## The buoyancy or Archimedean force

The force due to buoyancy is one of the most familiar forces occurring in a fluid and, rather famously, was known to Archimedes. It is the force that, among other things, allows objects to flow in water. The Archimedes principle is often stated as "Any object, partially or wholly immersed in a fluid, experiences an upward force equal to the weight of the fluid displaced by the object." Let's see why this is so.

Consider a container of still water and focus attention on a particular piece of water that is fully surrounded by other fluid. The parcel has a finite weight, of course, and it does not sink to the bottom of the container because it is held up by the pressure force provided by the rest of the fluid in the container. Because none of the water is moving, the weight of the parcel (its mass times the acceleration due to gravity, acting downward) must exactly equal the upward pressure forces provided by the rest of the fluid. Now, let us replace the parcel with a solid object of the same shape and size. The upward pressure force provided by the rest of the fluid remains the same; this, we just ascertained, is equal to the weight of the parcel of fluid displacedâ€”and this is Archimedes' principle. If the solid object is lighter than the weight of the fluid displaced, then there is a net upward force on it, and the object moves upward until it floats on the surface. If the solid object is heavier than the fluid displaced, the object sinks. These considerations apply to water itself. If we cool the water at the surface of the ocean, or add salt to it, it becomes more dense and therefore sinksâ€”and it can sink quite quickly. A parcel of water that is negatively buoyant at the surface of the polar ocean can sink to considerable depth in a concentrated convective plume in a matter of hours to days, with a corresponding vertical velocity of a few centimeters per second. Similarly, if we warm the water that is at the bottom of the ocean, it will become lighter and rise, although this tends to be a much slower process, spread out over a wide area.

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