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Specific gravity

Common symbols SG

SI unit N/A (unitless)

Derivations fromother quantities

Testing specific gravity of fuel.

Specific gravityFrom Wikipedia, the free encyclopedia

This page is about the measurement using water as areference. For a general use of specific gravity, seerelative density. See intensive property for theproperty implied by "specific".

Specific gravity is the ratio of the density of a substance tothe density (mass of the same unit volume) of a referencesubstance. Apparent specific gravity is the ratio of theweight of a volume of the substance to the weight of an equalvolume of the reference substance. The reference substance is nearlyalways water at its densest, (4°C) for liquids and for gases, air atroom temperature, (21°C). That being stated temperature andpressure must be specified for both the sample and the reference.Pressure is nearly always 1 atm equal to 101.325 kPa. Temperaturesfor both sample and reference vary from industry to industry. InBritish beer brewing practice the specific gravity as specified aboveis multiplied by 1000.[1] Specific gravity is commonly used inindustry as a simple means of obtaining information about theconcentration of solutions of various materials such as brines,hydrocarbons, sugar solutions (syrups, juices, honeys, brewers wort,must etc.) and acids.

Contents

1 Details2 Measurement: apparent and true specific gravity

2.1 Pycnometer2.2 Digital density meters

3 Examples4 See also5 References

Details

Specific gravity, as it is a ratio of densities, is a dimensionless quantity. Specific gravity varies withtemperature and pressure; reference and sample must be compared at the same temperature and pressure, orcorrected to a standard reference temperature and pressure. Substances with a specific gravity of 1 are

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neutrally buoyant in water, those with SG greater than one are denser than water, and so (ignoring surfacetension effects) will sink in it, and those with an SG of less than one are less dense than water, and so willfloat. In scientific work the relationship of mass to volume is usually expressed directly in terms of thedensity (mass per unit volume) of the substance under study. It is in industry where specific gravity findswide application, often for historical reasons.

True specific gravity can be expressed mathematically as:

where is the density of the sample and is the density of water.

The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air:

where represents the weight of sample and the weight of water, both measured in air.

It can be shown that true specific gravity can be computed from different properties:

where is the local acceleration due to gravity, is the volume of the sample and of water (the same forboth), is the density of the sample, is the density of water and represents a weightobtained in vacuum.

The density of water varies with temperature and pressure as does the density of the sample so that it isnecessary to specify the temperatures and pressures at which the densities or weights were determined. It isnearly always the case that measurements are made at nominally 1 atmosphere (1013.25 mbar ± thevariations caused by changing weather patterns) but as specific gravity usually refers to highlyincompressible aqueous solutions or other incompressible substances (such as petroleum products)variations in density caused by pressure are usually neglected at least where apparent specific gravity isbeing measured. For true (in vacuo) specific gravity calculations air pressure must be considered (seebelow). Temperatures are specified by the notation with representing the temperature at whichthe sample's density was determined and the temperature at which the reference (water) density isspecified. For example SG (20°C/4°C) would be understood to mean that the density of the sample wasdetermined at 20 °C and of the water at 4°C. Taking into account different sample and referencetemperatures we note that while (20°C/20°C) it is also the case that

(20°C/4°C). Here temperature is being specified usingthe current ITS-90 scale and the densities[2] used here and in the rest of this article are based on that scale.On the previous IPTS-68 scale the densities at 20 °C and 4 °C are, respectively, 0.9982071 and 0.9999720resulting in an SG (20°C/4°C) value for water of 0.9982343.

