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54-401: A hydrometer usually consists of a sealed hollow glass tube with a wider bottom portion for buoyancy , a ballast such as lead or mercury for stability, and a narrow stem with graduations for measuring. The liquid to test is poured into a tall container, often a graduated cylinder , and the hydrometer is gently lowered into the liquid until it floats freely. The point at which the surface of

108-447: A gravitational field or is accelerating due to a force other than gravity defining a "downward" direction. Buoyancy also applies to fluid mixtures, and is the most common driving force of convection currents. In these cases, the mathematical modelling is altered to apply to continua , but the principles remain the same. Examples of buoyancy driven flows include the spontaneous separation of air and water or oil and water. Buoyancy

162-464: 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: The surface integral can be transformed into a volume integral with the help of the Gauss theorem : where V is the measure of the volume in contact with the fluid, that

216-405: A body with arbitrary shape. 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. 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

270-611: A duplicate of the prototype archive meter, was then given as a gift to Ferdinand Rudolph Hassler . From 1803 until 1805 these two men worked together on a topological survey of the Canton of Bern . In 1819, he discovered the Great Comet of 1819, Comet Tralles , named after him. He was the inventor of the alcoholometer , a device for measuring the amount of alcohol in a liquid. He died in London, England . The crater Tralles on

324-513: A monopoly in the UK and Mary Dicas and her family enjoyed a similar monopoly in the US. A lactometer is used to check purity of cow's milk. The specific gravity of milk does not give a conclusive indication of its composition since milk contains a variety of substances that are either heavier or lighter than water. Additional tests for fat content are necessary to determine overall composition. The instrument

378-442: A result of the weight of the overlying fluid. Thus, the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle )

432-452: A solid suspended in a fluid is buoyed by a force equal to the weight of the fluid displaced by the submerged part of the suspended solid. The lower the density of the fluid, the deeper a hydrometer of a given weight sinks; the stem is calibrated to give a numerical reading. The hydrometer probably dates back to the Greek philosopher Archimedes (3rd century BC) who used its principles to find

486-433: 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

540-420: A thin stem rising from the top with calibrated markings. The sugar level can be determined by reading the value where the surface of the liquid crosses the scale. The higher the sugar content, the denser the solution, and thus the higher the bulb will float. A thermohydrometer is a hydrometer that has a thermometer enclosed in the float section. For measuring the density of petroleum products, such as fuel oils,

594-401: A volume equal to that of the object. This force is applied in a direction opposite to gravitational force, that is of magnitude: 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

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648-482: Is a function of the force of gravity or other source of acceleration on objects of different densities, and for that reason is considered an apparent force, in the same way that centrifugal force is an apparent force as a function of inertia. Buoyancy can exist without gravity in the presence of an inertial reference frame, but without an apparent "downward" direction of gravity or other source of acceleration, buoyancy does not exist. The center of buoyancy of an object

702-430: Is a hydrometer designed especially for use with dairy products. They are sometimes referred to by this specific name, sometimes as hydrometers. An alcoholmeter is a hydrometer that indicates the alcoholic strength of liquids which are essentially a mixture of alcohol and water. It is also known as a proof and Tralles hydrometer (after Johann Georg Tralles , but commonly misspelled as traille and tralle ). It measures

756-426: 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. The equation to calculate the pressure inside a fluid in equilibrium is: where f

810-442: Is caused by a greater specific gravity, assumed to be caused by the introduction of dissolved sugars or carbohydrate based material. A reading is taken before and after fermentation and approximate alcohol content is determined by subtracting the post fermentation reading from the pre-fermentation reading. These were important instruments for determining tax, and specific maker's instruments could be specified. Bartholomew Sikes had

864-416: Is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the displaced fluid. For this reason, an object whose average density is greater than that of the fluid in which it is submerged tends to sink. If the object is less dense than the liquid, the force can keep the object afloat. This can occur only in a non-inertial reference frame , which either has

