I read about heron's fountain recently and it got me thinking about liquid and air pressure and things like that.
And it led me to the following idea:

enter image description here

Basically what is happening here is that there is a container with water and oil.
Oil will float to the top as it is less dense than water.
At the bottom left there is some more oil and the gray circle is a one-way valve.

So my question is:

What will happen if I add a bit more oil at point A?

Would the oil go through the valve at the bottom and then flow up through the water and eventually overflow at the top and do this continuously forever once there is enough oil in the system, without more oil being added at A?
Or do I need some kind of external interference for the one-way valve to work ?

I suspect the valve might require pressure on one side to be more than the other side or something like that.
If that is the case, would it make a difference if I made the area on the left larger than the area on the right and kept adding oil at point A until the pressure from the oil on the left is large enough to force oil through the valve?

Update 1:
I understand that volume or amount of liquid is not important and it's all related to the height, thanks to Azzinoth for pointing that out.

Would it then make a difference at all if the height on the right is divided into different sections so the height on the left is more than the height of any of the sections on the right, or would it add up?
I am thinking the pressure from the oil on the left will push the oil into the first container on the bottom right through a one-way valve. And with enough pressure, into the second container, and the third and so on.
Or would the pressure of all three containers on the right add up and equal or exceed to pressure of the oil on the left?
Below is a diagram of what I mean: enter image description here


1 Answer 1


The valve will only open if the pressure in the left column is higher than in the right column. This only happens if fluid level in left column is higher than right column, because oil is lighter. Also the shape or base area does not matter for pressure. Pressure only depends on fluid density and height. See hydrostatic paradox.

  • $\begingroup$ Would it make any difference then if the outlet of the valve at the bottom is contained in another smaller area that has another one-way valve to the bigger area? Then, the amount of oil on the left will be more than the amount of water in the first container on the right and could then let oil in ?? Or would the pressure from both water areas add up? $\endgroup$
    – Quintonn
    Dec 24, 2020 at 12:03
  • $\begingroup$ @Quintonn The amount of oil or water does not matter, only the height. Again, look up the hydrostatic paradox. $\endgroup$
    – Azzinoth
    Dec 24, 2020 at 14:48
  • $\begingroup$ Yes I understood. What I'm asking is that instead of 2 even height containers on the left and right as in my picture above, I have 1 container on the left, and 3 containers on the right each 1 third the height of the one on the left, separated with a one way valve. If all the containers on the right are empty, the pressure on the left should be enough to fill up the first 2 containers on the right. Will it be able to fill up the 3rd container also by forcing more liquid through the valves and even more. My logic is that the valves prevent the containers higher contributing to the "height" $\endgroup$
    – Quintonn
    Dec 26, 2020 at 9:30
  • $\begingroup$ I don't understand how you can come to that conclusion. Maybe you are confusing one way valves with pumps? One way valves don't force anything, they are passive components. I believe your example will not work. But maybe without pictures I misunderstand your intention. Anyways, if you have problems understanding herons fountain, then I suggest you try to calculate the pressure at every point along the path in herons fountain and then think about which way the fluid must move at every point. $\endgroup$
    – Azzinoth
    Dec 26, 2020 at 9:52
  • $\begingroup$ I've added an updated image with the different containers. I hope it clarifies my previous question. Does the height stack up even through one way valves ? $\endgroup$
    – Quintonn
    Dec 27, 2020 at 12:23

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