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I'll try my best to explain my question with examples because I don't have much knowledge on the theory.

So say that I had a block of water in air, a cube of water, that is dropping. If the cube wasn't too big, I believe that as it will drop, then the air from underneath it will rush to either side of it, as the water displaces the air on it's way down. diagram

Now lets change the situation. Say I had the cube of water, but now its suspended in the air in a tank (like a fish tank), as shown in the picture. Here, I believe that there is the weight force of the water acting evenly downwards, but the air pressure may be different, as the whole system is bounded by the walls. Logically, I believe that the air would then rush through the center of the water cube, forming a bubble, allowing the water to rush down to the bottom. diagram Though this may be completely wrong, I'm not sure. So my question is, is that is there any possible shape for the water to be originally in, so that all the forces sort of balance so that there is no distortions in the shape, and that then the air will be compressed under the force? I understand that perhaps at the microscopic level, if we take into account the random motion of molecules, and other factors, that there will inevitably be some sort of inbalance, but macroscopically what would be the perfect shape? I'm not even sure if any of this makes any sense. Thanks for any help understanding.

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  • $\begingroup$ The shape you are looking for is that of a water drop falling, which is aerodynamic and holds the water together. However the drop cannot be as large as desired, since friction with air will cause it to vibrate and eventually split, so it would be nice to find out what is the maximum size of the drop, that remains in that shape. $\endgroup$
    – rmhleo
    Oct 12, 2014 at 11:32
  • $\begingroup$ A recent near duplicate of this (Why should water fall down from an upside down glass of water?) has some answers, too. $\endgroup$
    – Peter Cordes
    May 29, 2021 at 5:20

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The ideal shape for the water to just 'hang' is actually the cube that you've proposed. In this case all of the forces on the water are uniform across the interface. For one region to slip down, another needs to move up (as you've indicated in your diagram). But since every location is experiencing the same forces, there's no reason any spot to start moving.

This a state of exact equilibrium, as is the inverted case where the cube of water is below the cube of are. The difference between the two is what happens when you make even the most tiny disturbance to the surface. With the water on bottom, a disturbance will naturally shrink (raise a parcel of water above the surface and gravity will pull it back down). With the water on top, any disturbance will grow (just as you've drawn).

This general problem is called the Rayleigh-Taylor instability, you can find more here: http://en.wikipedia.org/wiki/Rayleigh%E2%80%93Taylor_instability

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  • $\begingroup$ But since every location is experiencing the same forces, there's no reason any spot to start moving. - there's surface tension around the edges of the tank, so the situation isn't perfectly uniform. Even ignoring thermal vibrations and so on, an ideal fluid that "wants" to wet the sides of the surface would I think pour out around the sides. And of course once any flow starts, you get farther from the unstable equilibrium very quickly. $\endgroup$
    – Peter Cordes
    May 29, 2021 at 5:25

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