Buoyancy

The forces at work in buoyancy

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. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Physics, a force is whatever can cause an object with Mass to Accelerate. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface 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. Vehicles, derived from the Latin word vehiculum, are non-living Means of transport. A boat is a Watercraft of modest size designed to float or plane on water and provide transport over it A ship /ʃɪp/ is a large vessel that floats on water Ships are generally distinguished from Boats based on size A balloon is a flexible bag filled with a type of Gas, such as Helium, Hydrogen, Nitrous oxide or air. Terminology In some countries airships are also known as dirigibles from the French (fr ''diriger'' to direct plus -ible) meaning "directable" Sedimentation describes the motion of Molecules in Solutions or particles in suspensions in response to an external force such as gravity

1 Archimedes' principle
2 Forces and equilibrium
- 2.1 Compressive fluids
- 2.2 Compressible objects
3 Density
4 References
5 See also
6 External links

Archimedes' principle

It is named after Archimedes of Syracuse, who first discovered this law. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer Syracuse (Siracusa Sicilian: Sarausa, Classical Greek: / transliterated Syrakousai) is a historic City in Vitruvius (De architectura IX. Marcus Vitruvius Pollio (born c 80–70 BC died after c 15 BC was a Roman Writer, Architect and Engineer (possibly praefectus fabrum De architectura ( Latin: "On architecture" is a treatise on Architecture written by the Roman Architect Vitruvius 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. Eureka ( Greek "I have found it" is an exclamation used as an Interjection to celebrate a discovery 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. The term Chinese people may refer to any of the following A person who resides in and holds citizenship of the People's Republic of China (including Hong Cao Chong (196 &ndash 208 was a son of the powerful 3rd century Chinese Chancellor Cao Cao. The Records of Three Kingdoms ( is the official and authoritative historical text on the period of Three Kingdoms covering from 189 to 280,

This is true only as long as one can neglect the surface tension (capillarity) acting on the body. For the work of fiction see Surface Tension (short story. Surface tension is a property of the surface of a Liquid that causes it to ^[1]

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. The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical 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. Construction On 4 March 1913 Congress authorized the construction of Arizona, the second and last of the ''Pennsylvania'' class of "super-dreadnought" Pearl Harbor is a Harbor on the Island of O{{okina}}ahu, Hawaii, west of Honolulu. 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:

$\frac { \mbox{Density of Object}} { \mbox {Density of Fluid} } = \frac { \mbox{Weight} } { \mbox{Weight} - \mbox{Apparent immersed weight} }\,$

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. Fluid statics (also called hydrostatics) is the Science of Fluids at rest and is a sub-field within Fluid mechanics. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Standard gravity, usually denoted by g 0 or g n is the nominal acceleration due to gravity at the Earth's surface at sea level 8 N/kg on Earth)

The force due to pressure is simply the pressure times the area. The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Using a cube as an example, the pressure on the top surface (for example) is thus

$F_{\mathrm{top}} = d^2 \rho h_{\mathrm{top}} g \,$

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

$F_{\mathrm{buoyancy}} = d^2 \rho h_{\mathrm{top}} g - d^2 \rho h_{\mathrm{bottom}} g \,$

which reduces to

$F_{\mathrm{buoyancy}} = d^2 \rho g ( {h_{\mathrm{top}}} - {h_{\mathrm{bottom}}})\,$

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

$F_{\mathrm{buoyancy}} = - d^3 \rho g \,$

$F_\mathrm{buoyancy} = - \rho V g \,$

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 volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different 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 the Physical sciences weight is a Measurement of the gravitational Force acting on an object In this context, displacement is the term used for the weight of the displaced fluid and, thus, is an equivalent term to buoyancy. In Fluid mechanics, displacement occurs when an object is immersed in a Fluid, pushing it out of the way and taking its

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

$F_\mathrm{net} = mg - \rho V g \,$

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 m_b that represents the effective mass of the object with respect to gravity

$m_{b} = m_{\mathrm{o}} \cdot \left( 1 - \frac{\rho_{\mathrm{f}}}{\rho_{\mathrm{o}}} \right)\,$

where $m_{\mathrm{o}}\,$ 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. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object 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.

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. Terminology In some countries airships are also known as dirigibles from the French (fr ''diriger'' to direct plus -ible) meaning "directable" 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. A submarine is a Watercraft that can operate independently below water as distinct from a Submersible that has only limited underwater capability

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. In Thermodynamics and Fluid mechanics, compressibility is a measure of the relative volume change of a Fluid or Solid as a response 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. 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.

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

^ 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). Year 2005 ( MMV) was a Common year starting on Saturday (link displays full calendar of the Gregorian calendar. Events 1180 - First Battle of Uji, starting the Genpei War in Japan 1305 - The Flemish

External links

A Cartesian diver or Cartesian devil is a classic Science experiment named for René Descartes, which demonstrates the principle of Buoyancy Divers wear weighting systems, weight belts or weights, generally made of Lead, to counteract the Buoyancy of other Diving equipment 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 of a Ship or Boat. It is a central concept in floating vessels as it provides the Buoyancy that keeps the vessel from sinking A hydrometer is an instrument used to measure the Specific gravity (or Relative density) of Liquids that is the ratio Some Gases are buoyant in Air because they have densities lower than that of air (about 1 Naval architecture is an engineering discipline dealing with the design construction and repair of marine vehicles A pontoon is a flat-bottomed Boat or the floats used to support a structure on water Quicksand is a Colloid Hydrogel consisting of fine Granular matter (such as Sand or Silt) Clay, and Salt fingering is a mixing process that occurs when warm salty water overlies cold fresh water A submarine is a Watercraft that can operate independently below water as distinct from a Submersible that has only limited underwater capability Thrust is a reaction force described quantitatively by Newton 's Second and Third Laws.

Dictionary

-noun

(physics) the upward force on a body immersed or partly immersed in a fluid
(by extension) resilience or cheerfulness

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