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Convection/Archimedes Principle

  1. Jul 22, 2010 #1
    I have just noticed that several texts describe warm fluids rising relative to cooler fluids due to their lower density. I think there may be a problem with this hypothesis.

    Low relative density causes solids to rise because of a sufficient surface area to mass ratio which allows the greater pressure of fluid below the solid (comparted to the pressure of the fluid above the object) to overcome the gravitational force acting down on the solid.

    The problem with using low density to describe warm fluids rising, is that fluids like air, do not have a "surface" for the fluid below it to push on.

    I think it is the fact that the particles of the warm fluid are moving faster, which allows them to simply bounce harder and better overcome gravity than particles that are not.

    This is one of those cases, where I am almost sure I am correct over the text. So in reality, I'm probably wrong.

    What do you guys think?
  2. jcsd
  3. Jul 22, 2010 #2
    I am not sure exactly what you are saying here. Could you elaborate?

    I would disagree. A sphere of iron sinks in water. You can beat this sphere of iron into a thin sheet with a very high surface area to mass ratio, but it will still sink.

    Yes, this sounds more familiar. Buoyancy depends on relative densities, not on surface areas.

    I never thought of it that! I had simply accepted that the textbook explanation for the buoyancy of solids should automatically also apply to the buoyancy of fluids. However, the textbook explanation for solids does seem to me to apply to fluids perfectly well without the need to consider bouncing particles overcoming gravity.

    Within a large body of cool fluid (say air) at rest, a pocket of warmer air will float due to its lower density. As you say, there is no solid surface surrounding the pocket of warmer air, so how can the warm pocket be "pushed"? But it can be pushed. Solids can push on solids, solids and fluids can push on each other, and fluids can push on fluids.

    I'll make a couple of assumptions about a typical warm air pocket:

    1. Suppose that the warm pocket of air is of reasonable volume. That is, its surface area to volume ratio is low. As such, the rate at which the pocket's temperature is equalising with the surrounding cool air is also very low. The pocket's temperature is effectively constant.
    2. Assume for simplicity's sake that the warm air pocket is sufficiently large that any small eddies and turblent air currents across its surface are so small as to negligibly warp the pocket's boundary over time. The pocket's shape and volume are effectively constant.

    The warm air pocket can be then treated as a semi-permanent entity, able to maintain its shape and temperature for a long period of time. In other words, the warm air pocket can be treated as a solid in these respects.

    Going back to your question about the mechanism of the "pushing" of fluids against fluids:
    There is no solid surface surrounding the warm air pocket, but there is a boundary where the cool air ends and the warm air begins. This is not a flat, perfect boundary. It is surely active with turbulence and swirling currents (etc.). The boundary is messy, but it is still a surface which can be pushed.
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