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As the principal use of specific gravity measurements in industry is determination of the concentrations ofsubstances in aqueous solutions and these are found in tables of SG vs concentration it is extremelyimportant that the analyst enter the table with the correct form of specific gravity. For example, in thebrewing industry, the Plato table lists sucrose concentration by weight against true SG, and was originally(20°C/4°C)[3] i.e. based on measurements of the density of sucrose solutions made at laboratorytemperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature atwhich water has its maximum density equal to 0.999972 g·cm−3 in SI units (or 62.43 lbm·ft−3 in

United States customary units). The ASBC table[4] in use today in North America, while it is derived fromthe original Plato table is for apparent specific gravity measurements at (20°C/20°C) on the IPTS-68 scalewhere the density of water is 0.9982071 g·cm−3. In the sugar, soft drink, honey, fruit juice and relatedindustries sucrose concentration by weight is taken from a table prepared by A. Brix which uses SG(17.5°C/17.5°C). As a final example, the British SG units are based on reference and sample temperaturesof 60F and are thus (15.56°C/15.56°C).

Given the specific gravity of a substance, its actual density can be calculated by rearranging the aboveformula:

Occasionally a reference substance other than water is specified (for example, air), in which case specificgravity means density relative to that reference.

Measurement: apparent and true specific gravity

Pycnometer

Specific gravity can be measured in a number of ways. The following illustration involving the use of thepycnometer is instructive. A pycnometer is simply a bottle which can be precisely filled to a specific, butnot necessarily accurately known volume, . Placed upon a balance of some sort it will exert a force .

where is the mass of the bottle and the gravitational acceleration at the location at which themeasurements are being made. is the density of the air at the ambient pressure and is the density ofthe material of which the bottle is made (usually glass) so that the second term is the mass of air displacedby the glass of the bottle whose weight, by Archimedes Principle must be subtracted. The bottle is, ofcourse, filled with air but as that air displaces an equal amount of air the weight of that air is canceled bythe weight of the air displaced. Now we fill the bottle with the reference fluid e.g. pure water. The forceexerted on the pan of the balance becomes:

If we subtract the force measured on the empty bottle from this (or tare the balance before making the watermeasurement) we obtain.

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where the subscript n indicated that this force is net of the force of the empty bottle. The bottle is nowemptied, thoroughly dried and refilled with the sample. The force, net of the empty bottle, is now:

where is the density of the sample. The ratio of the sample and water forces is:

This is called the Apparent Specific Gravity, denoted by subscript A, because it is what we would obtain ifwe took the ratio of net weighings in air from an analytical balance or used a hydrometer (the stemdisplaces air). Note that the result does not depend on the calibration of the balance. The only requirementon it is that it read linearly with force. Nor does depend on the actual volume of the pycnometer.

Further manipulation and finally substitution of ,the true specific gravity,(the subscript V is used

because this is often referred to as the specific gravity in vacuo) for gives the relationship between

apparent and true specific gravity.

In the usual case we will have measured weights and want the true specific gravity. This is found from

Since the density of dry air at 1013.25 mb at 20 °C is[5] 0.001205 g·cm−3 and that of water is 0.998203g·cm−3 the difference between true and apparent specific gravities for a substance with specific gravity(20°C/20°C) of about 1.100 would be 0.000120. Where the specific gravity of the sample is close to that ofwater (for example dilute ethanol solutions) the correction is even smaller.

Digital density meters

Hydrostatic Pressure-based Instruments: This technology relies upon Pascal's Principle which states thatthe pressure difference between two points within a vertical column of fluid is dependent upon the verticaldistance between the two points, the density of the fluid and the gravitational force. This technology is oftenused for tank gauging applications as a convenient means of liquid level and density measure.

Vibrating Element Transducers: This type of instrument requires a vibrating element to be placed in contactwith the fluid of interest. The resonant frequency of the element is measured and is related to the density ofthe fluid by a characterization that is dependent upon the design of the element. In modern laboratoriesprecise measurements of specific gravity are made using oscillating U-tube meters. These are capable ofmeasurement to 5 to 6 places beyond the decimal point and are used in the brewing, distilling,

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pharmaceutical, petroleum and other industries. The instruments measure the actual mass of fluid containedin a fixed volume at temperatures between 0 and 80 °C but as they are microprocessor based can calculateapparent or true specific gravity and contain tables relating these to the strengths of common acids, sugarsolutions, etc. The vibrating fork immersion probe is another good example of this technology. Thistechnology also includes many coriolis-type mass flow meters which are widely used in chemical andpetroleum industry for high accuracy mass flow measurement and can be configured to also output densityinformation based on the resonant frequency of the vibrating flow tubes.

