Buoyant Force: Pressure, Gravity & Upward Thrust

[muralidharan]

how does pressure on a submerged body in water experience an upward thrust ,when the cause of pressure is gravity, which can only be downwards

 

[Dale]

how does pressure on a submerged body in water experience an upward thrust ,when the cause of pressure is gravity, which can only be downwards

The premise of this question is wrong. Pressure is not caused by gravity. For example, the international space station is pressurized even though it is in microgravity. Pressure is a contact force between a fluid and a surface, it is not caused by gravity, and it acts in a direction perpendicular to the surface (which may be upwards).

 

[person_random_normal]

buoyant force is resultant of all of those forces* exerted by liquid on the floating body

* force acting at a point (which varies with variation of liquid column above the point) can be calculated if pressure is known

so you need to do ∫ P.dA , cyclic integral over whole surface of the body to get buoyant force
where - P is pressure at a particular point on the body
and dA is surface area of that infinitesimal region of body , where pressure is P

 

[person_random_normal]

Pressure is not caused by gravity.

!

you are wrong
pressure is force / area, that force may gravitational or something else, whatever

 

[Dale]

you are wrong

Consider a pressurized container of gas in 0 g. There is pressure and there is no gravity. Therefore, pressure is not caused by gravity.

Conversely, in an evacuated container there is no pressure, even in the presence of gravity. Gravity is neither necessary nor sufficient for pressure.

 

[Orodruin]

!

you are wrong
pressure is force / area, that force may gravitational or something else, whatever

You would do well not to make rash assertions that someone else is wrong. In particular when you are wrong yourself. As Dale has already stated, gravity is neither required for or directly causing pressure. That a fluid in a gravitational field experiences a pressure gradient, leading to a buoyant force, is a different thing.

 

[person_random_normal]

a fluid in a gravitational field experiences a pressure gradient, leading to a buoyant force, is a different thing.

That is the thing in this case !
and
pressure is force / area, that force may gravitational or something else, whatever

 

[Orodruin]

That is the thing in this case !

For the buoyant force, yes. This is just where Archimedes' principle comes from.

Also, you are wrong in your statement that pressure is a result from gravity:

pressure is force / area, that force may gravitational or something else, whatever

Gravitational force is a force on a mass, not an area force. That this force leads to internal forces causing a pressure gradient is something else entirely. The pressure force itself is a contact force, it certainly is not a gravitational force.

What you quoted from Dale and claimed was wrong was not a statement about the buoyant force, it was a statement about pressure. Pressure can be quite relevant even if the net buoyant force is zero - just go diving without equilibrating the pressure in your ears and you will see - or my favourite when flying, closing an empty PET bottle at maximum altitude and observing the effects as the flight descends.

 

[person_random_normal]

Pressure can be quite relevant even if the net buoyant force is zero

?

if we have pressure varying throughout the liquid column , buoyant force is non zero

 

[Orodruin]

?

if we have pressure varying throughout the liquid column , buoyant force is non zero

Poor choice of words, intended net buoyancy. This is the buoyant force minus the gravitational force.

Edit: Actually, not bad choice of words. I was talking about a situation where there is no (significant) gravitational field leading to a pressure gradient - as was Dale. What you will feel in your ears when you dive or go flying is not the result of a pressure gradient on your body - it is a very local phenomenon based on the pressure difference between the outside and inside of your ears.

 

[person_random_normal]

Hey Orodruin
what is this happening when i see your post #10 i can read this

For the buoyant force, yes. This is just where Archimedes' principle comes from.

What you quoted from Dale and claimed was wrong was not a statement about the buoyant force, it was a statement about pressure. Pressure can be quite relevant even if the net buoyant force is zero - just go diving without equilibrating the pressure in your ears and you will see - or my favourite when flying, closing an empty PET bottle at maximum altitude and observing the effects as the flight descends

but when i click on the reply option i can see this

For the buoyant force, yes. This is just where Archimedes' principle comes from.

