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The pressure increase with depth has nothing to do with compressibility nor molecular level physics.
It is simply the total weight of the fluid column above you that increases with depth. Take a water column from Earth, put it on Mars, and on the bottom you will have less pressure, due to the lower surface gravity, hence weight of the column.
The ...
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You are treating Liquids like Ideal gases and that is where the whole problem is arising. While analyzing ideal gases, we ignore the effect of gravity and variation of pressure with height, but in liquids, the effect of variation of pressure with height, due to the effect of gravity cannot be ignored.
Now if we take into account the effect of gravity then ...
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It implies that the average molecular kinetic energy of molecules at
depths will be greater than the average molecular kinetic energy at
the shallow water. Is it true? I do not find any literature confirming
this idea, so I need a confirmation on it.
The increase in water pressure with depth is due to the weight of all the water above pushing down ...
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For the sake of the argument, I will start off assuming a mercury manometer. The standard equation for pressure readings obtained from a mercury manometer, which is $\Delta P = \rho g h$, usually involves a very low density material on top of the mercury, where "$h$" is the difference in height between the legs of the manometer. When a material is used ...
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Please share more detail on what is the "extra space" between fluids. There is none in the picture.
No. For a pressure gauge only vertical (in case of normal gravity) pipe length matters. For instance, the setup in the picture could be really far from the main pipe and every equation holds. I also doubt that if you rotate the gauge 90 degrees to vertical it ...
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