Buoyancy

A metallic coin (an old British pound coin) floats in mercury due to the buoyancy force upon it and appears to float higher because of the surface tension of the mercury.

Archimedes' principle is named after Archimedes of Syracuse, who first discovered this law in 212 BC.^[4] For objects, floating and sunken, and in gases as well as liquids (i.e. a fluid), Archimedes' principle may be stated thus in terms of forces:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object

—with the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.^[5]

More tersely: buoyant force = weight of displaced fluid.

Archimedes' principle does not consider the surface tension (capillarity) acting on the body,^[6] but this additional force modifies only the amount of fluid displaced and the spatial distribution of the displacement, so the principle that buoyancy = weight of displaced fluid remains valid.

The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). In simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy. This is also known as upthrust.

Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyancy force: 10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is generally easier to lift an object up through the water than it is to pull it out of the water.

Assuming Archimedes' principle to be reformulated as follows,

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

then inserted into the quotient of weights, which has been expanded by the mutual volume

${\displaystyle {\frac {\text{density of object}}{\text{density of fluid}}}={\frac {\text{weight}}{\text{weight of displaced fluid}}},\,}$

yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes.:

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

(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.)

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

Example: A helium balloon in a moving car. During a period of increasing speed, the air mass inside the car moves in the direction opposite to the car's acceleration (i.e., towards the rear). The balloon is also pulled this way. However, because the balloon is buoyant relative to the air, it ends up being pushed "out of the way", and will actually drift in the same direction as the car's acceleration (i.e., forward). If the car slows down, the same balloon will begin to drift backward. For the same reason, as the car goes round a curve, the balloon will drift towards the inside of the curve.

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Mercury (element)

Mercury (element)

Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver and was formerly named hydrargyrum from the Greek words hydorcode: ell promoted to code: el (water) and argyroscode: ell promoted to code: el (silver). A heavy, silvery d-block element, mercury is the only metallic element that is known to be liquid at standard temperature and pressure; the only other element that is liquid under these conditions is the halogen bromine, though metals such as caesium, gallium, and rubidium melt just above room temperature.

Surface tension

Surface tension

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects to float on a water surface without becoming even partly submerged.

Archimedes' principle

Archimedes' principle

By Athrv Chandna (SAC) Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.

Ethanol

Ethanol

Ethanol is an organic compound. It is an alcohol with the chemical formula C2H6O. Its formula can also be written as CH3−CH2−OH or C2H5OH. Ethanol is a volatile, flammable, colorless liquid with a characteristic wine-like odor and pungent taste. It is a psychoactive recreational drug, and the active ingredient in alcoholic drinks.

Archimedes

Archimedes

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.

Syracuse, Sicily

Syracuse, Sicily

Syracuse is a historic city on the Italian island of Sicily, the capital of the Italian province of Syracuse. The city is notable for its rich Greek and Roman history, culture, amphitheatres, architecture, and as the birthplace and home of the pre-eminent mathematician and engineer Archimedes. This 2,700-year-old city played a key role in ancient times, when it was one of the major powers of the Mediterranean world. Syracuse is located in the southeast corner of the island of Sicily, next to the Gulf of Syracuse beside the Ionian Sea. It is situated in a drastic rise of land with 2,000 metres (6,600 ft) depths being close to the city offshore although the city itself is generally not so hilly in comparison.

Fluid

Fluid

In physics, a fluid is a liquid, gas, or other material that continuously deforms (flows) under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them.

Meniscus (liquid)

Meniscus (liquid)

The meniscus is the curve in the upper surface of a liquid close to the surface of the container or another object, produced by surface tension.

Newton (unit)

Newton (unit)

The newton is the unit of force in the International System of Units (SI). It is defined as 1 kg⋅m/s2, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.

Vacuum

Vacuum

A vacuum is a space devoid of matter. The word is derived from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure. The Latin term in vacuo is used to describe an object that is surrounded by a vacuum.

