Understanding Buoyancy & Its Causes

[TheLil'Turkey]

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?

More thorough explanation of my hypothesis (same as post 13): If a solid object is in water, the pressure on it is caused by the impacts of the water molecules. If the pressure is twice as high on the bottom of the object than on the top, then twice as many water molecules hit the bottom per unit time (assuming no macroscopic movement and everything's at the same temperature). Obviously the water's density at the bottom of the object isn't twice as high as it is at the top, but I'm pretty sure that the average time that a water molecule travels between impacts (and therefore also the average intermolecular distance, or average distance from the "edge" of one molecule to the "edge" of another) decreases extremely quickly with increasing density. I crudely visualize this 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 intermolecular distance. If the average intermolecular distance halves, the pressure doubles.

 

[DaveC426913]

No. Buoyancy works perfectly fine even in fluids that have a very low density gradient over their depth.

It may be better to think - not about buoyancy of the object - but about the weight of the surrounding heavier objects.

i.e. A 1in³ cork released near the bottom of a bucket of water will have water all around that that wants to be in the 1in³ space occupied by the cork. The water has enough weight (since 1in³ of water is significantly heavier), pushing down from above, to shove the cork out of the way. So does the water above that, all the way up to the surface.

 

[Doc Al]

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).

No. What matters is the increasing pressure with depth.

 

[TheLil'Turkey]

Of course, Al. But I want to understand what causes the increase of pressure with depth in terms of the molecules of the fluid.
I'd really appreciate a response from someone knowledgeable.

 

[Doc Al]

But I want to understand what causes the increase of pressure with depth in terms of the molecules of the fluid.

It's certainly true that a fluid under pressure will be squashed somewhat, even in nominally 'incompressible' fluids. But that will be a trivial increase in density. Is that what you're looking for?

 

[TheLil'Turkey]

I want to be sure that I understand buoyancy in terms of the molecules of the fluid and the forces they exert on a submerged solid.

 

[sophiecentaur]

No. What matters is the increasing pressure with depth.

Not sure about that as being the crucial issue. Is it not just a matter of relative density and. as Archimedes put it, volume of 'displaced fluid'.

If you take a cuboidal stick of uniform density, will it float higher out of the water (as a percentage of its volume) if it lays horizontally or if you force it to an upright position using frictionless rails or some such arrangement? Having it cuboidal (rectangular faces) makes for the simplest model as the upthrust will only be due to the horizontal, lowest face.
When it lays down, it will get upthrust from a large area with low pressure but, when pointing upright, the upthrust will be over a small area at a greater depth. In both cases, the hydrostatic pressure times the area of the lowest face is the same (I think?) - namely, the volume times ρg. Hence I think it will float with the same fraction immersed.
It is true to say that the horizontal position is the position with least potential - but is that relevant?

 

[russ_watters]

No. What matters is the increasing pressure with depth.

Clarification: it is the pressure gradient across an object. An object does not gain buoyancy as it sinks.

 

[sophiecentaur]

Yep. Ok.

 

[Doc Al]

Clarification: it is the pressure gradient across an object. An object does not gain buoyancy as it sinks.

Right. It's the pressure gradient (increasing pressure with depth) in the fluid and thus across an object that gives rise to the buoyant force. Archimedes' principle follows from that.

 

[Naty1]

I want to be sure that I understand buoyancy in terms of the molecules of the fluid

As others have implied, that is NOT the way to understand it.

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).

As directly noted above, that is [virtually] irrelevant to describing buoyancy.

But such thinking..such ideas and maybe different perspectives ARE good...

 

[boneh3ad]

Perhaps the simplest way to look at it is that the deeper you go in a fluid, the more of that fluid you have above it pushing down on it, so that fluid has to support all of the weight above it. Of course, the way a fluid exerts force is through molecular collisions, the integrated effect of which is called pressure. So, the deeper you go, the more molecular collisions must occur in a given area to supply a pressure high enough to hold the water above it up and the higher the pressure gets.

 

[TheLil'Turkey]

I'll explain myself in more detail now.

