# Dictionary Definition

buoyancy

### Noun

1 cheerfulness that bubbles to the surface [syn:
perkiness]

2 the property of something weightless and
insubstantial [syn: airiness]

3 irrepressible liveliness and good spirit; "I
admired his bouyancy and persistent good humor" [syn: irrepressibility]

# User Contributed Dictionary

## English

### Noun

buoyancy- the upward force on a body immersed or partly immersed in a fluid
- In the context of "by extension": resilience or cheerfulness

#### Translations

physics: upward force on an immersed body

resilience or cheerfulness

- Finnish: palautuvuus, peräänantamattomuus
- German: Belastbarkeit, Fröhlichkeit

##### Translations to be checked

- ttbc Spanish: Centro de carena

### See also

# Extensive Definition

In physics, buoyancy is the upward
force on an object
produced by the surrounding liquid or gas in which it is fully or
partially immersed, due to the pressure difference of the
fluid between the top and bottom of the object. The net upward
buoyancy force is equal to the magnitude of the weight of fluid
displaced by the body. This force enables the object to float or at
least to seem lighter. Buoyancy is important for many vehicles such as boats, ships, balloons, and airships, and plays a role in
diverse natural phenomena such as sedimentation.

## Archimedes' principle

It is named after Archimedes of
Syracuse,
who first discovered this law. Vitruvius
(De
architectura IX.9–12) recounts the famous story of Archimedes
making this discovery while in the bath (for which see eureka) but
the actual record of Archimedes' discoveries appears in his
two-volume work, On Floating Bodies. The ancient Chinese
child prodigy Cao Chong also
applied the principle of buoyancy in order to measure the accurate
weight of an elephant, as described in the Sanguo
Zhi.

This is true only as long as one can neglect the
surface
tension (capillarity) acting on the body.

The weight of the displaced fluid is directly
proportional to the volume of the displaced fluid (specifically if
the surrounding fluid is of uniform density). Thus, among objects
with equal masses, the one with greater volume has greater
buoyancy.

Suppose a rock's weight is measured as 10
newtons when suspended
by a string in a vacuum. Suppose that when the rock is lowered by
the string into water, it displaces water of weight 3 newtons. The
force it then exerts on the string from which it hangs will be 10
newtons minus the 3 newtons of buoyant force:
10 − 3 = 7 newtons. This same principle even
reduces the apparent weight of objects that have sunk completely to
the sea floor, such as the sunken battleship USS
Arizona at Pearl
Harbor, Hawaii. It is generally easier to lift an object up
through the water than it is to finally pull it out of the
water.

The density of the immersed object relative to
the density of the fluid is easily calculated without measuring any
volumes:

- \frac = \frac \,

## Forces and equilibrium

Pressure increases with depth below the surface of a liquid. Any object with a non-zero vertical depth will see different pressures on its top and bottom, with the pressure on the bottom being higher. This difference in pressure causes the upward buoyancy force.The hydrostatic
pressure at a depth h in a fluid is given by

P = \rho h g\,

where

- \rho\, is the density of the fluid,
- h\, is the depth (negative height), and
- g\, is the standard gravity (\scriptstyle\approx\, -9.8 N/kg on Earth)

The force due to pressure is simply the pressure
times the area. Using a cube as an example, the pressure on the top
surface (for example) is thus

- F_ = d^2 \rho h_ g \,

where d is the length of the cube's edges. The
buoyant force is then the difference between the forces at the top
and bottom

- F_ = d^2 \rho h_ g - d^2 \rho h_ g \,

which reduces to

- F_ = d^2 \rho g ( - )\,

in the case of a cube, the difference in h\,
between the top and bottom is -d\,, so

- F_ = - d^3 \rho g \,

or

- F_\mathrm = - \rho V g \,

- where V is the volume of the cube, d^3\,

The negative magnitude implies that it is in the
opposite direction to gravity. It can be demonstrated
mathematically that this formula holds true for any submerged
shape, not just a cube.

The buoyancy of an object depends, therefore,
only on two factors: the object's submerged volume, and, the density of the surrounding
fluid. The greater the object's volume and surrounding density of
the fluid, the more buoyant force it experiences. Thus the
magnitude of the buoyant force is simply equal to the weight of the displaced fluid. In
this context, displacement
is the term used for the weight of the displaced fluid and, thus,
is an equivalent term to buoyancy.

The total force on the object is thus the net
force of buoyancy and the object's weight

- F_\mathrm = mg - \rho V g \,

If the buoyancy of an (unrestrained and
unpowered) object exceeds its weight, it tends to rise. An object
whose weight exceeds its buoyancy tends to sink.

It is common to define a buoyant mass mb that
represents the effective mass of the object with respect to
gravity m_ = m_ \cdot \left( 1 - \frac \right)\,

where m_\, is the true (vacuum) mass of the
object, whereas ρo and ρf are the average densities of the object
and the surrounding fluid, respectively. Thus, if the two densities
are equal, ρo = ρf, the object appears to be weightless. If the
fluid density is greater than the average density of the object,
the object floats; if less, the object sinks.

