What do you really mean by fluid pressure?

Question

I feel like the more deeply I am studying about fluids in physics, the more I realize that I don't really understand the basic concept of fluid pressure. Like firstly what is meant by fluid pressure? Is it the pressure/force that fluid molecules apply on EACH OTHER, as they collide with each other innumerable times? Is it the pressure that is felt by the SIDES and BOTTOM of the container housing the fluid molecules or the OBJECTS (whether it is person swimming or boat) submerged in the fluid, when the fluid particles are colliding with their surface area?

Also how does gravity contribute to fluid pressure? Like I keep reading that fluid pressure is greater in the bottom of the container housing the fluid than at the top of the container, because the weight of fluid particles at top is pushing downwards on the particles at the bottom. But why is that the case really? Aren't fluid molecules colliding the same way (like same number, force of collisions), irrespective of whether they are in the bottom, middle or top of the container? Also we know that fluid particles (more so gas particles than liquids) are always in motion, then with this in mind would it be correct to assume, that in a container of fluid, lots of fluid particles bottom of container might always randomly travel (like travel a vertical distance up and thus exchange vertical positions) to the near top or middle of the container, thus sometimes transmitting pressure from bottom to top and then top to bottom of container (because of course particles/molecules are always colliding) all the time? If this assumption of mine is correct that, then where does the concept of fluid pressure increasing with greater depths come from?

I don't know if my assumptions in the foregoing paragraph are faulty and that is the reason why my understanding of fluid is skewed, but if any one can gives any sort of explanation of this topic, it would be great.

Answer 1

Is it the pressure/force that fluid molecules apply on EACH OTHER, as they collide with each other innumerable times? Is it the pressure that is felt by the SIDES and BOTTOM of the container housing the fluid molecules or the OBJECTS (whether it is person swimming or boat) submerged in the fluid, when the fluid particles are colliding with their surface area?

All of the above.

Aren't fluid molecules colliding the same way (like same number, force of collisions), irrespective of whether they are in the bottom, middle or top of the container?

No. If you imagine the fluid is made of rigid particles (molecules), each particle has mass. So if it is moving upwards, it is affected by gravity just like any other projectile, and it slows down. If it moves downwards, it speeds up again. Therefore the pressure at the bottom of a vertical column of fluid is greater than the pressure at the top.

Answer 2

Pressure is, $p=k_BnT$, (in an ideal gas) Boltzmann's constant times density times temperature. Pressure is the force per area that would be exerted on a container if you captured a bit of the fluid in a container, and this force is due to collisions with the walls of the container, but it is not due to collisions between particles inside the fluid. The particles within the fluid can be entirely collisionless between themselves and the pressure is still finite because it has a density and temperature. Density and temperature are ultimately defined from a distribution of particles with different velocities. When gravity is acting on the fluid, the reason the pressure is greater at the bottom is because gravity causes a density gradient and therefore an overall pressure gradient. Why is there a density gradient? Because there are particles at the bottom of the container that don't have enough energy to reach the top of the container (again think of a distribution of particles with different velocities). It doesn't have anything to do with particles at the top "pushing down" on the particles at the bottom. The particles may collide, and that acts to bring the fluid towards thermal equilibrium, but the fluid can be collisionless and there would still be a pressure gradient.

Edit: note that pressure in terms of collisions with a container or objects sitting in the fluid assumes there are collisions with the container or object. This concept of collisions with container walls is how you measure pressure, but it is not how it is defined. If the fluid doesn't experience collisions with the walls, then obviously you won't measure a finite pressure. For example, neutrinos hardly collide with anything, so you have to infer the pressure from other measurements, theory, assumptions, etc.