If a solid object is in water, the pressure on it is caused by the impacts of the water molecules. If the pressure is twice as high on the bottom of the object than on the top, then twice as many water molecules hit the bottom per unit time (assuming no macroscopic movement and everything's at the same temperature). Obviously the water's density at the bottom of the object isn't twice as high as it is at the top, but I'm pretty sure that the average time that a water molecule travels between impacts (and therefore also the average intermolecular distance, or average distance from the "edge" of one molecule to the "edge" of another) decreases extremely quickly with increasing density. I crudely visualize this 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 intermolecular distance. If the average intermolecular distance halves, the pressure doubles.

Is the General Physics Forum the correct one for this question? Should I have posted this in a more advanced forum?

 

[boneh3ad]

I'll explain myself in more detail now.

If a solid object is in water, the pressure on it is caused by the impacts of the water molecules. If the pressure is twice as high on the bottom of the object than on the top, then twice as many water molecules hit the bottom per unit time (assuming no macroscopic movement and everything's at the same temperature). Obviously the water's density at the bottom of the object isn't twice as high as it is at the top, but I'm pretty sure that the average time that a water molecule travels between impacts (and therefore also the average intermolecular distance) decreases extremely quickly with increasing density. I crudely visualize this 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 intermolecular distance. If the average intermolecular distance halves, the pressure doubles.

Is the General Physics Forum the correct one for this question? Should I have posted this in a more advanced forum?

Did you just skip over my response or just decide not to acknowledge it? The density need not change for the pressure to go up. That is how water still exerts a buoyant force on an object, because it is about as close to incompressible as you can get.

 

[TheLil'Turkey]

So, the deeper you go, the more molecular collisions must occur in a given area to supply a pressure high enough to hold the water above it up and the higher the pressure gets.

You don't understand my question in this thread. Of course the bolded is true, but how does a molecule deeper down "know" it has to collide more often? My hypothesis is that it's simply due to increased density. You haven't offered an alternative hypothesis.

The density need not change for the pressure to go up. That is how water still exerts a buoyant force on an object, because it is about as close to incompressible as you can get.

If my hypothesis is correct then the bolded is completely wrong. And there are substances far less compressible than water, so I don't know where you got that idea.

 

[boneh3ad]

You don't understand my question in this thread. Of course the bolded is true, but how does a molecule deeper down "know" it has to collide more often? My hypothesis is that it's simply due to increased density. You haven't offered an alternative hypothesis.

If my hypothesis is correct then the bolded is completely wrong. And there are substances far less compressible than water, so I don't know where you got that idea.

But that is just it. Your hypothesis is 100% incorrect. There are many, many counterexamples. Take for instance, anything floating in water. Water is so incompressible that it can effectively be treated as such. You could measure the density at the top of a lake, say Loch Ness since it is so deep, and get right around 1000 kg/m^3. Then you could go down to the bottom of the lake and get, to within 1% or so, that exact same reading.

Now, if we are talking air, then yes, as you get "deeper", the air gets more dense. This is precisely what happens in the atmosphere.

Now, how does it "know" it needs to exert more pressure? Newton's third law. The weight of the entire column of water above a given point is exerting pressure on that point. To remain in equilibrium, the water at that point must exert and equal pressure to that. Pascal's law, which is easy to derive, shows that pressure acts in all directions at once, so at a given point, the pressure exerted on a surface, including on an object, is equal to the pressure as a result of the hydrostatic pressure as described above. Density is not required to change.

 

[DaveC426913]

I see where he's going.

Take one cubic inch of water and examine the molecules in it. They bounce around inside that one cubic inch and, when they get near the boundary, they are repelled by other atoms in adjacent cubes.

Now, move that system one mile downward in the water column. The volume of water may not have compressed very much, but what exactly is happening to cause the molecules to be under pressure?

It seems to me, that, while the density has changed very little, it is enough to be the cause of the pressure.

If not, I don't see the flaw in the argument.

I can imagine replacing the water with something even less compressible. Say a cubic inch of steel. The atoms in this cube are super dense to start, crammed right up against each other and crammed right up against the boundary - no free room. Put that under a mile of steel, and you've got cubes pressing on the surface of our target cube with zero tolerance. It takes a vanishingly small amount of compression before the atoms from from cube are pushing on the target cube.

