In physics, buoyancy is the upward force on an object produced by the surrounding fluid (i.e., a liquid or a 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. Image File history File links No higher resolution available. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For other uses, see Force (disambiguation). ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... For other uses, see Liquid (disambiguation). ... For other uses, see Gas (disambiguation). ... This article is about pressure in the physical sciences. ... The Trikke is a Human Powered Vehicle (HPV) Automobiles are among the most commonly used engine powered vehicles. ... For other uses, see Boat (disambiguation). ... For other uses, see Ship (disambiguation). ... For other uses, see Balloon (disambiguation). ... USS Akron (ZRS-4) in flight, November 2, 1931 An airship or dirigible is a buoyant lighter-than-air aircraft that can be steered and propelled through the air. ... Sedimentation describes the motion of particles in solutions or suspensions in response to an external force such as gravity, centrifugal force or electric force. ...

[edit] 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. For other uses, see Archimedes (disambiguation). ... Syracuse (Italian, Siracusa, ancient Syracusa - see also List of traditional Greek place names) is a city on the eastern coast of Sicily and the capital of the province of Syracuse, Italy. ... Marcus Vitruvius Pollio (born c. ... De architectūra (Latin: On architecture) was a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus. ... Eureka (Eureka!, or Heureka; Greek (later ); IPA: (modern Greek), (ancient Greek, both former and later forms), Anglicised as ) is a famous exclamation attributed to Archimedes. ... Cao Chong 曹沖 (styled Cangshu 倉舒, 196 – 208) was a son of the great 3rd century Chinese warlord Cao Cao. ... The Sānguó Zhì (Chinese 三国志, or 三國誌), variously translated as Chronicles of the Three Kingdoms, Records of the Three States and Records of the Three Kingdoms, was the official and authoritative historical text on the Three Kingdoms Period compiled by Chen Shou during the Jin Dynasty (265-420). ...

This is true only as long as one can neglect the surface tension (capillarity) acting on the body.^[1] This box:      Surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. ...

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. This article is about the SI unit of force. ... For the memorial to USS Arizona (BB-39) in Pearl Harbor, see USS Arizona Memorial. ... This article is about the harbor in Hawaii. ...

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

[edit] 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 Hydrostatic pressure is the pressure exerted by a fluid due to its weight. ...

where

is the density of the fluid,

is the depth (negative height), and

is the standard gravity ( −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 For other uses, see Density (disambiguation). ... g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ... For other uses, see Newton (disambiguation). ... Kg redirects here. ... This article is about Earth as a planet. ...

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

which reduces to

in the case of a cube, the difference in between the top and bottom is , so

or

where V is the volume of the cube,

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. For other uses, see Volume (disambiguation). ... For other uses, see Density (disambiguation). ... For other uses, see Weight (disambiguation). ... In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. ...

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

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 m_b that represents the effective mass of the object with respect to gravity For other uses, see Mass (disambiguation). ...

where is the true (vacuum) mass of the object, whereas ρ_o and ρ_f are the average densities of the object and the surrounding fluid, respectively. Thus, if the two densities are equal, ρ_o = ρ_f, 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.

[edit] 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. USS Akron (ZRS-4) in flight, November 2, 1931 An airship or dirigible is a buoyant lighter-than-air aircraft that can be steered and propelled through the air. ... For other uses, see Submarine (disambiguation). ...

[edit] 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. Fluid Dynamics Compressibility (physics) is a measure of the relative volume change of fluid or solid as a response to a pressure (or mean stress) change: . For a gas the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal, while this difference is small in... Instability in systems is generally characterized by some of the outputs or internal states growing without bounds. ...

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.

[edit] 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.

[edit] References

1. ^ Floater clustering in a standing wave: Capillarity effects drive hydrophilic or hydrophobic particles to congregate at specific points on a wave (PDF) (2005-06-23).

This article does not cite any references or sources. (January 2008) Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed.

Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ... is the 174th day of the year (175th in leap years) in the Gregorian calendar. ... Image File history File links Question_book-3. ...

[edit] See also

Buoys redirects here. ... A buoyancy compensator (or buoyancy control device, BC or BCD) is a piece of diving equipment worn by divers to provide: life saving emergency buoyancy both underwater and on the surface. ... Cartesian diver A Cartesian diver is a classic science experiment, named for René Descartes, in which an eye dropper or other container open only at the bottom (the diver) is placed in a much larger container with flexible walls, such as a 2-liter soft drink bottle, and adjusted so... Divers wear weighting systems, weight belts or weights, generally made of lead, to counteract the buoyancy of other diving equipment, such as diving suits and aluminium diving cylinders. ... Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ... A hull is the body or frame of a ship or boat. ... A hydrometer is an instrument used to measure the specific gravity (or relative density) of liquids; that is, the ratio of the density of the liquid to the density of water. ... The expression lighter than air refers to objects, usually aircraft, that are buoyant in air because they have an average density that is less than that of air (usually because they contain gases that have a density that is lower than that of air). ... Steamer New York in c. ... A pontoon boat, like this small pleasure boat, typically floats and balances by means of two pontoons mounted lengthwise. ... This article or section does not adequately cite its references or sources. ... Salt fingering is a mixing process that occurs when warm salty water overlies cold fresh water. ... For other uses, see Submarine (disambiguation). ... Thrust is a reaction force described quantitatively by Newtons Second and Third Laws. ...

[edit] External links

Look up Buoyancy in
Wiktionary, the free dictionary.

• Falling in Water (Animation 1)
• Falling in Water (Animation 2)
• Falling in Water
• Buoyancy & Density - Video