Buoyancy

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In physics, buoyancy or upthrust , is an upward force generated by a fluid opposing the weight of the embedded object. In the liquid column, the pressure increases with depth as a result of the liquid weight above it. So the pressure at the bottom of the liquid column is greater than at the top of the column. Similarly, the pressure at the bottom of the object that is submerged in the liquid is greater than at the top of the object. This pressure difference produces a net upward force on the object. The magnitude of the force given is proportional to that pressure difference, and (as described by the Archimedes principle) is equivalent to the weight of the liquid that will occupy the volume of the object, ie the fluid removed.

For this reason, objects whose density is greater than submerged liquids tend to sink. If the object is less dense than liquid or shaped exactly (as in a boat), the force can keep the object afloat. This can occur only within the framework of non-inertial reference, which has a gravitational field or is accelerating due to a force other than gravity that determines the "down" direction. In situations of fluid statics, the buoyant force rises upward is equal to the magnitude of the weight of the fluid transferred by the body.

The floating center of an object is the center of mass of the volume of fluid removed.

Video Buoyancy

Prinsip Archimedes '

The Archimedes principle is named after Archimedes of Syracuse, who first discovered this law in 212 B.C. For objects, floating and drowning, and in gases and liquids (ie liquids), Archimedes' principle can be stated so in terms of strength:

Each object, entirely or partially immersed in a liquid, is supported by a force equal to the weight of the liquid transferred by the object.

- with clarification that for a concave object the volume of fluid being moved is the volume of the object, and for floating objects in the liquid, the weight of the transferred liquid is the weight of the object.

Shorter: Floating rate = weight of removed fluid.

The Archimedes principle does not take into account the surface tension (capillarity) acting on the body, but this additional power only modifies the amount of transferred fluid and the spatial distribution of the displacements, so the principle that Buoyancy = weight of the displaced fluid remains valid.

The weight of the replaced fluid is directly proportional to the volume of fluid being removed (if the surrounding fluid has a uniform density). In simple terms, the principle states that the buoyancy of the object is equal to the weight of the liquid transferred by the object, or the density of the fluid multiplied by the gravity-immersed volume of gravity, g. Thus, among objects entirely submerged with the same mass, objects with larger volumes have greater buoyancy. This is also known as upthrust.

Suppose the weight of the stone is measured as 10 newtons when suspended by a string in a vacuum with gravity working on it. Suppose that when the rock is lowered into the water, it replaces the heavy water of 3 newtons. The force which is then applied to the hanging string will be 10 newtons minus 3 newton buoyancy: 10--3 = 7 newtons. The buoyancy reduces the weight of visible objects that actually sink to the seafloor. It is generally easier to lift an object up through water than to pull it out of the water.

Dengan asumsi prinsip Archimedes harus dirumuskan kembali sebagai berikut,

${\ displaystyle {\ text {apparent immersed weight}} = {\ text {weight}} - {\ text {weight of displaced fluid}} \,}  ÂÂ$

kemudian dimasukkan ke dalam hasil bagi bobot, yang telah diperluas oleh volume timbal balik

${\ displaystyle {\ frac {\ text {density}} {\ text {density of fluid}}} = {\ frac {\ text {weight}} {\ text { berat cairan yang dipindahkan}}}, \,}  ÂÂ$

menghasilkan rumus di bawah ini. Kepadatan benda yang direndam relatif terhadap densitas cairan dapat dengan mudah dihitung tanpa mengukur volume apa pun.

${\ displaystyle {\ frac {\ text {density objek}} {\ text {density of fluid}}} = {\ frac {\ text {weight}} {{ \ text {weight}} - {\ text {apparent immersed weight}}}} \,}  ÂÂ$

(This formula is used for example in illustrating the measurement principle of dasymeter and hydrostatic weighing.)

Example: If you put the wood into the water, the buoyancy will keep it afloat.

Example: Helium balloon in a moving car. During periods of increased speed, the air mass in the car moves in opposite directions with the car's acceleration (ie, toward the rear). The balloon is also drawn in this direction. However, since the balloon floats relative to the air, the balloon will be pushed "out of the way", and will actually float in the same direction as the car acceleration (ie, advanced). If the car slows down, the same balloon will begin to drift backwards. For the same reason, when the car rotates around the corner, the balloon will float to the inside of the curve.

