We know that in liquids pressure increases with depth. We also know that pressure is nothing but the rate of change of momentum per unit time per unit area, during the collisions of different molecules with each other and also with the walls of the container. Now if the pressure is increasing with increasing the depth then the number of collisions per unit time must have increased at greater depths (assuming incompressible fluid).
It implies that the average molecular kinetic energy of molecules at depths will be greater than the average molecular kinetic energy at the shallow water. Is it true? I do not find any literature confirming this idea, so I need a confirmation on it.
If average molecular kinetic energy at depth is greater then what is responsible for it? How does it actually happen?
Does it also mean that the temperature of water at depths will be greater than the temperature at the shallow water because the average molecular kinetic energy at the depth is greater? Does it mean that water will itself develop some temperature gradient? Even if its earlier temperature was uniformly distributed?
Can the variation of pressure happen without the variation of density and without the variation of temperature? If NO, then how does it happen in ideal incompressible fluids, which we study and are taught everywhere?
Note 1: Here since we are talking about ideal liquid, so it will be incompressible, so the variation of density with depth can be ignored (unless the reader believes the variation of density is indispensable. In that case, I request the reader to also kindly comment on how then pressure variation can happen with depths in ideal incompressible liquids).
Note 2: I have seen similar questions on Stack Exchange to which most of the responses say that at the depth the weight of liquid above it will increase, the force will increase and hence the pressure will increase. I am not against that idea, but that is the macroscopic understanding of this phenomenon. I am asking for a microscopic understanding of this phenomenon.