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Ok, my colleague and I are having a debate that we need help with. Neither one of us works in this space (chemist and materials scientist) and we understand this should be pretty straight forward intro physics or fluid dynamics, but we are struggling to convince each other that one of us is right.

Here is the scenario, three identical tanks of the same volume with the same volume of liquid initially in them. Tank A has a single hole (size d) that is centered, Tank B has two holes each of which are the same (size d), separated by some distance X1. Tank C has two of the same sized holes, but now they are separated by a smaller distance X2 (X1 > X2).

In the current state, the height of the water isn’t high enough for gravity to overcome the surface tension and pull the liquid through the holes. If we keep adding water to the Tanks, one of us contends that water will begin flowing at three different heights for each tank, while the other contends that water will penetrate all the holes at the same height for all three scenarios. Can someone provide some insight? If you have an equation or a reference you can point out that would be great. Cheers. enter image description here

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  • $\begingroup$ Interesting question. I'm not even sure if more holes should make it easier for the water to flow out (which seems intuitively logical), or harder (since fixed pressure from the water depth is now resisted by multiple regions of surface tension, instead of just one). $\endgroup$
    – Nuclear Hoagie
    Commented May 26, 2020 at 17:22

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Since the holes are identical, the surface tension at each hole will be the same, which means that the net upward pressure due to surface tension at each hole will be the same, and equal to the pressure due to the height of water. Hence the number of holes makes no difference to the height of water. Also, pressure depends only on height of water, not on position.

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The pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity.

It is the column of water over the holes ,

The fluid pressure at a given depth does not depend upon the total mass or total volume of the liquid.

So as the holes are identical, they will behave identically as the pressure is increased by increasing the volume of water. So "water will penetrate all the holes at the same height for all three scenarios".

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