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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