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Se Adolf

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I have a cylinder of some dimensions. I have a compressible liquid inside. Assuming a constant temperature, no atmosphere, no convection currents within, because it is in a cylinder, there will be no variations in density horizontally (the fluid will have time to settle). Now because there is gravity, the liquid will be pulled down and because the volume of water on top increases as depth increases, the fluid will be more dense at the bottom than at the top. So I pick for example two densities: 0.5 and 1 with 0.5 at the very top of the cylinder and 1 at the very base of it. Something as follows:

https://ibb.co/DCWmTZH

https://ibb.co/DCWmTZH < Sloppy Diagram of what I mean

So my question is how can I model this? How can I get some kind of density function out of this? Please go easy on me, I don't really do physics, this is for a Mathematics investigation. Thank you in advance for help, I'm kinda desperate at this point :P.

https://ibb.co/DCWmTZH

https://ibb.co/DCWmTZH < Sloppy Diagram of what I mean

So my question is how can I model this? How can I get some kind of density function out of this? Please go easy on me, I don't really do physics, this is for a Mathematics investigation. Thank you in advance for help, I'm kinda desperate at this point :P.

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