Ultrasonic Transducer: Ultrasonic waves are passed from a source, through the fluid of interest, and into adetector which measures the acoustic spectroscopy of the waves. Fluid properties such as density andviscosity can be inferred from the spectrum.

Radiation-based Gauge: Radiation is passed from a source, through the fluid of interest, and into ascintillation detector, or counter. As the fluid density increases, the detected radiation "counts" willdecrease. The source is typically the radioactive isotope cesium-137, with a half-life of about 30 years. Akey advantage for this technology is that the instrument is not required to be in contact with the fluid –typically the source and detector are mounted on the outside of tanks or piping. .[6]

Buoyant Force Transducer: the buoyancy force produced by a float in a homogeneous liquid is equal to theweight of the liquid that is displaced by the float. Since buoyancy force is linear with respect to the densityof the liquid within which the float is submerged, the measure of the buoyancy force yields a measure of thedensity of the liquid. One commercially available unit claims the instrument is capable of measuringspecific gravity with an accuracy of +/- 0.005 SG units. The submersible probe head contains amathematically characterized spring-float system. When the head is immersed vertically in the liquid, thefloat moves vertically and the position of the float controls the position of a permanent magnet whosedisplacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signalsof the sensors are mixed in a dedicated electronics module that provides an output voltage whose magnitudeis a direct linear measure of the quantity to be measured.[7]

In-Line Continuous Measurement: Slurry is weighed as it travels through the metered section of pipe usinga patented, high resolution load cell. This section of pipe is of optimal length such that a truly representativemass of the slurry may be determined. This representative mass is then interrogated by the load cell 110times per second to ensure accurate and repeatable measurement of the slurry.

Examples

Helium gas has a density of 0.164g/liter[8] It is 0.139 times as dense as air.

Air has a density of 1.18g/l[8]

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Material Specific GravityBalsa wood 0.2Oak wood 0.75Ethanol 0.78Water 1Table salt 2.17Aluminium 2.7Iron 7.87Copper 8.96Lead 11.35Mercury 13.56Depleted uranium 19.1Gold 19.3Osmium 22.59

(Samples may vary, and these figures are approximate.)

Urine normally has a specific gravity between 1.003 and 1.035.Blood normally has a specific gravity of ~1.060.

See also

References

1. ^ Hough, J.S., Briggs, D.E., Stevens, R and Young, T.W. Malting and Brewing Science, Vol. II Hopped Wortand Beer, Chapman and Hall, London, 1991, p. 881

2. ^ Bettin, H.; Spieweck, F.: "Die Dichte des Wassers als Funktion der Temperatur nach Einführung desInternationalen Temperaturskala von 1990" PTB-Mitteilungen 100 (1990) pp. 195–196

API gravityBaumé scaleBuoyancyFluid mechanicsGravity (beer)HydrometerJolly balancePycnometerPlato scale

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3. ^ ASBC Methods of Analysis Preface to Table 1: Extract in Wort and Beer, American Society of BrewingChemists, St Paul, 2009

4. ^ ASBC Methods of Analysis op. cit. Table 1: Extract in Wort and Beer5. ^ DIN51 757 (04.1994): Testing of mineral oils and related materials; determination of density6. ^ Density – VEGA Americas, Inc (http://www.ohmartvega.com/en/nuclear_density_DSG.htm). Ohmartvega.com.

Retrieved on 2011-11-18.7. ^ Process Control Digital Electronic Hydrometer

(http://www.gardco.com/pages/density/electric_hydrometer.cfm). Gardco. Retrieved on 2011-11-18.

8. ^ a b UCSB (http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/36.39.html)

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