 

[TheLil'Turkey]

Thanks for your detailed reply, Dave. Since I'm still not 100% sure I'm right about this, I'd appreciate it if the forum mentors (and others) could chime in on this and hopefully even provide some proof. And sorry for being a little rude in this thread; I was frustrated with the way some people dismissed my hypothesis without offering any alternative, but I think this was in large part due to how poorly I initially explained my hypothesis.

 

[DaveC426913]

Thanks for your detailed reply, Dave. Since I'm still not 100% sure I'm right about this, I'd appreciate it if the forum mentors (and others) could chime in

I am not sure either, so don't go on me.

But I believe I got your argument, and tried to advocate for it to get you some definitive answers from the experts.

 

[maimonides]

In the kinetic theory of gases we consider the molecules to move freely and to interact only in collisions, or in other words, we have kinetic energy only and neglect long range forces and their potential.
You can´t do that for a fluid or a solid. If you work it out, there will be something like a mean potential energy which depends on the mean distance of the molecules.
So yes, you need compression for bouyancy - but you might not need very much of it.

 

[Doc Al]

So yes, you need compression for bouyancy - but you might not need very much of it.

Yes, perhaps the OP would be interested in learning about the bulk modulus of fluids (which tells you how much they compress). For example, water has a bulk modulus of about 2 x 10⁹ N/m². So, does water compress as pressure increases? Sure--but not very much.

But the OP is correct that there must be some compression as pressure increases.

 

[rahon]

But that is just it. Your hypothesis is 100% incorrect. There are many, many counterexamples. Take for instance, anything floating in water. Water is so incompressible that it can effectively be treated as such. You could measure the density at the top of a lake, say Loch Ness since it is so deep, and get right around 1000 kg/m^3. Then you could go down to the bottom of the lake and get, to within 1% or so, that exact same reading.

Now, if we are talking air, then yes, as you get "deeper", the air gets more dense. This is precisely what happens in the atmosphere.

Now, how does it "know" it needs to exert more pressure? Newton's third law. The weight of the entire column of water above a given point is exerting pressure on that point. To remain in equilibrium, the water at that point must exert and equal pressure to that. Pascal's law, which is easy to derive, shows that pressure acts in all directions at once, so at a given point, the pressure exerted on a surface, including on an object, is equal to the pressure as a result of the hydrostatic pressure as described above. Density is not required to change.

So you think that water density is not changed by depth? (even though it is deep enough like abyss?)

 

[russ_watters]

No, what is wrong is the cause/effect relationship: the increase in pressure increases the density, not the other way around.

 

[DaveC426913]

No, what is wrong is the cause/effect relationship: the increase in pressure increases the density, not the other way around.

Yeah, that's what I should have said.

Rather than suggesting that the density is the "cause" of the pressure (which is silly if taken at face value), I should have suggested that the pressure and the density are inextricably linked.

 

[TheLil'Turkey]

No, what is wrong is the cause/effect relationship: the increase in pressure increases the density, not the other way around.

My thinking is that on a macroscopic level, an increase in pressure causes an increase in density, but on a microscopic level it's the other way around. If a few water molecules in a large volume of water just happen to end up closer together than what is average for their depth over a very short time interval, then in that time interval, the pressure will be increased in their tiny volume due to the increase in density.

What I think we should all agree on is that pressure cannot increase with depth without density also increasing (assuming that there's just one substance at a constant temperature). I like Dave's way of putting it: the pressure and the density are inextricably linked.

 

[russ_watters]

No, you guys are missing the point. Pressure and compression are complementary if you choose to look at both pressure and compression. But pressure can be explained and calculated without compression while compression cannot be explained or calculated without pressure.

Compression is inexorably linked to pressure, but pressure is not inexorably linked to compression.

Consider this: a 1" square cross section, 100lb block of aluminum and a 1" square cross section, 100lb block of steel are placed on a table. Does the difference in compressibility of steel and aluminum affect the pressure applied to the table?

 

[russ_watters]

Moreover, your understanding of the link is wrong. In the OP, you said twice the pressure equals twice as many molecules hitting. That would be true if there were a 1:1 relationship between compression and pressure (which is true for a gas, but not a liquid). For water, twice as much pressure means about 1.0000000005x as many collisions. A tiny increase. Almost all of the pressure increase is manifest by higher force in the collisions.

