What is the explanation of Pascal's law at molecular level?

Question

What is the molecular explanation of Pascal's law?

Let us now consider what happens when we change the pressure on a fluid contained in a vessel. Consider a horizontal cylinder with a piston and three vertical tubes at different points. The pressure in the horizontal cylinder is indicated by the height of liquid column in the vertical tubes.It is necessarily the same in all. If we push the piston, the fluid level rises in all the tubes, again reaching the same level in each one of them.

I know this follows from Pascal's law but what is happening in the liquid when piston applies force is it being compressed or sth. How does piston change the magnitudes of pressure at all points inside the liquid. What happens if the fluid is confined and not confined when pressure is applied? I only need a qualitative intuitive explanation.

I can think that the transmission of fluid is by one molecule pushing the other but after it comes back to normal so how is pressure increased overall?

Answer 1

Firstly, Pascal's law is only applicable to incompressible, non viscous fluids (or ideal fluids like water). Therefore, in the molecular level there are no compressions. As a consequence: (Assume the classic case where a force is applied to a small piston connected to a larger piston.) As the fluid is incompressible the volume of the fluid passing out of the smaller piston is the volume of the fluid passing into larger piston. (Let area of larger piston be A and smaller piston be a, let the height increased in larger piston be x and height decreased in smaller piston be y). Thus, as the volume increase/decrease is same: ∆volume = area * (increase in height) Ax = ay. ----- 1

Now, as the fluid is non viscous, so no energy is lost. (Let the force applied on smaller piston be f and the force applied by bigger piston be F): Energy = force • displacement. Thus, fy = Fx. -----2

From 1 and 2 we get: f/a = F/A. Or the pressure transmitted throughout the liquid is undiminished.