Maps Buoyancy

Forces and balance

Persamaan untuk menghitung tekanan di dalam cairan dalam kesetimbangan adalah:

${\ displaystyle \ mathbf {f} \ operatorname {div} \, \ sigma = 0}  ÂÂ$

di mana f adalah densitas gaya yang diberikan oleh beberapa medan luar pada fluida, dan ? adalah tensor tegangan Cauchy. Dalam hal ini tensor tegangan sebanding dengan tensor identitas:

${\ displaystyle \ sigma _ {ij} = - p \ delta _ {ij}. \,}  ÂÂ$

Di sini? _ij adalah delta Kronecker. Menggunakan persamaan di atas menjadi:

${\ displaystyle \ mathbf {f} = \ nabla p. \,}  ÂÂ$

Dengan asumsi medan gaya luar adalah konservatif, yang dapat ditulis sebagai gradien negatif dari beberapa fungsi bernilai skalar:

${\ displaystyle \ mathbf {f} = - \ nabla \ Phi. \,}  ÂÂ$

Kemudian:

${\ displaystyle \ nabla (p \ Phi) = 0 \ Longrightarrow p \ Phi = {\ text {constant}}. \,}  ÂÂ$

Therefore, the open surface form of a fluid is equal to the equipotential plane of the outer conservative force field applied. Leave point z -axis down. In this case the field is gravity, so? = - ? _f gz where g is the acceleration of gravity, ? _f is the mass density of the fluid. Taking the pressure as zero on the surface, where z is zero, the constant will be zero, so the pressure inside the liquid, when it is subject to gravity, is

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂpÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â=Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{          ?                 Â                            g     Â¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯         .                       {\ displaystyle p = \ rho _ {f} gz. \,}  Â}

So the pressure increases with depth below the liquid surface, as z shows the distance from the liquid surface into it. Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the pressure at the bottom becoming larger. This pressure difference causes a buoyant upward force.

The buoyancy force given to the body can now be easily calculated, since the internal pressure of the fluid is known. The force given to the body can be calculated by integrating the voltage tensor to the surface of the body in contact with the fluid:

${\ displaystyle \ mathbf {B} = \ oint \ sigma \, d \ mathbf {A}.}$

Integral permukaan dapat diubah menjadi volume integral dengan bantuan teorema Gauss:

${\ displaystyle \ mathbf {B} = \ int \ operatorname {div} \ sigma \, dV = - \ int \ mathbf {f} \, dV = - \ rho _ {f} \ mathbf {g} \ int \, dV = - \ rho _ {f} \ mathbf {g} V}  ÂÂ$

where V is the volume measure in contact with the liquid, ie the volume of the submerged body part, because the fluid does not give force to the outside body part. about that.

The magnitude of buoyancy can be slightly appreciated from the following arguments. Consider any object of the form and the random volume V which is surrounded by liquids. The force given to the liquid in the object in the liquid is equal to the weight of the liquid with the same volume as the object. This force is applied in the opposite direction of the gravitational force, namely:

${\ displaystyle B = \ rho _ {f} V_ {\ text {disp}} \, g, \,}$

where ? _f is the fluid density, V _disp is the volume of the liquid body transferred, and g is acceleration of gravity at the intended location.

If the volume of this fluid is replaced by solid objects with the exact same shape, the force given the liquid above it must be exactly the same as above. In other words, the "floating style" of the dying body is directed towards the opposite of gravity and is as large as

${\ displaystyle B = \ rho _ {f} Vg. \,} Â Â$

Gaya total pada objek harus nol jika menjadi situasi statika fluida sehingga prinsip Archimedes dapat diterapkan, dan dengan demikian merupakan penjumlahan gaya apung dan berat objek.

${\ displaystyle F _ {\ text {net}} = 0 = mg- \ rho _ {f} V_ {\ text {disp}} g \,}  ÂÂ$

If the buoyancy of an uncontrolled and non-powered object exceeds its weight, it tends to rise. An object that weighs more than its buoyancy tends to sink. The calculation of the upward force of a submerged object during its acceleration period can not be performed by the Archimedes principle alone; it is necessary to consider the dynamics of objects that involve buoyancy. Once fully submerged to the liquid floor or rising to the surface and settling, the Archimedes principle can be applied on its own. For floating objects, only the submerged volume moves the water. For submerged objects, the entire volume will replace water, and there will be additional force reactions from the solid floor.