 

[TheLil'Turkey]

Pressure and compression are complementary if you choose to look at both pressure and compression. But pressure can be explained and calculated without compression while compression cannot be explained or calculated without pressure.

How can it be explained?

Consider this: a 1" square cross section, 100lb block of aluminum and a 1" square cross section, 100lb block of steel are placed on a table. Does the difference in compressibility of steel and aluminum affect the pressure applied to the table?

No, but that's unrelated to this topic.

 

[TheLil'Turkey]

Moreover, your understanding of the link is wrong. In the OP, you said twice the pressure equals twice as many molecules hitting. That would be true if there were a 1:1 relationship between compression and pressure (which is true for a gas, but not a liquid). For water, twice as much pressure means about 1.0000000005x as many collisions. A tiny increase. Almost all of the pressure increase is manifest by higher force in the collisions.

You clearly need to go back and reread the OP.
edit: One of the things you're missing is that molecules are not infinitely small.
edit 2: Why do you believe the bolded?

 

[russ_watters]

How can it be explained?

No, but that's unrelated to this topic.

Same answer for both: pressure is a function if weight and cross section only. You can ignore compressibility because it is irrelevant. You can't turn it around and use compressibility but ignore pressure...because compressibility is a function of pressure.

 

[russ_watters]

You clearly need to go back and reread the OP.
edit: One of the things you're missing is that molecules are not infinitely small.
edit 2: Why do you believe the bolded?

I don't think so. You said:

If the pressure is twice as high on the bottom of the object than on the top, then twice as many water molecules hit the bottom per unit time.

Again, that is true for a gas, but not true for a liquid and requires a 1:1 relationship between density and pressure as per the ideal gas law: p1*V1=p2*v2

I really think your misunderstanding of what a "liquid" is is key and I missed it before and repeated some of the improper terminology you used. Specifically: "collissions". Unlike a gas, there is no distance betwen molecules in a liquid. So collissions only happen when one molecule moves out of the way and another replaces it. These collissions are utterly irrelevant to describing pressure in a liquid.

Compression in a gas happens because the free distance between molecules gets smaller. Compression in a liquid or solid happens because the molecules themselves get compressed -- which is why they only compress by such a tiny amount.

So my bolded description isn't quite worded right and should be: All of the pressure increase is manifest by the higher force in the contact point between water molecules.

 

[TheLil'Turkey]

I ask again, Russ: why do you believe that if you double the pressure (keeping temperature constant), you double the "force in the collisions?"

 

[russ_watters]

I'm going to stop using the word "collision" because it is wrong:

If you double the pressure, the number of molecules contacting a surface changes by a negligible amount, so the force they apply must double.

 

[TheLil'Turkey]

All of the pressure increase is manifest by the higher force in the contact point between water molecules.

So in your own, personal atomic model, the molecules in a solid or liquid are perfectly still regardless of the temperature?

 

[russ_watters]

So in your own, personal atomic model, the molecules in a solid or liquid are perfectly still regardless of the temperature?

I didn't say that, and temperature is irrelevant here. For proof, consider an open cylindrical container of water. Increase its temperature. Has the density at the bottom changed? Has the pressure?

And please calm down: this ts not my model, this is how it works and I'm just the one explaining it to you.

 

[TheLil'Turkey]

consider an open cylindrical container of water. Increase its temperature. Has the density at the bottom changed? Has the pressure?

Good question! Assuming it starts out at room temperature and you heat it from there, I'd say that the density at the bottom decreases (and therefore the average time that a water molecule travels between collisions increases), and the average speed of a water molecule increases. Furthermore, the density and speed change in just such a way so that the pressure stays the same.

 

[russ_watters]

Density decreases: correct.

For the rest, you are saying that the average time between collisions increases and their average energy increases and the two effects cancel out. Since the molecules do not break contact with each other, there are no collisions, per se, but otherwise, it is correct.

So you have just shown that pressure is not a function of compressibility in this case.

 

[chingel]

How would the increased density and decreased distance between molecules result in increased pressure?

