Is there a buoyancy force or not?

[Studiot]

Haven't you guys been busy while I've been having my dinner?

I owe you an apology, Mapes. I took the weight of your second box to be greater than the water it displaced. If its weight was less it could mean that the vertical stresses acting on the support box are either greater than or less than the horizontal ones.

But consider there is actually no need for your second box at all in the argument.
Once the second box is firmly fixed to the support it effectively becomes part of the support.
So you could consider any horizontal section through the support and ask

As a result of the poisson effect is there a bouyancy force tending to lift the material above the section away (upwards) from the material below?

As an aside. What if the second box overhangs the support?
There will indeed be an upward bouyancy force acting on the second box given by the horizontal area of overhang times the pressure at the overhang.

Similarly suppose your support box was T shaped. There would be a bouyancy force acting on the underside area of the T in contact with the fluid.

Your suggestion is tantamount to saying that a T shaped support would experience a bouyancy force equal to the weight of fluid in its entire volume, not just the exposed flange.

 

[stewartcs]

I'm not quite able to visualize your second thought experiment, the one with the spring scale inside the rigid cylinder. A diagram would help. But please, think about the current thought experiment before switching to a new one, so I can see which specific equation or calculation you disagree with.

Here is a diagram.

Note that the white part is evacuated.

CS

 

[Mapes]

No, I've not bothered looking closely at the equations because there is no need to.

Wow. Well, there's nothing I can do about that.

Whether the cylinder or supports are elastic or perfectly rigid is irrelevant with respect to buoyant force. A perfectly rigid member that has pressure acting on the bottom surface will still have a buoyant force. If the pressure isn't acting on the bottom it will not (presuming no other pressure ledges again).

Agree, agree, respectfully don't agree.

Remove the elastic members from your example and make them rigid. Do your equations still hold?

Yes; the equations do not include the stiffness of any components.

Are you still arguing that if there is no hydrostatic pressure acting on the bottom of the cylinder that it will experience a buoyant force?

Yes, it's what I showed in post #42 and in more detail in post #44 with stress states calculated via a free-body diagram (not shown).

 

[stewartcs]

Wow. Well, there's nothing I can do about that.



Agree, agree, respectfully don't agree.



Yes; the equations do not include the stiffness of any components.



Yes, it's what I showed in post #42 and in more detail in post #44 with stress states calculated via a free-body diagram (not shown).

Sorry didn't mean to sound so rude on that first comment!

I don't see how you can call the reaction at the bottom of the cylinder a buoyant force since it has nothing to do with the hydrostatic pressure acting directly on the other object. Maybe I'm missing your point.

How about this...Using your equations show how the reaction at the bottom (the thing you're calling a buoyant force) is equivalent to the weight of the displaced fluid.

CS

 

[stewartcs]

Yes; the equations do not include the stiffness of any components.

By rigid I mean the shape doesn't change which means there is no Poisson's Effect. Take away that effect and take another look at your position.

CS

 

[stewartcs]

EDIT: Perhaps we're getting away the main issue here. My only point is that it's not sufficient to say "The water has nowhere to push up, so no buoyant force can exist." There are configurations (like my diagram in #20) where the water can push sideways (laterally) and cause the vertical extent of a solid support to increase through the Poisson effect. This is equivalent to a buoyant force, since it doesn't occur until the empty cylinder has been attached.

The problem I have with your argument is that it puts a material dependency on the buoyant force when there is none. What happens if the material properties change? Does the buoyant force change as well?

CS

 

[Mapes]

As a result of the poisson effect is there a bouyancy force tending to lift the material above the section away (upwards) from the material below?

By rigid I mean the shape doesn't change which means there is no Poisson's Effect. Take away that effect and take another look at your position.

That Poisson effect stuff was a wrong approach I took to try to understand the problem. In the end, it has a minimal effect for a sufficiently stiff support. So forget about Poisson contraction or elongation, it's not relevant. I've added a note to the bottom of post #39 to make this clear. Sorry about the detour, I'm been trying to converge toward a solution too. But I stand behind the position that an empty cylinder is buoyant even when its bottom is not exposed to water, based on the comparison of stress states in posts #42 and #44.