Agar prinsip Archimedes dapat digunakan sendiri, objek yang dimaksud harus berada dalam ekuilibrium (penjumlahan gaya pada objek harus nol), oleh karena itu;

${\ displaystyle mg = \ rho _ {f} V_ {\ text {disp}} g, \,}  ÂÂ$

dan maka dari itu

${\ displaystyle m = \ rho _ {f} V_ {\ text {disp}}. \,}  ÂÂ$

shows that the depth to be cast is a floating object, and the volume of fluid it will replace, is independent of the gravitational field regardless of its geographic location.

( Note: If the liquid in question is sea water, it will not have the same density (? ) in each location For this reason, the ship can display Plimsoll line.)

This can be a coercive case in addition to just buoyancy and gravity come into play. This is the case if the object is under control or if the object sinks to a solid floor. An object that tends to float requires a force to hold the T voltage in order to remain completely submerged. An object that tends to drown will eventually have the normal constraint power N given to it by a solid floor. The constraint force can be a voltage in the spring scale that measures the weight in the fluid, and how the apparent weights are defined.

Jika objek sebaliknya akan mengambang, ketegangan untuk menahannya sepenuhnya terendam adalah:

${\ displaystyle T = \ rho _ {f} Vg-mg. \,}  ÂÂ$

Ketika benda yang tenggelam tenggelam di lantai yang padat, ia mengalami kekuatan normal:

${\ displaystyle N = mg- \ rho _ {f} Vg. \,}  ÂÂ$

Another possible formula for calculating the buoyancy of an object is to find the actual weight of a particular object in the air (calculated in Newton), and the actual weight of the object in water (in Newton). To find the power of buoyancy that acts on an object while in the air, using this particular information, this formula applies:

Floating force = weight of object in empty space - weight of object immersed in liquid

The final result will be measured in Newton.

Air density is very small compared to most solids and liquids. For this reason, the weight of an object in the air is approximately equal to its actual weight in a vacuum. The buoyancy of air is negligible for most objects during measurement in air because errors are usually insignificant (typically less than 0.1% except for objects with very low average density such as balloons or mild foams).

Simplified model

A simplified explanation for the integration of pressures above the contact area can be expressed as follows:

Consider the cube embedded in a liquid with a horizontal upper surface.

The sides are identical in the region, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force is generated from the hydrostatic pressure, which is perpendicular to the surface plane of each side.

There are two pairs of opposite sides, therefore the resulting horizontal power is balanced in an orthogonal direction, and the resulting force is zero.

Upward force on the cube is the pressure on the bottom surface that is integrated above the area. The surface is at a constant depth, so the pressure is constant. Therefore, the integral of the pressure above the surface area under the horizontal cube is the hydrostatic pressure at that depth multiplied by the bottom surface area.

Similarly, the downward force in the cube is the pressure on the top surface that is integrated over its territory. The surface is at a constant depth, so the pressure is constant. Therefore, the integral of the pressure above the upper surface area of ​​the horizontal cube is the hydrostatic pressure at that depth multiplied by the upper surface area.

Since this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resulting power difference is exactly the same as the weight of the liquid that will fill the volume of the cube if it does not exist.

This means that the resulting upward force in the cube is equal to the weight of the liquid that will enter into the volume of the cube, and the force down on the cube is its weight, in the absence of an external force.

This analogy applies to cube size variations.

If two cubes are placed side by side with each contact, the resultant pressure and force on the side or parts are in balance and negligible, since the contact surface is equal in shape, size and pressure distribution, therefore the buoyancy of the two contacted cubes is the sum of buoyancies of each cube. This analogy can be extended to the number of volatile stones.

An object of any kind can be approximated as a group of contacting cubes, and as the size of the cube decreases, the approximate accuracy will increase. The limiting case for infinite small cubes is the exact equivalent.

The oblique surface does not cancel the analogy because the resultant force can be broken down into orthogonal components and each is handled in the same way.

Static stability

A floating object is stable if it tends to return itself to the equilibrium position after a small displacement. For example, floating objects will generally have vertical stability, as if the object is pushed down a bit, this will create a larger buoyant force, which, unbalanced by gravity, will push the object back up.

