Isothermal Expansion of Water/Moving Boundary
I've been wondering how water reacts in a closed, rigid system with one moving boundary. Assuming the system is perfectly filled with water, and one side of the boundary moves (increasing the volume), how does this affect the pressure in the system?
Since water is incompressible, I would think that moving one boundary would dramatically increase the pressure on the other boundaries within the container (since the water attempts to maintain its original volume). However, I don't get how to modify the formulas for Bulk Modulus to prove this is true.
I want to create a water-filled probe that rests on the skin and then move a boundary of that probe to raise the skin. In my mind, this should act much like a reverse hydraulic lift, forcing the skin to lift as the other boundary is drawn away. However, I don't know this with certainty and I don't get how to show this relation in exact, quantitative terms. I would appreciate any help that could be provided in modelling this system to be as realistic as possible.
Thanks for your help!