Before asking this question I searched for the answer on the web (in particular on Physics.SE) and here are some that I found:

• In an incompressible Ideal fluid, can the pressure increase with depth?

• Why do water molecule apply more pressure (i.e., more force) at depth?

...,etc. Whichever question did I saw it didn't gave a reliable answer. In particular everyone tried to explain it with the fact that for a fluid to be in static equilibrium the pressure at a depth must counter the weight of the water above it and hence is equal to $\rho g h$. Well that's simple and anyone can get the macroscopic picture but what about the microscopic one? In particular the answer here user Bob Jacobsen says:

The questioner seems to want a "microscopic" explanation, but there is no microscopic explanation for the pressure at depth $D$ in terms of microscopic phenomena at $D$; it's determined by the total material above.

(I have highlighted the part that I want the reader to notice) I don't think so. I mean for every phenomena (as far as I know) at macroscopic level there exists a microscopic explanation (for example gas law (kinetic theory), etc.). Let's consider pressure in a gas which is explained by the microscopic phenomena of collision of atoms/molecules of the gas which depends:

• on the number of collision (which is proportional to the amount of molecules present nearby)

• the speed of the particles present (which is related to the macroscopic phenomena of temperature).

My chemistry textbook dedicated a whole section to describe how there is no fundamental way to distinguish between liquids and gases (unless there exists a surface, see supercritical fluids and this video for reference.) So for me it is quite reasonable to use explanation for pressure in gases for fluids.

Now as for the two reasons for pressure one can neglect the number of colliding molecules (as density varies negligibly with depth in liquids). So the other reasonable explanation is due to the increase of speed with depth. But this then implies variation of temperature with depth in fluids which I can't reason out as being true. So this implies that there must be some other reason to explain this.

So

• What is the correct microscopic explanation of the variation of pressure with depth?

• If the variation of speed of molecules with depth is true then what might be the reason for it?

Thanks!

Before asking this question I searched for the answer on the web (in particular on Physics.SE) and here are some that I found:

• In an incompressible Ideal fluid, can the pressure increase with depth?

• Why do water molecule apply more pressure (i.e., more force) at depth?

..., etc. But the answer there seem to not answer the question properly. In particular everyone tried to explain it with the fact that for a fluid to be in static equilibrium the pressure at a depth must counter the weight of the water above it and hence is equal to $\rho g h$. Well that's simple and anyone can get the macroscopic picture but what about the microscopic one? In particular the answer here user Bob Jacobsen says:

The questioner seems to want a "microscopic" explanation, but there is no microscopic explanation for the pressure at depth $D$ in terms of microscopic phenomena at $D$; it's determined by the total material above.

(I have highlighted the part that I want the reader to notice) I don't think so. I mean for every phenomena (as far as I know) at macroscopic level there exists a microscopic explanation (for example gas law (kinetic theory), etc.). Let's consider pressure in a gas which is explained by the microscopic phenomena of collision of atoms/molecules of the gas which depends:

• on the number of collision (which is proportional to the amount of molecules present nearby)

• the speed of the particles present (which is related to the macroscopic phenomena of temperature).

My chemistry textbook dedicated a whole section to describe how there is no fundamental way to distinguish between liquids and gases (unless there exists a surface, see supercritical fluids and this video for reference.) So for me it is quite reasonable to use explanation for pressure in gases for fluids.

Now as for the two reasons for pressure one can neglect the number of colliding molecules (as density varies negligibly with depth in liquids). So the other reasonable explanation is due to the increase of speed with depth. But this then implies variation of temperature with depth in fluids which I can't reason out as being true. So this implies that there must be some other reason to explain this.

So

• What is the correct microscopic explanation of the variation of pressure with depth?

• If the variation of speed of molecules with depth is true then what might be the reason for it?

Thanks!