The upward buoyant is a conservative force?

AI Thread Summary
The discussion centers on whether upward buoyancy is a conservative force, allowing for the assignment of potential values at various points. It is established that buoyancy can be considered conservative since it relates to gravitational forces, which are inherently conservative. The concept of buoyant potential is debated, with some asserting it should be defined similarly to gravitational potential, while others question its consistency across varying depths. The buoyant force is linked to pressure gradients rather than absolute pressure, and the work done in submerging objects is highlighted as a key factor in defining buoyant potential. Overall, the conversation emphasizes the need for clarity in understanding buoyant forces and their potential energy implications.
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The upward buoyant meets the definition of conservative force, ¿isn't it?
 
Please help me. In my country (Peru) this has caused quite a debate
 
Unfortunately I don't understand Spanish, but:

  • yes buoyancy is a conservative force;
  • it is possible to assign a numerical value for buoyant potential at any point: this is equal to pressure

For a start on further detail try this.
 
MrAnchovy said:
it is possible to assign a numerical value for buoyant potential at any point: this is equal to pressure
Common misconception. It is actually equal to weight density, not pressure.
 
I'm not sure of how "Bouyant Potential" could be defined. Its units would have to be in Joules, presumably.
 
What do you mean by weight density? Does it vary according to depth? If not, are you saying that buoyant potential is constant wrt depth? But the work done in submersing an object (of unit volume) from depth ## d ## to ## d + \delta d ## is obviously non-zero so buoyant potential cannot be equal at these two points? Are the statements ## \mathbf{f_B} = - \nabla p ## etc. in the wikipedia article linked to incorrect, or am I misinterpreting them?
 
The force which causes buoyancy is ultimately gravity which is conservative in Newtonian physics. If you pay attention to the gravitational potential energy of the fluid as well as that of the object then you can easily define the systems PE.
 
MrAnchovy said:
What do you mean by weight density?
Density is mass / volume. Weight density is weight / volume.
Does it vary according to depth?
Not significantly, since water is not very compressible.
If not, are you saying that buoyant potential is constant wrt depth?
The buoyancy of an object of a certain volume is essentially unchanged with depth.

The link says the buoyant force is equal to the gradient of pressure, not the pressure itself.
 
  • #10
sophiecentaur said:
I'm not sure of how "Bouyant Potential" could be defined. Its units would have to be in Joules, presumably.

I infer that it could be defined analgously to gravitational potential (Joules per unit mass), and electrical potential (Joules per unit charge) and, being the work done in submersing an object of unit volume from zero depth, would have units of Joules per unit volume.

I'll admit that I am not an expert in buoyancy and I have not confirmed the statements I have gleaned from Wikipedia, not having appropriate textbooks to hand. However the guy was desparate for an answer and no one else seemed to be interested - and the answers seem clear to me from the (mathematical) definition of a conservative field.
 
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  • #11
russ_watters said:
Density is mass / volume. Weight density is weight / volume. Not significantly, since water is not very compressible. The buoyancy of an object of a certain volume is essentially unchanged with depth.

The link says the buoyant force is equal to the gradient of pressure, not the pressure itself.

We are at cross-purposes. I am describing the buoyant potential, not the buoyant force. In a conservative field (where the curl of the force is zero, which it clearly is for buoyancy), force is the gradient of the potential.
 
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  • #12
It would help just to go back to basics and the elementary physics that's taught in school. How can there be any disagreement on this? The units and equations are all very well established. The same confusion occurs when talking about the gravitational force and potential inside a planet but it all fits perfectly with the basic theory.
 
  • #13
Back to basics:

Bouyant force per unit volume is equal to the weight of fluid displaced per unit volume i.e. the weight density ## \rho g ##. For an incompressible fluid (this is basic after all), the mass density ## \rho ## is constant.

Define the potential at the surface ## P(0) ## to be zero.

The potential at depth D, ## P(D) ## is defined as the work done in submersing an object of unit volume from the surface to depth ## D ## and is given by force x distance i.e. ## \rho g D ##.

Note that pressure in an incompressible fluid is also ## \rho g D ##.
 
  • #14
Thanks for you comments.
What do you think about the way I solve this problem:
A hemisphere of 8 kg mass and 20 cm radius is at the bottom of a tank containing water. Find out the minimum work that an agent must to do to extract the hemisphere of the water.(g = 10 m/s2)
Here I used the concept "buoyant potential energy"
http://1.bp.blogspot.com/-JCGQhbXlp...Y8/KFlG_qKBhpo/s1600/prob_ener_pot_hid_01.jpg
Please, look here how I solved this problem.
http://cpreuni.blogspot.com/2012/12/trabajo-minimo-para-sacar-un-hemisferio_16.html
The answer is 3,43 joules.
Thanks in advance for your attention
Greetings from Peru
 

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