### Compressive fluids

The atmosphere's density depends upon altitude.
As an airship rises in
the atmosphere, its buoyancy reduces as the density of the
surrounding air reduces. The density of water is essentially
constant: as a submarine expels water from
its buoyancy tanks (by pumping them full of air) it rises because
its volume stays the same (the volume of water it displaces if it
is fully submerged) while its weight is decreased.

### Compressible objects

As a floating object rises or falls the forces external to it change and, as all objects are compressible to some extent or another, so does the object's volume. Buoyancy depends on volume and so an object's buoyancy reduces if it is compressed and increases if it expands.If an object at equilibrium has a compressibility less
than that of the surrounding fluid, the object's equilibrium is
stable and it remains at rest. If, however, its compressibility is
greater, its equilibrium is then unstable, and it rises and
expands on the slightest upward perturbation, or falls and
compresses on the slightest downward perturbation.

Submarines rise and dive by filling large tanks
with seawater. To dive, the tanks are opened to allow air to
exhaust out the top of the tanks, while the water flows in from the
bottom. Once the weight has been balanced so the overall density of
the submarine is equal to the water around it, it has neutral
buoyancy and will remain at that depth. Normally, precautions are
taken to ensure that no air has been left in the tanks. If air were
left in the tanks and the submarine were to descend even slightly,
the increased pressure of the water would compress the remaining
air in the tanks, reducing its volume. Since buoyancy is a function
of volume, this would cause a decrease in buoyancy, and the
submarine would continue to descend.

The height of a balloon tends to be stable. As a
balloon rises it tends to increase in volume with reducing
atmospheric pressure, but the balloon's cargo does not expand. The
average density of the balloon decreases less, therefore, than that
of the surrounding air. The balloon's buoyancy reduces because the
weight of the displaced air is reduced. A rising balloon tends to
stop rising. Similarly a sinking balloon tends to stop
sinking.

## Density

If the weight of an object is less than the weight of the fluid the object would displace if it were fully submerged, then the object has an average density less than the fluid and has a buoyancy greater than its weight. If the fluid has a surface, such as water in a lake or the sea, the object will float at a level where it displaces the same weight of fluid as the weight of the object. If the object is immersed in the fluid, such as a submerged submarine or air in a balloon, it will tend to rise. If the object has exactly the same density as the fluid, then its buoyancy equals its weight. It will tend neither to sink nor float. An object with a higher average density than the fluid has less buoyancy than weight and it will sink. A ship floats because although it is made of steel, which is more dense than water, it encloses a volume of air and the resulting shape has an average density less than that of the water.## References

## See also

## External links

buoyancy in Arabic: طفو

buoyancy in Bulgarian: Плаваемост

buoyancy in Catalan: Principi d'Arquimedes

buoyancy in Czech: Archimédův zákon

buoyancy in Danish: Opdrift (statisk)

buoyancy in German: Archimedisches Prinzip

buoyancy in Estonian: Üleslükkejõud

buoyancy in Spanish: Principio de
Arquímedes

buoyancy in Esperanto: Flosemo

buoyancy in French: Poussée d'Archimède

buoyancy in Hindi: उत्प्लावन बल

buoyancy in Croatian: Arhimedov zakon

buoyancy in Italian: Principio di
Archimede

buoyancy in Hebrew: חוק ארכימדס

buoyancy in Georgian: არქიმედეს კანონი

buoyancy in Kazakh: Архимед заңы

buoyancy in Hungarian: Arkhimédész
törvénye

buoyancy in Malay (macrolanguage):
Keapungan

buoyancy in Dutch: Wet van Archimedes

buoyancy in Japanese: アルキメデスの原理

buoyancy in Norwegian Nynorsk: Oppdrift

buoyancy in Polish: Prawo Archimedesa

buoyancy in Portuguese: Princípio de
Arquimedes

buoyancy in Romanian: Principiul lui
Arhimede

buoyancy in Russian: Закон Архимеда

buoyancy in Simple English: Buoyancy

buoyancy in Slovak: Archimedov zákon

buoyancy in Slovenian: Arhimedov zakon

buoyancy in Serbian: Архимедов закон

buoyancy in Finnish: Noste

buoyancy in Swedish: Arkimedes princip

buoyancy in Vietnamese: Lực đẩy Archimedes

buoyancy in Ukrainian: Закон Архімеда

buoyancy in Chinese: 浮力

# Synonyms, Antonyms and Related Words

adaptability, airiness, ascent, bounce, bounciness, breeziness, bubbliness, buoyance, carefreeness, chirpiness, daintiness, debonairness, delicacy, downiness, effervescence, elasticity, ethereality, extensibility, exuberance, flexibility, floatability, fluffiness, foaminess, frothiness, gentleness, give, gossameriness, jauntiness, lack of weight,
levitation, levity, light heart, lightheartedness,
lightness, lightsomeness, liveliness, perkiness, pertness, rebound, resilience, resiliency, responsiveness, snap, softness, spring, springiness, stretch, stretchability, stretchiness, tenderness, tone, tonicity, tonus, unheaviness, volatility, weightlessness, yeastiness