Density of Water: Is It the Same Everywhere?

[Gh778]

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)

 

[Borek]

Gravitation & compressibility make it quite unlikely, although it depends how exact is your "exactly", as water compressibility is quite low.

 

[Gh778]

exactly is exactly the same value, precision at 1e-3000 if necessary

 

[Borek]

Then the answer is "no".