Dasymeter

Dasymeter

A dasymeter was meant initially as a device to demonstrate the buoyant effect of gases like air. A dasymeter which allows weighing acts as a densimeter used to measure the density of gases.

Hydrostatic weighing

Hydrostatic weighing

Hydrostatic weighing, also referred to as underwater weighing, hydrostatic body composition analysis and hydrodensitometry, is a technique for measuring the density of a living person's body. It is a direct application of Archimedes' principle, that an object displaces its own volume of water.

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The equation to calculate the pressure inside a fluid in equilibrium is:

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

where f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:

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

Here δ_ij is the Kronecker delta. Using this the above equation becomes:

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

Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function:

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

Then:

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

Therefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative force field. Let the z-axis point downward. In this case the field is gravity, so Φ = −ρ_fgz where g is the gravitational acceleration, ρ_f is the mass density of the fluid. Taking the pressure as zero at the surface, where z is zero, the constant will be zero, so the pressure inside the fluid, when it is subject to gravity, is

${\displaystyle p=\rho _{f}gz.\,}$

So pressure increases with depth below the surface of a liquid, as z denotes the distance from the surface of the liquid into it. Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the pressure on the bottom being greater. This difference in pressure causes the upward buoyancy force.

The buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known. The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is in contact with the fluid:

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

The surface integral can be transformed into a volume integral with the help of the Gauss theorem:

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

where V is the measure of the volume in contact with the fluid, that is the volume of the submerged part of the body, since the fluid doesn't exert force on the part of the body which is outside of it.

The magnitude of buoyancy force may be appreciated a bit more from the following argument. Consider any object of arbitrary shape and volume V surrounded by a liquid. The force the liquid exerts on an object within the liquid is equal to the weight of the liquid with a volume equal to that of the object. This force is applied in a direction opposite to gravitational force, that is of magnitude:

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

where ρ_f is the density of the fluid, V_disp is the volume of the displaced body of liquid, and g is the gravitational acceleration at the location in question.

If this volume of liquid is replaced by a solid body of exactly the same shape, the force the liquid exerts on it must be exactly the same as above. In other words, the "buoyancy force" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to

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

Though the above derivation of Archimedes principle is correct, a recent paper by the Brazilian physicist Fabio M. S. Lima brings a more general approach for the evaluation of the buoyant force exerted by any fluid (even non-homogeneous) on a body with arbitrary shape.^[7] Interestingly, this method leads to the prediction that the buoyant force exerted on a rectangular block touching the bottom of a container points downward! Indeed, this downward buoyant force has been confirmed experimentally.^[8]

The net force on the object must be zero if it is to be a situation of fluid statics such that Archimedes principle is applicable, and is thus the sum of the buoyancy force and the object's weight

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

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. Calculation of the upwards force on a submerged object during its accelerating period cannot be done by the Archimedes principle alone; it is necessary to consider dynamics of an object involving buoyancy. Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be applied alone. For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor.

In order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero), therefore;

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

and therefore

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

showing that the depth to which a floating object will sink, and the volume of fluid it will displace, is independent of the gravitational field regardless of geographic location.

(Note: If the fluid in question is seawater, it will not have the same density (ρ) at every location, since the density depends on temperature and salinity. For this reason, a ship may display a Plimsoll line.)

It can be the case that forces other than just buoyancy and gravity come into play. This is the case if the object is restrained or if the object sinks to the solid floor. An object which tends to float requires a tension restraint force T in order to remain fully submerged. An object which tends to sink will eventually have a normal force of constraint N exerted upon it by the solid floor. The constraint force can be tension in a spring scale measuring its weight in the fluid, and is how apparent weight is defined.

If the object would otherwise float, the tension to restrain it fully submerged is:

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

When a sinking object settles on the solid floor, it experiences a normal force of:

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

Another possible formula for calculating buoyancy of an object is by finding the apparent weight of that particular object in the air (calculated in Newtons), and apparent weight of that object in the water (in Newtons). To find the force of buoyancy acting on the object when in air, using this particular information, this formula applies:

Buoyancy force = weight of object in empty space − weight of object immersed in fluid

The final result would be measured in Newtons.

