In-Depth Pascal's Law Explanation

[Von Neumann]

Problem:

The general idea makes sense intuitively to me, but most sources I've found cite Pascal's Law merely as scientific fact with not much explanation. What I'm wondering is why pressure applied at one point in a fluid is transmitted undiminished to all other points? Is it a concept due to the inherent properties of fluids that I must simply accept?

 

[haruspex]

Could probably derive it from conservation of energy and incompressibility of the fluid. Consider two pistons located within the fluid. The difference between work done expanding one and allowing the other to shrink by the same volume must be balanced by the net change in PE of the fluid.

 

[rude man]

If p were not the same in all directions then a particle would be accelerated in some direction, which doesn't happen.

 

[haruspex]

If p were not the same in all directions then a particle would be accelerated in some direction, which doesn't happen.

I don't think that was the question. It's to do with pressures at different locations, not different directions.

 

[rude man]

I don't think that was the question. It's to do with pressures at different locations, not different directions.

Oh yes? "Pascal's law or the principle of transmission of fluid-pressure is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure ratio (initial difference) remains the same.[1"
-wikipedia, italics mine.

If I go deeper I go to a different location where the pressure is not the same, is it ...