# Buoyancy

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.

Buoyancy acts against the force of gravity and so makes objects seem lighter with respect to gravity. To represent this effect, which is important for sedimentation, it is common to define a buoyant mass mb that represents the effective mass of the object with respect to gravity

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

## Forces and equilibrium

Buoyancy provides an upward force on the object. The magnitude of this force is equal to the weight of the displaced fluid. (Displacement is the term used for the weight of the displaced fluid and, thus, is an equivalent term to buoyancy.) The buoyancy of an object depends, therefore, only upon 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. 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.

The atmosphere's density depends upon altitude. As an airship rises in the atmosphere, therefore, 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.

The buoyant force can be expressed using the following equation:

where

is the density of the fluid;
V is the volume of the object submerged;
g is the standard gravity ( 9.81 N/kg on Earth). A negative sign must be used because the buoyancy acts in the opposite direction to the acceleration due to gravity.

### 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.

A submarine is more compressible than the surrounding water. As depth increases, the resulting pressure causes the submarine's volume to decrease more than the volume of the surrounding water decreases. Buoyancy depends upon the object's volume and the weight of the displaced fluid. Volume has decreased so the weight displaced has decreased which means a decrease in buoyancy and the submarine tends to sink further. A rising submarine expands more than the surrounding water, so tends to rise further.

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.

## Archimedes' principle

The Falkirk Wheel boat lift relies on Archimedes principle. A boat in the wheel always displaces its weight in water so the two sides of the wheel remain balanced even if there is a boat only in one side.
Archimedes' principle, or the law of upthrust, is:

"When a solid body is partially or completely immersed in water, the apparent loss in weight will be equal to the weight of the displaced liquid."

In other words, when a body is partially or completely immersed in a liquid, then it experiences an upward buoyant force which is equal to the weight of the fluid displaced by the immersed part of the body.

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.[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. 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:

## 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 so 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 a balloon in the air, it will tend to rise. If the object has exactly the same density as the liquid, 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.

## Applications

Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
FLUID (Fast Light User Interface Designer) is a graphical editor that is used to produce FLTK source code. FLUID edits and saves its state in text .fl files, which can be edited in a text editor for finer control over display and behavior.
Liquid is one of the four principal states of matter. A liquid is a fluid that can freely form a distinct surface at the boundaries of its bulk material.

## Characteristics

A liquid's shape is determined by, not confined to, the container it fills.
Gas is one of the four major states of matter, consisting of freely moving atoms or molecules without a definite shape. Compared to the solid and liquid states of matter a gas has lower density and a lower viscosity.
Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.

Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
Vehicles are non-living means of transport. They are most often man-made (e.g. bicycles, cars, motorcycles, trains, ships, and aircraft), although some other means of transport which are not made by man can also be called vehicles; examples include icebergs and floating tree trunks.
A boat is a watercraft designed to float or plane on, and provide transport over, water. Usually this water will be inland (lakes) or in protected coastal areas. However, boats such as the whaleboat were historically designed to be operated from a ship in an offshore environment.
ship is a large watercraft capable of offshore navigation. Ships may be operated by:
• Governments (military, rescue, research, transportation)
• Private companies and institutions (transportation, offshore resources, research)
• Individuals (large yachts, research).

balloon is a flexible bag normally filled with a gas, such as helium, hydrogen, nitrous oxide or air. Early balloons were made of dried animal bladders. Modern balloons can be made from materials such as rubber, latex, polychloroprene or a nylon fabric.
airship or dirigible is a buoyant lighter-than-air aircraft that can be steered and propelled through the air. Unlike aerodynamic vehicles such as fixed-wing aircraft and helicopters which stay aloft by moving an airfoil through the air in order to produce lift,
Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
Sedimentation describes the motion of molecules in solutions or particles in suspensions in response to an external force such as gravity, centrifugal force or electric force.
Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
weight is a measurement of the gravitational force acting on an object. Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight is roughly proportional to its mass.
In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place, so that it can be weighed.

An object that sinks also displaces an amount of fluid equal to the object's volume.
The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
airship or dirigible is a buoyant lighter-than-air aircraft that can be steered and propelled through the air. Unlike aerodynamic vehicles such as fixed-wing aircraft and helicopters which stay aloft by moving an airfoil through the air in order to produce lift,
submarine is a watercraft that can operate underwater. Military submarines were first widely used in World War I and are used by all major navies today. Civilian submarines and submersibles are used for scientific work at depths too great for human divers.
Standard gravity, usually denoted by g0 or gn, is the nominal acceleration due to gravity at the Earth's surface at sea level. By definition it is equal to exactly 9.80665  m·s−2 (approx. 32.174 ft·s−2).
The newton (symbol: N) is the SI derived unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics.

## Definition

A newton
kilogram or kilogramme (symbol: kg) is the SI base unit of mass. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water.
EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001. Their greatest hit, their debut single "time after time", peaked at #13 in the Oricon singles chart.
compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.

where V is volume and p is pressure.
Instability in systems is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior.
Archimedes of Syracuse (Greek: Άρχιμήδης c. 287 BC – c. 212 BC) was an ancient Greek mathematician, physicist and engineer.
Archimedes of Syracuse (Greek: Άρχιμήδης c. 287 BC – c. 212 BC) was an ancient Greek mathematician, physicist and engineer.
Country Italy
Region Sicily
Province Siracusa (SR)
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