If liquid pressure is higher at greater depths, particles colliding with the container exert more force, and this is only possible if they collide with greater velocities (assuming mass to be identical for each particle). If, let's say, the system starts out with every particle having the same speed, why does it always end up so that the particles lower down move faster? Can someone help me complete the chain?
$\begingroup$ . . . . . exert more force, and this is only possible if they collide with greater velocities or more often per second. $\endgroup$– FarcherMar 27 at 15:54
$\begingroup$ Well, that chain is wrong, so... $\endgroup$– Jon CusterMar 27 at 15:54
$\begingroup$ @Jon Custer How come? $\endgroup$– SakMar 27 at 15:57
$\begingroup$ What determines how many particles collide per unit time? How does that scale with pressure? $\endgroup$– Jon CusterMar 27 at 15:58
$\begingroup$ @JonCuster But why do you assume that the increase in pressure at greater depths is due to an increase in the frequency of collisions rather than an increase in the velocity of particles? If that is an established fact, please explain. $\endgroup$– SakMar 27 at 16:03
First let me note that technically, even within your argument, the collision velocity could be higher or the collision frequency could be higher. Hence pressure in a gas is proportional to temperature and gas density.
But anyway - think of pressure in a liquid more like this:
The circles are the size of the atoms/molecules. The springs between them are their repulsive forces. The line at the bottom is the container in question. Water (and many other liquids) is "incompressible" in the sense that as pressure increases, its density doesn't change much. But it does change. As the pressure increases, the molecules get slightly closer together, and hence exert bigger forces on one another, and hence will exert a bigger force on a container put inside the liquid. I've also attempted to illustrate how this pressure increases with depth. The bottom "spring" holds up all four molecules above it. The top one only holds up one molecule. Note that the springs are always small compared to the molecule size - hence the "incompressibility" of water. The inter-molecule spacing is always dominated by the size of the molecule itself, and molecules only get slightly closer together when a very big force pushes them together.
And just as a final, direct, comment on your model - the wall doesn't occasionally get an impact from a molecule in a liquid. In a liquid, the walls of the container are always in contact with molecules from the liquid (experiencing close range forces with nearly as many molecules as can fit on the surface of the container).
EDIT-added in response to a question from OP-Pressure is the force the substance exerts on a containing wall (say a metal box that I put underwater). Consider a molecule touching the wall - it is being pushed toward the wall by the "spring" above it. In order to contain the liquid, the wall has to push back equally on the molecule to oppose the forces from other molecules pushing the molecule into the wall (that's the spring between the wall and the bottom molecule in my picture).
All of this has been quite handwavy - I warmly welcome discussions in more depth of the physics in the comments. I think this is an appropriate level of complexity for the question being asked.