Air's density is very small compared to most solids and liquids. For this reason, the weight of an object in air is approximately the same as its true weight in a vacuum. The buoyancy of air is neglected for most objects during a measurement in air because the error is usually insignificant (typically less than 0.1% except for objects of very low average density such as a balloon or light foam).

Simplified model

Pressure distribution on an immersed cube

Forces on an immersed cube

Approximation of an arbitrary volume as a group of cubes

A simplified explanation for the integration of the pressure over the contact area may be stated as follows:

Consider a cube immersed in a fluid with the upper surface horizontal.

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

There are two pairs of opposing sides, therefore the resultant horizontal forces balance in both orthogonal directions, and the resultant force is zero.

The upward force on the cube is the pressure on the bottom surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal bottom surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the bottom surface.

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

As 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 resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.

This means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the volume of the cube, and the downward force on the cube is its weight, in the absence of external forces.

This analogy is valid for variations in the size of the cube.

If two cubes are placed alongside each other with a face of each in contact, the pressures and resultant forces on the sides or parts thereof in contact are balanced and may be disregarded, as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy of two cubes in contact is the sum of the buoyancies of each cube. This analogy can be extended to an arbitrary number of cubes.

An object of any shape can be approximated as a group of cubes in contact with each other, and as the size of the cube is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence.

Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.

Static stability

Illustration of the stability of bottom-heavy (left) and top-heavy (right) ships with respect to the positions of their centres of buoyancy (CB) and gravity (CG)

A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement. For example, floating objects will generally have vertical stability, as if the object is pushed down slightly, this will create a greater buoyancy force, which, unbalanced by the weight force, will push the object back up.

Rotational stability is of great importance to floating vessels. Given a small angular displacement, the vessel may return to its original position (stable), move away from its original position (unstable), or remain where it is (neutral).

Rotational stability depends on the relative lines of action of forces on an object. The upward buoyancy force on an object acts through the center of buoyancy, being the centroid of the displaced volume of fluid. The weight force on the object acts through its center of gravity. A buoyant object will be stable if the center of gravity is beneath the center of buoyancy because any angular displacement will then produce a 'righting moment'.

The stability of a buoyant object at the surface is more complex, and it may remain stable even if the center of gravity is above the center of buoyancy, provided that when disturbed from the equilibrium position, the center of buoyancy moves further to the same side that the center of gravity moves, thus providing a positive righting moment. If this occurs, the floating object is said to have a positive metacentric height. This situation is typically valid for a range of heel angles, beyond which the center of buoyancy does not move enough to provide a positive righting moment, and the object becomes unstable. It is possible to shift from positive to negative or vice versa more than once during a heeling disturbance, and many shapes are stable in more than one position.

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Cauchy stress tensor

Cauchy stress tensor

In continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e:

Kronecker delta

Kronecker delta

In mathematics, the Kronecker delta is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise:

Force

Force

In physics, a force is an influence that causes the motion of an object with mass to change its velocity, i.e., to accelerate. It can be a push or a pull, always with magnitude and direction, making it a vector quantity. It is measured in the SI unit of newton (N) and represented by the symbol F.

Density

Density

Density is the substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

Gravitational acceleration

Gravitational acceleration

In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum. This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies; the measurement and analysis of these rates is known as gravimetry.

Net force

Net force

In mechanics, the net force is the vector sum of forces acting on a particle or object. The net force is a single force that replaces the effect of the original forces on the particle's motion. It gives the particle the same acceleration as all those actual forces together as described by Newton's second law of motion.

Acceleration

Acceleration

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities. The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes:the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.

Gravitational field

Gravitational field

In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). Equivalently, it is measured in meters per second squared (m/s2).