A molecule is constantly being bulled down by gravitational force. For a molecule to stay roughly in it's position, the average force it hits the bottom molecules or gets hit by the bottom molecules has to be equal to the gravitational force (minus the average force it gets hit by the molecules above of course), it doesn't matter what the distance is.

If you put pressure on a molecule, it's mass doesn't change, it can apply more average force by hitting more often and/or with more speed. Probably both happen as the pressure increases in a liquid.

 

[TheLil'Turkey]

Density decreases: correct.

For the rest, you are saying that the average time between collisions increases and their average energy increases and the two effects cancel out. Since the molecules do not break contact with each other, there are no collisions, per se, but otherwise, it is correct.

If you would prefer to say something like "average time that a molecule travels before it changes direction" rather than "average time that a molecule travels between collisions" that's perfectly fine. In fact I'd appreciate it if someone could tell me what the standard terminology is.

So you have just shown that pressure is not a function of compressibility in this case.

This follows from what I've been saying all along. I kept temperature constant in my earlier explanations because I thought that way it would be easier to understand.

If you put pressure on a molecule, it's mass doesn't change, it can apply more average force by hitting more often and/or with more speed. Probably both happen as the pressure increases in a liquid.

My hypothesis is based on my assumption that increased pressure is due (at least almost entirely) to the increased frequency of the collisions if the temperature is constant. That frequency is directly proportional to the the average distance a molecule travels before it changes direction, and as that distance decreases, density increases. I assume that the molecules only gain speed if you increase the temperature.

 

[Doc Al]

My hypothesis is based on my assumption that increased pressure is due (at least almost entirely) to the increased frequency of the collisions if the temperature is constant. That frequency is directly proportional to the the average distance a molecule travels before it changes direction, and as that distance decreases, density increases.

If your hypothesis were true, then density would be proportional to pressure. But as has been stated several times, the density of fluids such as water doesn't change much even when pressure changes greatly.

Yes, when fluids are under increased pressure the molecules are forced together a bit. But it doesn't take much to resist the increased pressure, due to strong short-range repulsive forces between the molecules. That's why the bulk modulus of water is so high.

 

[sophiecentaur]

So in your own, personal atomic model, the molecules in a solid or liquid are perfectly still regardless of the temperature?

What you say, implies that hydrostatic pressure should be a (first order) function of temperature?

 

[sophiecentaur]

If your hypothesis were true, then density would be proportional to pressure. But as has been stated several times, the density of fluids such as water doesn't change much even when pressure changes greatly.

Yes, when fluids are under increased pressure the molecules are forced together a bit. But it doesn't take much to resist the increased pressure, due to strong short-range repulsive forces between the molecules. That's why the bulk modulus of water is so high.

I agree. Modelling a liquid as a gas will not get anywhere useful.

 

[russ_watters]

If you would prefer to say something like "average time that a molecule travels before it changes direction" rather than "average time that a molecule travels between collisions" that's perfectly fine. In fact I'd appreciate it if someone could tell me what the standard terminology is.

The molecules are vibrating, but are always in contact with each other. That's the key that you're missing.

This follows from what I've been saying all along.

No, it doesn't:

My hypothesis is based on my assumption that increased pressure is due (at least almost entirely) to the increased frequency of the collisions if the temperature is constant.

I know - and it is still wrong. Again:

1. There are no collissions since water molecules are in constant contact with each other and compression has no effect on the number of molecules in contact with each other.
2. The oscillation of the molecules due to their temperature does not affect how much force they apply to each other.

That frequency is directly proportional to the the average distance a molecule travels before it changes direction, and as that distance decreases, density increases. I assume that the molecules only gain speed if you increase the temperature.

In determining the pressure in an open container, it just plain doesn't matter how fast they are vibrating, as the example with temperature showed. Think of the molecules as springs with masses stuck in the middle of them. Place one of these spring-masses on a table and it applies a certain force. Set it oscillating and it applies a variable force, but the average force doesn't change. Set it oscillating faster and the average force still doesn't change. The oscillation just doesn't have anything to do with the average force.