Rotational stability is essential for floating vessels. Given the small angle displacement, the vessel can return to its original position (stable), away from its original position (unstable), or stay in place (neutral).

The stability of rotation depends on the relative line of action force on an object. The upward buoyancy force on the object acts through the buoyancy center, becoming the center of the volume of fluid being removed. The weight of the object acts through its center of gravity. The floating object will be stable if the center of gravity is below the buoyancy center because any angular displacement will produce the 'right moment'.

The stability of buoyant objects on the surface is more complex, and may remain stable even if the center of gravity is above the buoyancy center, provided that when disturbed from the equilibrium position, the center of buoyancy moves farther to the same side. that the center of gravity moves, thus giving a positive crossing moment. If this happens, the floating object is said to have a positive metacentric height. This situation usually applies to different heel angles, beyond which the buoyancy center is not moving enough to provide a positive crossing moment, and the object becomes unstable. It is possible to shift from positive to negative or vice versa more than once during heeling disorders, and many forms are stable in more than one position.

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Liquid and adjustable objects

The density of the atmosphere depends on the altitude. When a plane rises in the atmosphere, its buoyancy decreases as the density of the surrounding air decreases. Conversely, when the submarine takes the water out of the floating tank, it rises because its volume is constant (the volume of water it displaces when it is completely submerged) while its mass decreases.

Compressed items

When an object floats up or down, the external force changes and, since all objects can be compressed to some extent or another, so does the volume of the object. The buoyancy depends on the volume and the buoyancy of the object decreases when compacted and increases as it expands.

If an object at equilibrium has less compressibility than the surrounding liquid, the balance of the object is stable and remains stationary. However, if the compressibility is greater, the balance then becomes unstable, and rises and extends in slightly upward disturbance, or falls and compresses the disturbance slightly downward.

Submarine

Submarines rise and dive by filling large ballast tanks with sea water. For diving, the tanks are opened to allow air out of the top of the tank, while water flows from below. Once the weight has been balanced so that the overall density of the submarine is equal to the surrounding water, it has a neutral buoyancy and will remain at that depth. Most of the military submarines operate with slightly negative buoyancy and maintain depth by using "lifting" the stabilizers with forward motion.

Balloons

The altitude at which the balloon rises tends to be stable. As the balloon rises, it tends to increase its volume by reducing atmospheric pressure, but the balloon itself does not expand as much as the air it occupies. The average balloon density is reduced less than the surrounding air. Reduced air weight is reduced. The rising balloon stopped rising then and the transferred air was just as heavy. Similarly, the sinking balloon tends to stop drowning.

Diver

Underwater divers is a common example of an unstable buoyancy problem due to compressibility. Divers usually wear exposure clothing that depends on gas-filled space for insulation, and may also use a float compensator, which is an improved variable volume buoyancy bag to increase buoyancy and decrease to reduce buoyancy. The desired condition is usually neutral buoyancy when the diver swims in the middle of the water, and the condition is unstable, so the diver constantly makes good adjustments by controlling the lung volume, and must adjust the contents of the float compensator if the depth varies.

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Density

If the weight of an object is less than the weight of the fluid removed when submerged, then the object has a smaller average density of liquid and when fully submerged will experience a buoyant force greater than its own weight. If the liquid has a surface, such as water in a lake or sea, the object will float and settle at a rate at which it replaces the weight of the liquid equal to the weight of the object. If the object is immersed in a liquid, such as submerged submarine or air in a balloon, it will tend to rise. If the object has exactly the same density as the liquid, then its buoyancy is equal to its weight. It will remain submerged in the liquid, but will not drown or float, although disturbance in both directions will cause it to move away from its position. An object with an average density higher than a liquid will not experience more buoyancy than weight and will sink. A ship will float even though it may be made of steel (which is much denser than water), because it encloses the volume of air (which is much denser than water), and the resulting shape has an average density of less than water.

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See also

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References

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External links

• Water Fall
• The Archimedes Principle - background and experiment
• BuoyancyQuest (a website featuring floating video controls)
• W. H. Besant (1889) Basic Hydrostatic from Google Books.
• The definition of NASA buoyancy

Source of the article : Wikipedia