system
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human
How are the two explanations of pressure in a fluid (kinetic and gravitational) related?

Both online and in my physics courses I’ve seen two seemingly very different accounts for pressure in a fluid at hydrostatic equilibrium:

· The first posits that pressure is a macroscopic measure of the impacts of fluid particles on a surface submerged in the fluid. It is therefore a function of the temperature of the fluid and its density.

· The second explains pressure by the weight of the volume of fluid above each point. It therefore depends on its density and the depth in the fluid (or the altitude in the case of the atmosphere).

I can’t figure out how the two are related. The first explanation requires no gravity, while the second would imply zero pressure in a zero g environment. What am I missing? Is the first explanation only valid for gases and not liquids? And if so, why?

And on that note, I would also like to ask how the second explanation accounts for pressure being a scalar and not a vector: if it is merely the reaction force which balances the weight of the fluid above (per unit area), then why is it the same along axes perpendicular to the vertical?
gpt
The first explanation implicitly requires gravity, or some other external force, because without a force holding the fluid together, those little collisions will just bounce all the molecules apart in quite short order. This is what distinguishes a fluid from a solid. 

A solid, even if subjected to essentially zero external force (pressure), maintains structural integrity because the bonds between the constituent particles are strong enough that it's kinetically unlikely for any given particle to gain enough energy through random fluctuation to escape from the bulk. Now, of course, even solids, if subjected to true vacuum, will evaporate over time, given enough time, but at typical temperatures and pressures for most applications for solid materials used structurally, you don't have to worry about your solid subliming.

Fluids, on the other hand, have to have some external force applied to confine them to a particular region. If they don't, the fluid particles will bounce off of each other and whatever surroundings they do have in the bulk, and in the direction where they don't have a constraint, they'll just keep going indefinitely. This is what happens if you have a pressure vessel that's got a pinhole leak: there's net acceleration of fluid towards the leak because there is no surface there to provide balancing force to confine the fluid anymore.

As for why pressure induced by gravity is uniform, that's guaranteed by the condition of hydrostatic equilibrium. Imagine a tiny parcel of fluid. Because fluids flow when subjected to pressure, if the pressure felt by this tiny parcel of fluid was different in any direction, it would flow in the direction of the net applied force. Since we are saying that there is no net fluid flow in hydrostatics, pressure for any tiny parcel of fluid has to be isotropic.