918-409: Is graduated into a hundred parts. Milk is poured in and allowed to stand until the cream has formed, then the depth of the cream deposit in degrees determines the quality of the milk. If the milk sample is pure, the lactometer floats higher than if it is adulterated or impure. A saccharometer is a type of hydrometer used for determining the amount of sugar in a solution, invented by Thomas Thomson . It

972-403: Is performed if the grain sizes are too small for sieve analysis . The basis for this test is Stokes' Law for falling spheres in a viscous fluid in which the terminal velocity of fall depends on the grain diameter and the densities of the grain in suspension and of the fluid. The grain diameter thus can be calculated from a knowledge of the distance and time of fall. The hydrometer also determines

1026-402: Is the center of gravity of the displaced volume of fluid. Archimedes' principle is named after Archimedes of Syracuse , who first discovered this law in 212 BC. 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

1080-518: 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: Here δ ij is the Kronecker delta . Using this the above equation becomes: Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function: Then: Therefore,

1134-407: Is the volume of the submerged part of the body, since the fluid does not 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

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1188-457: Is used primarily by winemakers and brewers , and it can also be used in making sorbets and ice-creams. The first brewers' saccharometer was constructed by Benjamin Martin (with distillation in mind), and initially used for brewing by James Baverstock Sr in 1770. Henry Thrale adopted its use and it was later popularized by John Richardson in 1784. It consists of a large weighted glass bulb with

1242-415: 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). A simplified explanation for

1296-580: The Accademia del Cimento. It appeared again in the 1675 work of Robert Boyle (who coined the name "hydrometer" ), with types devised by Antoine Baumé (the Baumé scale ), William Nicholson , and Jacques Alexandre César Charles in the late 18th century, more or less contemporarily with Benjamin Sikes ' discovery of the device by which the alcoholic content of a liquid can be automatically determined. The use of

1350-413: The Sikes device was made obligatory by British law in 1818. The hydrometer sinks deeper in low-density liquids such as kerosene , gasoline , and alcohol , and less deep in high-density liquids such as brine , milk , and acids . It is usual for hydrometers to be used with dense liquids to have the mark 1.000 (for water) near the top of the stem, and those for use with lighter liquids to have 1.000 near

1404-446: The application; for this battery chemistry the specific gravity of the electrolyte is not related to the state of charge of the battery. A battery hydrometer with thermometer (thermohydrometer) measures the temperature-compensated specific gravity and electrolyte temperature. Another automotive use of hydrometers is testing the quality of the antifreeze solution used for engine cooling. The degree of freeze protection can be related to

1458-478: 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. Johann Georg Tralles Johann Georg Tralles (15 October 1763 – 19 November 1822)

1512-399: The body, 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

1566-420: The bottom. In many industries a set of hydrometers is used (1.0–0.95, 0.95–.) to have instruments covering the range of specific gravities that may be encountered. Modern hydrometers usually measure specific gravity but different scales were (and sometimes still are) used in certain industries. Examples include: Specialized hydrometers are frequently named for their use: a lactometer, for example,

1620-411: 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

1674-417: The density (and so concentration) of the antifreeze; different types of antifreeze have different relations between measured density and freezing point. An acidometer, or acidimeter, is a hydrometer used to measure the specific gravity of an acid . A barkometer is calibrated to test the strength of tanning liquors used in tanning leather . A salinometer is a hydrometer used to measure the salt content of

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1728-421: The density of the sulfuric acid solution used as electrolyte . A hydrometer calibrated to read specific gravity relative to water at 60 °F (16 °C) is a standard tool for servicing automobile batteries . Tables are used to correct the reading to the standard temperature. Hydrometers are also used for maintenance of wet-cell nickel-cadmium batteries to ensure the electrolyte is of the proper strength for

1782-450: The density of the fluid. Where no sugar or other dissolved substances are present, the specific gravity of a solution of ethanol in water can be directly correlated to the concentration of alcohol. Saccharometers for measuring sugar-water mixtures measure densities greater than water. Many have scales marked with volume percents of "potential alcohol", based on a pre-calculated specific gravity. A higher "potential alcohol" reading on this scale

