At the microscopic level, why does pressure in a liquid increase with depth? It must be that particles deeper in the fluid are moving faster than more shallow particles, but what causes them to move faster? And why isn't there a corresponding temperature increase? #iteachphysics

This is also messing with me because my brain in so ingrained in Bernoulli's principle at this point. For a static fluid, higher pressure regions *are* due to faster individual fluid particles. The are just moving randomly and average over all directions to a speed of zero.

Bernoulli's principle, faster fluid implying lower pressure, only applies to the velocity of the *net* fluid flow. It doesn't say anything about the speed of any one particle.

Higher pressure will always be caused by more particle velocity being normal to the surface.