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# Buoyancy

If one places a copper ball in a pail of water it will sink, whereas a wooden ball will float. Whether or not a given object will sink or float in a fluid is determined by the buoyant force on the object. The buoyant force is essentially caused by the difference between the pressure at the top of the object, which pushes it downward, and the pressure at the bottom, which pushes it upward. Since the pressure at the bottom is always greater than at the top, every object submerged in a fluid necessarily feels an upward buoyant force. Of course, objects also feel a downward force due to gravity, and the difference between the gravitational force and buoyant force on a submerged object determines whether that object will sink, or rise to the surface. If the weight is greater than the buoyant force, the object sinks, and vice versa. It was Archimedes (supposedly while in his bath), who realized that submerged objects always displace fluid upwards (the level of water in the bathtub rose when Archimedes got in). Thus, he reasoned that the buoyant force on an object must be equal to the weight of fluid that object displaces. If the weight of an object is greater than the weight of displaced fluid, it will sink, wherease if the weight of the object is less than the weight of displaced fluid, it will rise. Moreover, it is evident that the volume of displaced fluid is precisely equal to the volume of the submerged part of the object, so that the difference between the buoyant force and the weight is determined by the relative density of the object and the fluid. In particular, we come to Archimide's principle, which implies that

This explains why wood and styrofoam float on water, whereas concrete and steel sink. It also explains why it is nonetheless possible to make boats out of steel or even concrete. As long as there are portions of the boat below the surface of the water that are hollow (i.e. contain air), the effective density of the boat can be less than that of water even though the real density of the material is greater.

Next: Bernoulli's Principle Up: Fluids Previous: Pressure
modtech@theory.uwinnipeg.ca
1999-09-29