1836-443: The density of various liquids. An early description of a hydrometer comes from a Latin poem, written in the 2nd century AD by Remnius, who compared the use of a hydrometer to the method of fluid displacement used by Archimedes to determine the gold content of Hiero II's crown. Hypatia of Alexandria (b. c. 350– 370; d.   415 CE), an important female Greek mathematician, is the first person traditionally associated with

1890-402: The feed water to a marine steam boiler. A urinometer is a medical hydrometer designed for urinalysis . As urine's specific gravity is dictated by its ratio of solutes (wastes) to water, a urinometer makes it possible to quickly assess a patient's overall level of hydration. A hydrometer analysis is the process by which fine-grained soils, silts and clays , are graded. Hydrometer analysis

1944-409: 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

1998-414: The fluid, when it is subject to gravity, is 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

2052-407: The forces on the object must be zero), therefore; and therefore 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. 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

2106-408: The hydrometer. In a letter, Synesius of Cyrene asks Hypatia, his teacher, to make a hydrometer for him: The instrument in question is a cylindrical tube, which has the shape of a flute and is about the same size. It has notches in a perpendicular line, by means of which we are able to test the weight of the waters. A cone forms a lid at one of the extremities, closely fitted to the tube. The cone and

2160-472: 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

2214-493: 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 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

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2268-503: The liquid touches the stem of the hydrometer correlates to relative density. Hydrometers can contain any number of scales along the stem corresponding to properties correlating to the density. Hydrometers are calibrated for different uses, such as a lactometer for measuring the density (creaminess) of milk, a saccharometer for measuring the density of sugar in a liquid, or an alcoholometer for measuring higher levels of alcohol in spirits . The hydrometer makes use of Archimedes' principle :

2322-402: 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

2376-416: 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

2430-416: 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 f gz 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

2484-409: 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,

2538-432: The specific gravity (or density) of the suspension, and this enables the fraction of particles of a certain equivalent particle diameter to be calculated. Buoyancy Buoyancy ( / ˈ b ɔɪ ən s i , ˈ b uː j ən s i / ), or upthrust is a net upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as

2592-431: The specimen is usually heated in a temperature jacket with a thermometer placed behind it since density is dependent on temperature. Light oils are placed in cooling jackets, typically at 15 °C. Very light oils with many volatile components are measured in a variable volume container using a floating piston sampling device to minimize light end losses. The state of charge of a lead-acid battery can be estimated from

2646-500: The sum of the buoyancy force 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. 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

2700-653: The tension to restrain it fully submerged is: When a sinking object settles on the solid floor, it experiences a normal force of: 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: The final result would be measured in Newtons. Air's density

2754-606: The tube have one base only. This is called the baryllium. Whenever you place the tube in water, it remains erect. You can then count the notches at your ease, and in this way ascertain the weight of the water. According to the Encyclopedia of the History of Arabic Science , it was used by Abū Rayhān al-Bīrūnī in the 11th century and described by Al-Khazini in the 12th century. It was rediscovered in 1612 by Galileo and his circle of friends, and used in experiments especially at

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2808-410: The water than it is to pull it out of the water. Assuming Archimedes' principle to be reformulated as follows, then inserted into the quotient of weights, which has been expanded by the mutual volume 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: (This formula is used for example in describing

2862-410: 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. More tersely: buoyant force = weight of displaced fluid. Archimedes' principle does not consider the surface tension (capillarity) acting on

2916-731: Was a German mathematician and physicist . He was born in Hamburg, Germany and was educated at the University of Göttingen beginning in 1783. He became a professor at the University of Bern in 1785. In 1810, he became a professor of mathematics at the University of Berlin . In 1798 he served as the Swiss representative to the French metric convocation , and was a member of its committee on weights and measures. An iron "committee" meter,

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