# The upward buoyant is a conservative force?

1. Mar 14, 2013

### orlan2r

2. Mar 15, 2013

### orlan2r

The upward buoyant meets the definition of conservative force, ¿isn't it?

3. Mar 15, 2013

### orlan2r

4. Mar 16, 2013

### MrAnchovy

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.

5. Mar 16, 2013

### Staff: Mentor

Common misconception. It is actually equal to weight density, not pressure.

6. Mar 16, 2013

### sophiecentaur

I'm not sure of how "Bouyant Potential" could be defined. Its units would have to be in Joules, presumably.

7. Mar 16, 2013

### MrAnchovy

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?

8. Mar 16, 2013

### Staff: Mentor

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.

9. Mar 16, 2013

### Staff: Mentor

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.

10. Mar 16, 2013

### MrAnchovy

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 text books to hand. However the guy was desparate for an answer and noone else seemed to be interested - and the answers seem clear to me from the (mathematical) definition of a conservative field.

Last edited: Mar 16, 2013
11. Mar 16, 2013

### MrAnchovy

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.

Last edited: Mar 17, 2013
12. Mar 17, 2013

### sophiecentaur

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. Mar 17, 2013

### MrAnchovy

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. Apr 21, 2013