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. Archimedes' principle is a
law of physics fundamental to fluid mechanics.
Archimedes of Syracuse formulated this principle,
which bears his name.
Explanation
In his treatise on hydrostatics, On Floating
Bodies, Archimedes states:
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
Practically seen, the Archimedes principle
allows the volume of an object to be measured
by measuring the volume of the liquid it displaces
after submerging, and the buoyancy of an object
immersed in a liquid to be calculated.
For any immersed object, the volume of the
submerged portion equals the volume of fluid
it displaces. E.g., by submerging in water
half of a sealed 1-liter container, we displace
a half-liter volume of fluid, regardless of
the container's contents. If we fully submerge
the same container, we then displace one liter
of liquid, which exactly equals the volume
of the 1-liter container.
An empty 1-litre plastic bottle released in
the air will fall down due to the gravitational
force of the Earth acting on it. If the same
bottle is released under water, the same gravitational
force acts on it, but it will be pushed upwards
towards the surface of the water. The extra
force that pushes the bottle upwards comes
from the upthrust or Archimedes force.
Formula
Cube immersed in a fluid, with its sides parallel
to the direction of gravity. The fluid will
exert a normal force on each face, and therefore
only the forces on the top and bottom faces
will contribute to buoyancy. The pressure
difference between the bottom and the top
face is directly proportional to the height.
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. By extending this reasoning
to irregular shapes, we can see that, whatever
the shape of the submerged body, the buoyant
force is equal to the weight of the fluid
displaced.
The weight of the displaced fluid is directly
proportional to the volume of the displaced
fluid. The weight of the object in the fluid
is reduced, because of the force acting on
it, which is called upthrust. In simple terms,
the principle states that the buoyant force
on an object is equal to the weight of the
fluid displaced by the object, or the density
of the fluid multiplied by the submerged volume
times the gravitational constant, g. Thus,
among completely submerged objects with equal
masses, objects with greater volume have greater
buoyancy.
Suppose a rock's weight is measured as 10
Newtons when suspended by a string in a vacuum
with gravity acting on it. Suppose that when
the rock is lowered into water, it displaces
water of weight 3 Newtons. The force it then
exerts on the string from which it hangs would
be 10 Newtons minus the 3 Newtons of buoyant
force: 10 − 3 = 7 Newtons. Buoyancy reduces
the apparent weight of objects that have sunk
completely to the sea floor. It is generally
easier to lift an object up through the water
than it is to pull it out of the water.
For a fully submerged object, Archimedes'
principle can be reformulated as follows,
then inserted into the quotient of weights,
which has been expanded by the mutual volume
yields the formula below. The density of the
immersed object relative to the density of
the fluid can easily be calculated without
measuring any volumes:
(This formula is used for example in describing
the measuring principle of a dasymeter and
of hydrostatic weighing.)
Example: If you drop wood into water, buoyancy
will keep it afloat.
Example: A helium balloon in a moving car.
When increasing speed or driving in a curve,
the air moves in the opposite direction to
the car's acceleration. However, due to buoyancy,
the balloon is pushed "out of the way" by
the air, and will actually drift in the same
direction as the car's acceleration.
When an object is immersed in a liquid, the
liquid exerts an upward force, which is known
as the buoyant force, that is proportional
to the weight of the displaced liquid. The
sum force acting on the object, then, is proportional
to the difference between the weight of the
object and the weight of displaced liquid,
hence equilibrium buoyancy is achieved when
these two weights are equal consider a ball
immersed in a liquid.the liquid experiences
an upthrust which is the buoyant force.in
otherwise is proportional to the weight of
the liquid displaced.the total force acting
on the object at thatb point in time is proportional
to the difference between the weight exacted
by the object and the weight of the displaced
liquid hence equilibrium is attend.
Refinements
Archimedes' principle does not consider the
surface tension acting on the body. Moreover,
Archimedes' principle has been found to break
down in complex fluids.
Principle of flotation
Archimedes' principle shows buoyant force
and displacement of fluid. However, the concept
of Archimedes' principle can be applied when
considering why objects float. Proposition
5 of Archimedes' treatise On Floating Bodies
states that:
Any floating object displaces its own weight
of fluid.
— Archimedes of Syracuse
In other words, for an object floating on
a liquid surface or floating submerged in
a liquid the weight of the displaced liquid
equals the weight of the object. Thus, only
in the special case of floating does the buoyant
force acting on an object equal the objects
weight. Consider a 1-ton block of solid iron.
As iron is nearly eight times denser than
water, it displaces only 1/8 ton of water
when submerged, which is not enough to keep
it afloat. Suppose the same iron block is
reshaped into a bowl. It still weighs 1 ton,
but when it is put in water, it displaces
a greater volume of water than when it was
a block. The deeper the iron bowl is immersed,
the more water it displaces, and the greater
the buoyant force acting on it. When the buoyant
force equals 1 ton, it will sink no farther.
When any boat displaces a weight of water
equal to its own weight, it floats. This is
often called the "principle of flotation":
A floating object displaces a weight of fluid
equal to its own weight. Every ship, submarine,
and dirigible must be designed to displace
a weight of fluid equal to its own weight.
A 10,000-ton ship must be built wide enough
to displace 10,000 tons of water before it
sinks too deep in the water. The same is true
for vessels in air: a dirigible that weighs
100 tons needs to displace 100 tons of air.
If it displaces more, it rises; if it displaces
less, it falls. If the dirigible displaces
exactly its weight, it hovers at a constant
altitude.
It is important to realize that, while they
are related to it, the principle of flotation
and the concept that a submerged object displaces
a volume of fluid equal to its own volume
are not Archimedes' principle. Archimedes'
principle, as stated above, equates the buoyant
force to the weight of the fluid displaced.
See also
"Eureka", reportedly exclaimed by Archimedes
upon discovery that the volume of displaced
fluid is equal to the volume of the submerged
object
References
