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Consider an imaginary cube of liquid as shown in the figure.

Figure 1

Why should all the forces on the cube be same? The cube can be stationary even if the forces on parallel, opposite vertical sides are equal and opposite in direction. The cube can be arbitrarily small or large.

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Based on the answer by Steeven, I just want to consider a similar hypothetical experiment of that sort. Imagine a container with rigid, smooth balls. If I apply pressure $P$ on all the sides of this container, will I get this much amount of increased pressure on the upper and lower sides? I think that more the spheres are small and more in number, the more pronounced the above-mentioned effect will be seen.(This is my guess)

Apoorv Potnis
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1 Answers1

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The cube can be stationary even if the forces on parallel, opposite sides are equal and opposite in direction

Yes, if we were talking about cubic boxes stacked on top of each other. But consider fluid molecules as spheres. A top/bottom pressure will make it squeeze out sideways because they never are perfectly aligned. This is in fact what defines a fluid in contrast to a solid - that it spontaneously takes the shape of its container.

When they are squeezed out sideways, there must be a sideways force holding them back. Depending on how they are stacked, the sideways force will be bigger or smaller than the top/bottom forces. Imagine spheres on top of each other. The more they are displaced from a symmetry line (the smaller the angle of the centre--to centre line), the more do they tend to sliding further down from each other and the sideways force must be larger to hold them in place.

On average, the sideways pressure in all directions averages out to equal to the top/bottom pressure.

Steeven
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  • I want to consider a similar hypothetical experiment of this sort. Imagine a container with rigid, smooth balls. If I apply pressure $P$ on all the sides of this container, will I get this much amount of increased pressure on the upper and lower sides? I think that more the spheres are small and more in number, the more pronounced the above-mentioned effect will be seen.(This is my guess) – Apoorv Potnis Oct 31 '17 at 17:18
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    @ApoorvPotnis This is an old comment that I never came about to reply to, I can see. Nevertheless, let me reply now: Yes, if you apply a pressure $P$ from all sides, then also the pressure on the upper and lower sides will be $P$. Otherwise you wouldn't have had to apply pressure $P$. There can be differences, though, due to gravitational forces but that might only be relevant for larger bodies of liquid. And yes, the idealised sphere-shaped molecules must be small and many in order for the ideal fluid behaviour of taking the shape of the container to always happen as expected. – Steeven Jun 08 '21 at 07:35