Also, you are wrong in your statement that pressure is a result from gravity:

Gravitational force is a force on a mass, not an area force. That this force leads to internal forces causing a pressure gradient is something else entirely. The pressure force itself is a contact force, it certainly is not a gravitational force.

What you quoted from Dale and claimed was wrong was not a statement about the buoyant force, it was a statement about pressure. Pressure can be quite relevant even if the net buoyant force is zero - just go diving without equilibrating the pressure in your ears and you will see - or my favourite when flying, closing an empty PET bottle at maximum altitude and observing the effects as the flight descends

why am i not seeing the underlined thing while just viewing the thread
i asked this to you cause you are a staff member of PF

<<Mentor note: Edited for quotes>>

 

[Orodruin]

Please use quotes properly. Otherwise it is impossible to know what you are saying and what you are quoting. I edited the post shortly after posting it. You must have loaded it in the meantime.

 

[person_random_normal]

Poor choice of words, intended net buoyancy. This is the buoyant force minus the gravitational force.

Edit: Actually, not bad choice of words. I was talking about a situation where there is no (significant) gravitational field leading to a pressure gradient - as was Dale. What you will feel in your ears when you dive or go flying is not the result of a pressure gradient on your body - it is a very local phenomenon based on the pressure difference between the outside and inside of your ears.

this has nothing to do with buoyancy,
buoyancy is resultant of all the 'local' forces (exerted by fluid on the body inside the fluid)

 

[person_random_normal]

Please use quotes properly. Otherwise it is impossible to know what you are saying and what you are quoting. I edited the post shortly after posting it. You must have loaded it in the meantime.

Sorry

 

[person_random_normal]

murlidharn,
have you got this all ??

 

[Orodruin]

murlidharn,
have you got this all ??

Of course he has not, he has not been logged in since before post #2 was made.

 

[Orodruin]

this has nothing to do with buoyancy,
buoyancy is resultant of all the 'local' forces (exerted by fluid on the body inside the fluid)

Exactly, neither did Dale's quote that you claim is wrong. It never mentioned buoyancy. Please read the posts that you are going to claim are wrong.

 

[sophiecentaur]

This thread has veered right away from the OP. The whole of the question involves a 'real' earthbound situation and its level of knowledge requires a suitable answer and not a high level PF response plus a squabble amongst the better informed.
If the OP ever returns, I would like to reassure him / her that the first level answer to this question is fairly simple:
Gravity causes the pressure under water (On Earth, of course). That pressure at any level is due to the weight of water above (forget about the atmosphere and its pressure, it is only an added sophistication). The lower you go, the greater the pressure. Fluid pressure acts in all directions (up/down/sideways) and will be the same at that level, all over a bath / lake / ocean. It's there whether or not there is an object for it to act on and a fluid will flow until the pressure balances out everywhere.
Assume, for simplicity, that we are dealing with a cylinder with a vertical axis; you can extend the argument to any shape, later. The upwards pressure on the bottom face of the cylinder is greater than the downwards pressure on the top. The pressure against the sides is the same in all directions at any level, so it cancels out. The buoyant force ('upthrust' was our favourite word at school and still is, with students) will depend on the area of the cylinder faces (Pressure times area). The pressure depends on the height difference so the upthrust will be equal to the volume occupied by the cylinder (the volume of water that's 'displaced') times the density of the water that isn't there times g. This is Archimedes' Principle.
Note, for cylinders of the same volume, the buoyant force will be the same. The distance from top to bottom may be less but the total area will be more so you get the same answer.

 

[Dale]

That is the thing in this case !
and
pressure is force / area, that force may gravitational or something else, whatever

For A to cause B there are several conditions. Most importantly, A must be a necessary and sufficient condition for B. As I have shown above, gravity is neither necessary nor sufficient for pressure, therefore gravity is not the cause of pressure.

In this case there is gravity and there is pressure and buoyancy is related to both, but gravity is still not the cause of pressure. This is important because of the logic of the OP, which goes: gravity causes pressure, gravity points down, therefore pressure must point down. The recognition that gravity does not cause pressure allows the OP to then learn what does cause it, and then correct his chain of logic.