Your suggestion is tantamount to saying that a T shaped support would experience a bouyancy force equal to the weight of fluid in its entire volume, not just the exposed flange.

Yes, exactly. The buoyant force depends on the volume of water displaced, not on the shape of the cylinder or its orientation or attachment method. Otherwise you could create an non-conservative force at will simply by attaching it or detaching it, or by rotating it effortlessly. This would constitute a perpetual motion device.

The problem I have with your argument is that it puts a material dependency on the buoyant force when there is none. What happens if the material properties change? Does the buoyant force change as well?

CS

Asked and answered in post #42. The buoyant force that I argue exists is independent of the support stiffness or of any material properties except for cylinder weight. No material properties of the support appear in the buoyant force prediction \rho g A(h-t_\mathrm{supp})-W_\mathrm{cyl}\approx\rho g Ah.

I want to emphasize that the only reason to consider a non-rigid support in the thought experiment is to have some way of measuring a buoyant force. If the support is initially made twice as stiff, the strain gauge will elongate half as much when the empty cylinder is attached, for example. As the support stiffness approaches infinity, the ratio of the strain gauge elongation to the support stiffness remains constant and proportional to the buoyant force.

 

[stewartcs]

Yes, exactly. The buoyant force depends on the volume of water displaced, not on the shape of the cylinder or its orientation or attachment method. Otherwise you could create an non-conservative force at will simply by attaching it or detaching it, or by rotating it effortlessly. This would constitute a perpetual motion device.

The buoyant force doesn't not simply depend on the volume displaced. Take a look at the picture in post #52. The cylinder obviously displaces water, however it will experience no buoyant force.

Asked and answered in post #42. The buoyant force that I argue exists is independent of the support stiffness or of any material properties except for cylinder weight. No material properties of the support appear in the buoyant force prediction \rho g A(h-t_\mathrm{supp})-W_\mathrm{cyl}\approx\rho g Ah.

The object's weight has nothing to do with the buoyant force.

http://hyperphysics.phy-astr.gsu.edu/Hbase/pbuoy.html#bcomp

Although that site gives an incomplete explanation since it only refers to the displaced volume and doesn't explicitly talk about the pressure field.

CS

 

[elect_eng]

To those saying that the buoyant force completely disappears if liquid is excluded from the bottom of the cylinder, please consider again my diagram in post #20, where no liquid contacts the cylinder bottom, but I predict a measurable upward displacement and associated force. Is there an error in this reasoning?

Yes, there is an error in your reasoning. You have stated that an empty cylinder is sitting on the platform. This very statement is an acknowledgment that there is no buoyant force. An empty cylinder would normally float. OK, you glue it then because you think there is buoyant force, but it's not necessary to glue it.

You have correctly noted that the force (or pressure) on the top of the platform has changed, when the cylinder is placed, but buoyant force is all about the force on the cylinder not on container. If there is a gap between the cylinder and the platform, then there is buoyant force on the cylinder, and downward pressure on the top of the platform. The water in between is pushing in both directions- upward on the cylinder and downward on the platform. When the seal is made and no water is in between, both forces are gone. The cylinder has no buoyant force and the platform top no longer feels the water pressure (it feels atmospheric pressure plus the cylinder's weight per unit water-plane area.

Did you read my post #21 that followed yours. I mentioned the stresses on the container. They are indeed important, but they should not be interpreted as buoyant force.

 

[Mapes]

OK, got it. I've been interpreting any stress changes in the system due to the presence of the cylinder as buoyant forces, but this was misguided. And I realize that several of you have worked hard to point this out to me. This has been a great learning experience in visualizing forces and energies. Studiot, stewartcs elect_eng, and russ, thanks for a very stimulating discussion!

 

[Studiot]

Here is a small quizz.

Which of these objects experience a bouyancy force?