Then do it again, but this time push down on the top of the spring. The force applied to the table increases. Set the spring-mass in motion: the average force remains at the new value, but the oscillation frequency is higher than it was without you pushing down on the spring. So what caused what? The push-down on the top of the spring both causes the frequency to change and causes the force on the table to change. The frequency does not cause the force to change.

[snip] I kept temperature constant in my earlier explanations because I thought that way it would be easier to understand.

Indeed - but by putting temperature back in, you proved that compression/expansion is an effect of temperature change, not a cause of pressure change. Compression/expansion is an effect of pressure change, but the inverse is not true: pressure change is not an effect of compression/expansion in this case.

Just to make sure we stay grounded to the OP, here's the first sentence:

I think buoyancy is caused by the increase in density with depth.

In other words: density increase causes pressure increase, causes buoyancy increase.

Trouble is, even for a hypothetical incompressible fluid, pressure is still a function of depth. How can A be the cause of B if eliminating A doesn't eliminate B?

 

[TheLil'Turkey]

If your hypothesis were true, then density would be proportional to pressure. But as has been stated several times, the density of fluids such as water doesn't change much even when pressure changes greatly.

Did you even read the OP or post 13? The bolded couldn't be more incorrect. If my hypothesis were true, then the change in density would be proportional to pressure.

And looking at the graph at http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html, the change in the density of water is about -0.05 kg per cubic meter per bar at constant temperature. I think that with this graph, everyone can now agree that I'm right.

 

[TheLil'Turkey]

I agree. Modelling a liquid as a gas will not get anywhere useful.

While true, that has nothing to do with this thread. A gas is modeled with the assumption that the volume of the molecules is 0, where as in my model, the radius of a molecule is assumed to be huge relative to the average distance it will travel before changing direction.

 

[Doc Al]

Did you even read the OP or post 13? The bolded couldn't be more incorrect. If my hypothesis were true, then the change in density would be proportional to pressure.

Did you read what you actually wrote that I responded to? (You're bouncing all over the place.)

 

[TheLil'Turkey]

Did you read what you actually wrote that I responded to? (You're bouncing all over the place.)

I assume you're talking about this

as that distance decreases, density increases

This does not imply that the density is directly proportional to the pressure. Because the volume of a molecule is not zero, it implies that the change in density is directly proportional to the pressure. At this point I can only recommend that you read or reread all my posts in this thread.

 

[sophiecentaur]

But what has any of this bickering got to do with a simple explanation of hydrostatic pressure? Water is not incompressible BUT, when you fall in the water and you float, its compressibility has no measurable effect on the depth to which you sink anddoesn't need to be brought into the argument. There is a very simple explanation which involves a linear increase in pressure with depth.

Detailed Gas models do not assume point molecules. They take into account, the intermolecular forces just as models of liquids do. It just so happens that the modulus of a gas is very much lower than that of a liquid. But, except in World-scale (/extreme) situations, the variations of density of water is hardly relevant.
The OP is clearly not correct because there is a better and more accurate explanation. Arguing that the density variation is relevant just seems to me to show a reluctance to acknowledge - being based on the ideas used in the gas model. Sometimes arm-waving has to yield to accepted and reliable (appropriate) models.

 

[TheLil'Turkey]

How does the vibration frequency of molecules in a liquid or solid vary with pressure? The answer to that determines if I'm right.

 

[sophiecentaur]

For a linear force law will the frequency of vibration be independent of the pressure. (Simple harmonic oscillator theory). For moderate pressures, the force law will be linear.

But how is this at all relevant or how does it justify the contents of the OP, which don't make sense? You are using a model that just doesn't apply to 'condensed matter'. You seem to be hung up on a version of 'the Kinetic Theory of Gases' and it doesn't fit the situation. 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). The volume in a gas is pretty much directly proportional to the Temperature under constant pressure - not so for a liquid. The RMS movement of molecules in a liquid is about the same as for a gas but the mean free path is only about the diameter of a molecule (a 'springy ball'). The frequency of oscillation about the mean position will be the same over a large range of pressures (/individual forces). What counts is the mean force, which relates just to the weight of liquid above. This mean force is applied to the sides of the immersed object.

Let'f face it. That's what we can actually observe every day!