Density of Water: Is It the Same Everywhere?

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The density of water is not exactly the same everywhere in a disk of water, particularly in scenarios influenced by gravity and external conditions. In the first case, on Earth, gravitational forces create slight variations in density due to the disk's size and the presence of gas. In the second case, in space, while compressibility is low, gravitational effects still lead to density differences. The precision of "exactly" is critical; if it requires extreme accuracy, the answer remains "no." Therefore, variations in density are expected under both conditions.
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I would like to know if density is exactly the same everywhere in a disk full of water except at one part where there is gas. All are fixed: disk of water, and container of gas. I don't want the value of density just to know if density is exactly the same everywhere in disk of water. 2 cases:

a/ disk is put on Earth, gravity is perpendiculary to the screen, diameter of disk is 10 km (theoretical study and I suppose gravity from Earth perfect)

b/ disk is in space, it's size is 10000 km of diameter (all is fixed by external theoretical system)
 

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Gravitation & compressibility make it quite unlikely, although it depends how exact is your "exactly", as water compressibility is quite low.
 
exactly is exactly the same value, precision at 1e-3000 if necessary
 
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Then the answer is "no".
 
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