Again, gravity does not cause pressure. It is neither necessary nor sufficient. Please do not post further misinformation to the effect that it is the cause.

 

[sophiecentaur]

For A to cause B there are several conditions. Most importantly, A must be a necessary and sufficient condition for B. As I have shown above, gravity is neither necessary nor sufficient for pressure, therefore gravity is not the cause of pressure.

In this case there is gravity and there is pressure and buoyancy is related to both, but gravity is still not the cause of pressure. This is important because of the logic of the OP, which goes: gravity causes pressure, gravity points down, therefore pressure must point down. The recognition that gravity does not cause pressure allows the OP to then learn what does cause it, and then correct his chain of logic.

Again, gravity does not cause pressure. It is neither necessary nor sufficient. Please do not post further misinformation to the effect that it is the cause.

There is concrete thinking and there is formal thinking. All your points are quite correct (unarguable, in fact) but are they helping a questioner who wants a concrete view of the phenomenon? (It's a 'B' question)

 

[Dale]

Gravity causes the pressure under water (On Earth, of course).

Not you too. No, gravity does not cause pressure! See above. If I take a scuba tank and fill it up, then the pressure is much higher than it was previously, but the gravity is not any different.

Gravity is not the cause of pressure. Full stop.

For a hydrostatic fluid gravity causes a pressure gradient. Gravity does not cause fluid pressure, gravity plus the hydrostatic condition together imply a pressure gradient.

The pressure is the isotropic part of the internal stress within the fluid, it is the force per unit area normal to a surface, which means that the direction of the force from pressure depends on the direction of the surface, not the direction of gravity.

 

[Dale]

There is concrete thinking and there is formal thinking. All your points are quite correct (unarguable, in fact) but are they helping a questioner who wants a concrete view of the phenomenon? (It's a 'B' question)

The OP has presented a specific chain of logic which is based on a flawed premise. I don't know how you expect him to learn if the flawed premise is not addressed. If you (falsely) agree and say "gravity causes pressure" then his reasoning that "therefore it must point down" is much harder to address.

It is not turning a B question into an A to point out a false premise. The part that is making it difficult is all of the other respondents who are arguing against the "unarguable".

 

[sophiecentaur]

gravity causes pressure, gravity points down, therefore pressure must point down.

The same argument could have been made about the function of a see-saw. Gravity acts downwards so the lighter person should move down. Reductio ad absurdum can be a good argument.

Gravity is not the cause of pressure. Full stop.

Hmm. The pressure at the depth of water in this particular context, is only there because of the local gravitational field. ("full stop" ) That is the level of the question. Specific answer to specific questions are quite acceptable in many circumstances. In circuit questions, we quite happily talk about the "battery" in the circuit and that is as good as 'emf source'. I think you should give the thread some slack and acknowledge that it's horses for courses. If no one had brought up that issue in the first place we would have put it to bed with three or four posts. Someone should probably have included a bit of a caveat with the words 'in this case, the pressure is due to the gravity' near the top then we wouldn't be getting hot under the collar.
Like I said, earlier, concrete and formal explanations both have their place. WE both know that, if you google with the term 'hydrostatic pressure' you will find
P = ρhg in pretty much every hit. That's all the OP needed.

 

[Dale]

The same argument could have been made about the function of a see-saw. Gravity acts downwards so the lighter person should move down. Reductio ad absurdum can be a good argument.

That actually was exactly the other argument that I was considering.

Hmm. The pressure at the depth of water in this particular context, is only there because of the local gravitational field. ("full stop" )

No. Consider an object submerged in a hydrostatic fluid inside a pressure vessel. The pressure can be substantially increased independently of the gravitational field. Only the pressure gradient is there because of the gravitational field.

Specific answer to specific questions are quite acceptable in many circumstances.

