Buoyancy
and Archimedes Principle
WHAT IS BUOYANCY?
Buoyancy is a force exerted by a liquid or
gas that opposes an object's weight. Buoyancy can also be
stated as the weight of displaced fluid. Pressure in a fluid
increases with depth as a result of the weight of the overlying
fluid (see hydrostatic
pressure). Thus an object submerged in a fluid, experiences
greater pressure at the bottom of the fluid than at the top.
This difference in pressure results in a net force that tends
to accelerate an object upwards. The magnitude of that force
is proportional to the difference in the pressure between
the top and the bottom of the column, and is also equivalent
to the weight of the fluid that would otherwise occupy the
column, i.e. the displaced fluid. It is for that reason that
an object whose density is greater than that of the fluid
that it is submerged in will sink. Archimedes' principle allows
for the experimental determination of density by providing
an easy and accurate method for determining the volume of
an irregularly shaped object. See also: Mass,
Volume Density..for interactive activities.
Archimedes' principle is named after Archimedes
of Syracuse, who first discovered this law in 212 B.C. Archimedes'
principle may be stated thus in terms of forces:
Any object, wholly or partially immersed
in a fluid, is buoyed up by a force equal to the weight of
the fluid displaced by the object.
— Archimedes of Syracuse
ABOUT ARCHIMEDES
Archimedes was the son of an astronomer. He had traveled
to Alexandria, Egypt, a place of great learning, where
he studied the works of some other mathematicians, like
Euclid and Conon. Archimedes helped his friend King
Hiero II by creating machines for the king's army. The
pulley was one of these inventions, but Archimedes thought
the study of mathematics was the most important thing
he could do. Archimedes wrote some books about Mathematics,
including On Floating Bodies. Archimedes died
during the Siege of Syracuse when he was killed by a
Roman soldier despite orders that he should not be harmed 
For objects, floating and sunken, and in
gases as well as liquids, Archimedes' principle may be stated
in terms of forces:
Any object, wholly or partially immersed
in a fluid, is buoyed up by a force equal to the weight
of the fluid displaced by the object. with the clarifications
that for a sunken object the volume of displaced fluid is
the volume of the object, and for a floating object on a
liquid, the weight of the displaced liquid is the weight
of the object.

Archimedes' principle indicates
that the upward buoyant force that is exerted on a
body immersed in a fluid, whether fully or partially
submerged, is equal to the weight of the fluid that
the body displaces.
Notice that the acting forces increase
with the depth of the fluid.
The resultant of all forces upward
is called buoyancy and is equal to the weight of the
displaced fluid.

Archimedes principle allows the buoyancy
of an object partially or wholly immersed in a liquid to be
calculated. The downward force on the object is simply its
weight. The upward, or buoyant, force on the object is that
stated by Archimedes' principle, above. Thus the net upward
force on the object is the difference between the buoyant
force and its weight. If this net force is positive, the object
floats; if negative, the object sinks; and if zero, the object
is neutrally buoyant  that is, it remains in place without
either rising or sinking. In simple words Archimedes principle
states that when a body is partially or completely immersed
in a fluid, it experiences an apparent loss in weight which
is equal to the weight of the fluid displaced by the immersed
part of the body.
Note: Archimedes' principle does not
consider the surface tension (capillarity) acting on the body
but this additional force modifies only the amount of fluid
displaced, so the principle that Buoyancy = weight of
displaced fluid remains valid.
Consider a cube immersed in a fluid, with
its sides parallel to the direction of gravity.. Only the
forces on the top and bottom faces of the cube will contribute
to buoyancy. The pressure difference between the bottom and
the top face is directly proportional to the height (difference
in depth). Multiplying the pressure difference by the area
of a face gives the net force on the cube  the buoyancy,
or the weight of the fluid displaced.
FORMULAS
For a fully submerged
object, Archimedes' principle can be formulated as
follows:
apparent immersed weight
= weight of object  weight of displaced fluid
density of object/density
of fluid = weight/(weight of displaced fluid)
density of object/density
of fluid =weight/(weight  apparent immersed weight)
__________________________
The "buoyancy
force" on a submerged body is directed
in the opposite direction to gravity and is equal
in magnitude to:
(density of fluid)(Volume of displace fluid)(acceleration)

When will an object float or balloon
rise?
A object will float in a fluid if the density
of that object is less than the density of the fluid.
Example: If you drop wood into water, buoyancy
will keep it afloat. Wood is less dense than water.
Hot air balloons rise into the air because
the density of the air (warmer air) inside the balloon is
less dense than the air outside the balloon (cooler air).
The balloon and the basket displaces a fluid that is heavier
than the balloon and the basket, so it has a buoyant force
acting on the system. Balloons tend to fly better in the morning,
when the surrounding air is cool.
SAMPLE
PROBLEM
A steel block with a density of 7800 kg/m3
is suspended from a string in a beaker of
water so that the block is completely submerged but not resting
on the bottom. The block is a
cube with sides of 3 cm (0.03 m).
Buoyant force = weight of displaced water
= mass of water * acceleration due to gravity
= density of water * volume of cube * g
= 1x10^{3} kg/m^{ 3} * 27*106 m3 9.8 m/s2
= 2.65 *101 N = 0.265 N
weight
of block = mass g
W= mg = 2.106 x 101 kg x 9.8 m/s2 = 2.106x9.8 x 101 kg*m/s2
= 20.64 x 101 N
= 2.064 N kg*m/s2 = N (Newton)
