Understanding Buoyancy & Its Causes

[TheLil'Turkey]

If you are looking for a Classical Model then a network of masses, separated by springs, is a far better model than point (/small radius) masses flying around at high speed for most of the time (as in a gas).

I've been advocating what you describe here as "a Classical Model" with one difference: that the velocity of the water molecules is constant between "collisions." Thinking about it for a moment, I'd guess that the spring model is closer to reality than mine, but they both make the same prediction which is point of this thread: that pressure and density are inextricably linked in 1 substance.

From my OP:

I crudely visualize my model as water molecules being huge (and in constant motion) with tiny spaces between them. This would mean that a tiny percentage increase in density would lead to an enormous percentage decrease in the average distance from the "edge" of one molecule to the "edge" of another.

 

[TheLil'Turkey]

I thought about the classical model of condensed matter sophiecentaur described since it seems more realistic than mine. One way in which the 2 models differ is that the classical one predicts that the frequency of "collisions" doesn't change with pressure, but that the force of the "collisions" increases with pressure (if I'm understanding it right). This is the opposite of what mine predicts.

 

[sophiecentaur]

The liquid state is a weird, mid point between the vapour and solid phases. For most substances (?), where the pressures are not (planetary core) extreme the temperature range in which they exist as liquid is pretty limited. Pure metals have very narrow temperature ranges in the transition stage from one state to another.

Molecular separation is much the same in a liquid as in the solid so I should think that a solid-like model would be more likely to apply so a liquid would be more likely to behave like a 'very flexible' solid than a 'highly compressed' gas.

The term "force of collisions" doesn't go down well with me, I'm afraid. You need to talk of Momentum Change (Impulse) or Kinetic Energy because when does this force of yours apply?

I wish you'd comment on my query about the OP which seems so wrong that the rest of this thread can't be resolved without sorting out the issue.

 

[TheLil'Turkey]

I wish you'd comment on my query about the OP which seems so wrong that the rest of this thread can't be resolved without sorting out the issue.

I assume you're talking about this:

But how is this (referring to the relationship between the pressure and frequency of the molecules of a liquid or solid) at all relevant or how does it justify the contents of the OP, which don't make sense?

My model predicts that frequency increases with pressure. The classical model predicts that they're not related. I suspect that the latter is correct, but could someone please provide some data?

The term "force of collisions" doesn't go down well with me, I'm afraid. You need to talk of Momentum Change (Impulse) or Kinetic Energy

Ya, I should've used the term impulse.

 

[sophiecentaur]

No I was referring to the very first statement:
"I think that buoyancy is caused by the increase of density with depth (the deeper you go, the more molecules there are per unit volume). Therefore an object in a fluid will be hit by more of the fluid molecules from below than from above (even if the difference is only a tiny fraction of 1%). Is this correct?"

This cannot be right because the density increases at a minuscule rate with depth (incompressible, almost) yet the pressure is directly proportional to depth.

Also
"My model predicts that frequency increases with pressure. The classical model predicts that they're not related. I suspect that the latter is correct, but could someone please provide some data?"

I have already explained why the classical model predicts what it does.
The 'spaces between' the molecules that are present in a gas (where your kinetic ideas do apply) are not present in a liquid. In a liquid you just have (classically) coupled oscillators.If you have an almost linear force / displacement law then the frequency of oscillations will not change if there is an overall increase in that force - the oscillators just operate around a different mean point. (In the same way that a mass on a spring will oscillate at the same frequency when hanging down, standing up or in zero gravity).

 

[TheLil'Turkey]

No I was referring to the very first statement:
"I think that buoyancy is caused by the increase of density with depth (the deeper you go, the more molecules there are per unit volume). Therefore an object in a fluid will be hit by more of the fluid molecules from below than from above (even if the difference is only a tiny fraction of 1%). Is this correct?"

This cannot be right because the density increases at a minuscule rate with depth (incompressible, almost) yet the pressure is directly proportional to depth.

As I explained before, the model I proposed predicts the bolded. My second statement in the OP explains this. But another thing it predicts (which I now understand is wrong) is that the vibrational frequency of a condensed material in real life increases with pressure (for normal pressures).

I have already explained why the classical model predicts what it does.

I was talking about a real condensed substance, not a model. But I found something just as good: a graph of intermolecular attraction vs. distance between the centers of molecules. What was wrong with the model I proposed was that I imagined the distance axis of this type of graph being severely compressed.
edit: One thing that should have tipped us all off that my initial model is wrong is that if it were true, condensation would be impossible - all matter would be gas. I didn't realize it made that prediction until right now.

Now I finally feel happy with my understanding of pressure and density and I also see how Hooke's Law fits into the classical model of condensed matter. Even though this took so long, it was definitely worthwhile for me :)