I do agree with this as long as the specific answer does not incorrectly teach a wrong general principle. Saying that pressure is caused by gravity is flat out wrong, both in general and in specific. It was stated by the OP (and now by two others including yourself), so clearly it is a common misconception.

if you google with the term 'hydrostatic pressure' you will find
P = ρhg in pretty much every hit. That's all the OP needed.

I don't think so. I don't see any indication that the OP is not familiar with the formula for hydrostatic pressure. He just didn't understand how it could point any direction other than downwards given the premise that it is caused by gravity. Citing the formula doesn't address the specific reasoning of the OP.

 

[Orodruin]

is only there because of the local gravitational field.

(My emphasis)
No, this is definitely false. Pressure is note dependent on the local gravitational field, even in hydrostatics. It is accumulated from the global matter distribution, the fluid state and distribution.

 

[Chestermiller]

I agree with Dale. The OP seems to think that a gravitational field is the only thing that can cause pressure in a fluid. This misconception needs to be corrected before proceeding further with the actual discussion of his question.

Here are some additional features of pressure that the OP needs to understand:

1. As sophiecentaur points out, according to Pascal's principle, at a given location in a fluid, pressure acts equally in all directions. We say that pressure is an isotropic stress.

2. At any location in a fluid, the pressure force per unit area exerted by the fluid on any solid boundary surface or, for that matter, any conceptual boundary surface between two adjacent parcels of fluid within the bulk of the fluid, always acts perpendicular to the surface. This applies irrespective of the orientation of the surface. The surface can be horizontal, vertical, or at any oddball orientation. This is what Dale was saying in one of his posts.

3. In hydrostatic equilibrium situations, fluid pressure increases in the direction of the gravitational attraction.

4. To get the buoyant force on an object of arbitrary shape at hydrostatic equilibrium, one can integrate the pressure force per unit area vectorially over the entire surface of the object, taking into account (of course) the fact that the pressure is acting perpendicular to the surface of the object at each location on its surface. But, this gives exactly the same result as Archimedes principle, to wit the buoyant force is just equal to the weight of the displaced volume of fluid.

 

[russ_watters]

I agree that the main issue here is the idea that pressure can "change direction", not what "causes" it.

It may be useful to consider what happens when you depress a piston into a cylinder containing a fluid. Clearly, the piston applies a force in one direction. It may be easy to see how you get a reaction in the opposite direction, but what about the pressure applied to the sides of the piston...?

 

[Dale]

It may be useful to consider what happens when you depress a piston into a cylinder containing a fluid. Clearly, the piston applies a force in one direction. It may be easy to see how you get a reaction in the opposite direction, but what about the pressure applied to the sides of the piston...?

To expand on that, consider the resulting stream of fluid if a hole is poked in the side.

 

[sophiecentaur]

The OP seems to think that a gravitational field is the only thing that can cause pressure in a fluid.

You could well be right but, in the context of Buoyancy of a floating object (see the title) than the only relevant thing that produces the pressure is the weight of fluid on top and that is not caused by anything other than g (pretty well uniform at any relevant height). After a description around Archimedes' principle, 'other causes' of pressure could have been introduced - after getting some response from the OP.
Pascal's Principle was a good idea to introduce and it links (with a nice authoritative name) the downwards force due to gravity with a force in any other direction.
What is the point of introducing other reasons for the existence of pressure in order to explain flotation, which happens (in virtually any situation that I can think of) in bodies of fluid under the influence of gravity. This is a B QUESTION so why not limit replies appropriately? I am not arguing with any of the Physics that's been quoted here but I think all that stuff may have driven the OP away. Did we want that?

 

[sophiecentaur]

PF does spend a lot of time discussing the way terms are or should be used and it is not always fruitful. I really feel that they should be used according to context.

BTW, I Googled "Hydrostatic Pressure" and the passage at the very top of the page said
"Hydrostatic pressure is the pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. Hydrostatic pressure increases in proportion to depth measured from the surface because of the increasing weight of fluid exerting downward force from above."

