are attached with plumber's epoxy. The hoses are simple nylon (I think? The material for that isn't really important.) tubing and are attached to the nozzles with twist ties.
The first mistake was using the plumber's epoxy. I used it because it's simple and fast and I'd seen it used successfully in a similar application before. Unfortunately, after I was half done attaching the nozzles I saw the instructions said it's not recommended for use with polyethylene, which is what milk jugs are made of. As you can see, the epoxy didn't bond with the milk jugs, which broke the air seal. This is most visible on the leftmost nozzle in the picture above. Beyond that first failure the rest is more speculative. My apparatus has both lower chambers at the same height, which means the water has a long way to rise from the blue topped milk jug to go through the fountain spout at the top. The air moving between the pink chamber and the blue chamber will rise much easier, so I believe raising the blue chamber to shorten this distance will improve performance. Also, it takes a substantial amount of water to fill the tubes between the chambers, at least compared to the amount of water in the red bowl. Priming the tubes with water would probably improve performance, but hopefully that will prove unnecessary. Finally, as the water drained from the red bowl I didn't consider that it would form a vortex. That pushes some air down the tube as well as water. I don't think that's a problem, in fact it might make the machine run a little longer, but it's something I will pay attention to in my next attempt.