Seawater

Seawater

Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5%. This means that every kilogram of seawater has approximately 35 grams (1.2 oz) of dissolved salts. The average density at the surface is 1.025 kg/L. Seawater is denser than both fresh water and pure water because the dissolved salts increase the mass by a larger proportion than the volume. The freezing point of seawater decreases as salt concentration increases. At typical salinity, it freezes at about −2 °C (28 °F). The coldest seawater still in the liquid state ever recorded was found in 2010, in a stream under an Antarctic glacier: the measured temperature was −2.6 °C (27.3 °F). Seawater pH is typically limited to a range between 7.5 and 8.4. However, there is no universally accepted reference pH-scale for seawater and the difference between measurements based on different reference scales may be up to 0.14 units.

Salinity

Salinity

Salinity is the saltiness or amount of salt dissolved in a body of water, called saline water. It is usually measured in g/L or g/kg.

Normal force

Normal force

In mechanics, the normal force is the component of a contact force that is perpendicular to the surface that an object contacts, as in Figure 1. In this instance normal is used in the geometric sense and means perpendicular, as opposed to the common language use of normal meaning "ordinary" or "expected". A person standing still on a platform is acted upon by gravity, which would pull them down towards the Earth's core unless there were a countervailing force from the resistance of the platform's molecules, a force which is named the "normal force".

Centroid

Centroid

In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in n-dimensional Euclidean space.

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The atmosphere's density depends upon altitude. As an airship rises in the atmosphere, its buoyancy decreases as the density of the surrounding air decreases. In contrast, as a submarine expels water from its buoyancy tanks, it rises because its volume is constant (the volume of water it displaces if it is fully submerged) while its mass 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

Submarines rise and dive by filling large ballast 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. Most military submarines operate with a slightly negative buoyancy and maintain depth by using the "lift" of the stabilizers with forward motion.

Balloons

The height to which a balloon rises tends to be stable. As a balloon rises it tends to increase in volume with reducing atmospheric pressure, but the balloon itself does not expand as much as the air on which it rides. The average density of the balloon decreases less than that of the surrounding air. The weight of the displaced air is reduced. A rising balloon stops rising when it and the displaced air are equal in weight. Similarly, a sinking balloon tends to stop sinking.

Divers

Underwater divers are a common example of the problem of unstable buoyancy due to compressibility. The diver typically wears an exposure suit which relies on gas-filled spaces for insulation, and may also wear a buoyancy compensator, which is a variable volume buoyancy bag which is inflated to increase buoyancy and deflated to decrease buoyancy. The desired condition is usually neutral buoyancy when the diver is swimming in mid-water, and this condition is unstable, so the diver is constantly making fine adjustments by control of lung volume, and has to adjust the contents of the buoyancy compensator if the depth varies.

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Airship

Airship

An airship or dirigible balloon is a type of aerostat or lighter-than-air aircraft that can navigate through the air under its own power. Aerostats gain their lift from a lifting gas that is less dense than the surrounding air.

Submarine

Submarine

A submarine is a watercraft capable of independent operation underwater. It differs from a submersible, which has more limited underwater capability. The term is also sometimes used historically or colloquially to refer to remotely operated vehicles and robots, as well as medium-sized or smaller vessels, such as the midget submarine and the wet sub. Submarines are referred to as boats rather than ships irrespective of their size.

Compressibility

Compressibility

In thermodynamics and fluid mechanics, the compressibility is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure change. In its simple form, the compressibility may be expressed as,

Ballast

Ballast

Ballast is material that is used to provide stability to a vehicle or structure. Ballast, other than cargo, may be placed in a vehicle, often a ship or the gondola of a balloon or airship, to provide stability. A compartment within a boat, ship, submarine, or other floating structure that holds water is called a ballast tank. Water should move in and out from the ballast tank to balance the ship. In a vessel that travels on the water, the ballast will remain below the water level, to counteract the effects of weight above the water level. The ballast may be redistributed in the vessel or disposed of altogether to change its effects on the movement of the vessel.