Is that general enough to be correct? I would agree that it's not but it's what's behind Archimedes Principle. Is it not better to use the term Hydraulic Pressure or just Pressure to describe the pressure to all possible causes?

 

[Chestermiller]

You could well be right but, in the context of Buoyancy of a floating object (see the title) than the only relevant thing that produces the pressure is the weight of fluid on top and that is not caused by anything other than g (pretty well uniform at any relevant height). After a description around Archimedes' principle, 'other causes' of pressure could have been introduced - after getting some response from the OP.
Pascal's Principle was a good idea to introduce and it links (with a nice authoritative name) the downwards force due to gravity with a force in any other direction.
What is the point of introducing other reasons for the existence of pressure in order to explain flotation, which happens (in virtually any situation that I can think of) in bodies of fluid under the influence of gravity. This is a B QUESTION so why not limit replies appropriately? I am not arguing with any of the Physics that's been quoted here but I think all that stuff may have driven the OP away. Did we want that?

The OP was asking about the physical mechanism responsible for buoyancy. But, to start with, he implied that pressure is caused only by gravity. Dale felt it was necessary to correct the frequent misconception of PF posters that gravity is the only thing that can give rise to pressure, before proceeding to a discussion of the actual physical mechanism. I also felt compelled to set the record straight on this.

With regard tot he actual physical mechanism, Shreyas Samudra indicated by the buoyant force could be determined simply by integrating the pressure (as a scalar) over the surface area of the body. I felt compelled to correct this, and add that the integration had to be done vectorially, taking into account the normalcy of the pressure force at each location on the surface.

 

[sophiecentaur]

The OP was asking about the physical mechanism responsible for buoyancy. But, to start with, he implied that pressure is caused only by gravity. Dale felt it was necessary to correct the frequent misconception of PF posters that gravity is the only thing that can give rise to pressure, before proceeding to a discussion of the actual physical mechanism. I also felt compelled to set the record straight on this.

With regard tot he actual physical mechanism, Shreyas Samudra indicated by the buoyant force could be determined simply be integrating the pressure (as a scalar) over the surface area of the body. I felt compelled to correct this, and add that the integration had to be done vectorially, taking into account the normalcy of the pressure force at each location on the surface.

I agree with nearly all of that. But, in the context, the only 'cause' is gravity. We're talking elementary physics where abstract concepts like Pressure are certainly not appreciated fully by students. If the OP had only worded his question "the cause of THE pressure is gravity" then how could anyone have objected? Overkill responses can be very counter productive - our guy seems to have just gone away as a result.

 

[Chestermiller]

I agree with nearly all of that. But, in the context, the only 'cause' is gravity. We're talking elementary physics where abstract concepts like Pressure are certainly not appreciated fully by students. If the OP had only worded his question "the cause of THE pressure is gravity" then how could anyone have objected? Overkill responses can be very counter productive - our guy seems to have just gone away as a result.

I disagree. We owe it to our members to correct misconceptions, particularly misconceptions that, experience shows, are shared by many others. With regard to the OP, if he has left, that is unfortunate. But he is certainly not the only member who reads this thread and who can benefit from our correcting this misconception (rather than allowing it to stand and be reinforced).

In the end, it's just a judgment call.

 

[Dale]

Overkill responses can be very counter productive

If you felt that it was overkill then you could have simply formulated your own simpler but correct response instead of going out of your way (multiple times) to argue against a correct response (indeed one that you yourself describe as "unarguable").

I certainly have no objection to other correct explanations.

 

[sophiecentaur]

If you felt that it was overkill then you could have simply formulated your own simpler but correct response instead of going out of your way (multiple times) to argue against a correct response (indeed one that you yourself describe as "unarguable").

I thought that was exactly what I did in post #18. Perhaps I should have started the post with my explanation and ended with the remark about the 'high level' disagreements. I never argued against the more advanced stuff about pressure (I agree with it all, of course). I guess a less grumpy response on my part would have avoided this. My apologies.