I have this homework on how a Heron's fountain works. The exact assigment is as follows: "Construct a Heron's fountain and explain what (which variables) influences the height of the fountain."
I've already constructed it and it works well, but I'm not so sure about the second part of the problem.
I understand that the water is making a fountain due to the increased pressure in the "bottle b" (see picture) which pushes the water up through the tube d. I also understand that the air is getting to the bottle b via tube e, because the air itself in "bottle c" is being pushed by the water that is coming down from "bottle a" (tube f).
But in the end I totally confused myself: so what does the pressure in bottle b depend on? Is it the hydrostatic force? Am I even asking the right question? I got into a loop and I need to get out of it, help me please!
The Attempt at a Solution
I suggest from these equations that the height of the heron's fountain directly depends on pressure in "bottle b" and that the relevant parameters are V (volume of the liquid) ρ (viscosity of the liquid) and Δh (difference in heights - the length of a tube connecting "bottle a" and "bottle c".
But I'm not very sure of anything right now, I would be very glad if someone gets me onto the right track.