Balloon

Balloon

A balloon is a flexible bag that can be inflated with a gas, such as helium, hydrogen, nitrous oxide, oxygen, and air. For special tasks, balloons can be filled with smoke, liquid water, granular media, or light sources. Modern day balloons are made from materials such as rubber, latex, polychloroprene, or a nylon fabric, and can come in many different colors. Some early balloons were made of dried animal bladders, such as the pig bladder. Some balloons are used for decorative purposes or entertaining purposes, while others are used for practical purposes such as meteorology, medical treatment, military defense, or transportation. A balloon's properties, including its low density and low cost, have led to a wide range of applications.

Buoyancy compensator (diving)

Buoyancy compensator (diving)

A buoyancy compensator (BC), also called a buoyancy control device (BCD), stabilizer, stabilisor, stab jacket, wing or adjustable buoyancy life jacket (ABLJ), depending on design, is a type of diving equipment which is worn by divers to establish neutral buoyancy underwater and positive buoyancy at the surface, when needed.

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Density column of liquids and solids: baby oil, rubbing alcohol (with red food colouring), vegetable oil, wax, water (with blue food colouring) and aluminium

If the weight of an object is less than the weight of the displaced fluid when fully submerged, then the object has an average density that is less than the fluid and when fully submerged will experience a buoyancy force greater than its own weight.^[9] If the fluid has a surface, such as water in a lake or the sea, the object will float and settle 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 remain submerged in the fluid, but it will neither sink nor float, although a disturbance in either direction will cause it to drift away from its position. An object with a higher average density than the fluid will never experience more buoyancy than weight and it will sink. A ship will float even though it may be made of steel (which is much denser than water), because it encloses a volume of air (which is much less dense than water), and the resulting shape has an average density less than that of the water.

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Baby oil

Baby oil

Baby oil is, in general terms, an inert oil for the purpose of keeping skin soft and supple. It is often used on babies for the purpose of maintaining "baby-soft" skin, but it is also often used by adults for skincare and massage.

Rubbing alcohol

Rubbing alcohol

Rubbing alcohol is either an isopropyl alcohol or an ethanol-based liquid, with isopropyl alcohol products being the most widely available. The comparable British Pharmacopoeia (BP) is surgical spirit. Rubbing alcohol is denatured and undrinkable even if it is ethanol-based, due to the bitterants added.

Vegetable oil

Vegetable oil

Vegetable oils, or vegetable fats, are oils extracted from seeds or from other parts of fruits. Like animal fats, vegetable fats are mixtures of triglycerides. Soybean oil, grape seed oil, and cocoa butter are examples of seed oils, or fats from seeds. Olive oil, palm oil, and rice bran oil are examples of fats from other parts of fruits. In common usage, vegetable oil may refer exclusively to vegetable fats which are liquid at room temperature. Vegetable oils are usually edible.

Wax

Wax

Waxes are a diverse class of organic compounds that are lipophilic, malleable solids near ambient temperatures. They include higher alkanes and lipids, typically with melting points above about 40 °C (104 °F), melting to give low viscosity liquids. Waxes are insoluble in water but soluble in nonpolar organic solvents such as hexane, benzene and chloroform. Natural waxes of different types are produced by plants and animals and occur in petroleum.

Water

Water

Water is an inorganic compound with the chemical formula H2O. It is a transparent, tasteless, odorless, and nearly colorless chemical substance, and it is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a solvent). It is vital for all known forms of life, despite not providing food, energy or organic micronutrients. Its chemical formula, H2O, indicates that each of its molecules contains one oxygen and two hydrogen atoms, connected by covalent bonds. The hydrogen atoms are attached to the oxygen atom at an angle of 104.45°. "Water" is also the name of the liquid state of H2O at standard temperature and pressure.

Aluminium

Aluminium

Aluminium is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It has a great affinity towards oxygen, and forms a protective layer of oxide on the surface when exposed to air. Aluminium visually resembles silver, both in its color and in its great ability to reflect light. It is soft, non-magnetic and ductile. It has one stable isotope, 27Al; this isotope is very common, making aluminium the twelfth most common element in the Universe. The radioactivity of 26Al is used in radiodating.