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Wikipedia

Relative density

Relative density, or specific gravity,[1][2] is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest (at 4 °C or 39.2 °F); for gases, the reference is air at room temperature (20 °C or 68 °F). The term "relative density" (often abbreviated r.d. or RD) is often preferred in scientific usage, whereas the term "specific gravity" is deprecated.

Specific gravity
Common symbols
SG
SI unitUnitless
Derivations from
other quantities
A United States Navy Aviation boatswain's mate tests the specific gravity of JP-5 fuel

If a substance's relative density is less than 1 then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water, then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.

Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm (101.325 kPa). Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry. In British brewing practice, the specific gravity, as specified above, is multiplied by 1000.[3] Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, must weight (syrups, juices, honeys, brewers wort, must, etc.) and acids.

Basic calculation

Relative density ( ) or specific gravity ( ) is a dimensionless quantity, as it is the ratio of either densities or weights

 
where   is relative density,   is the density of the substance being measured, and   is the density of the reference. (By convention  , the Greek letter rho, denotes density.)

The reference material can be indicated using subscripts:   which means "the relative density of substance with respect to reference". If the reference is not explicitly stated then it is normally assumed to be water at 4 °C (or, more precisely, 3.98 °C, which is the temperature at which water reaches its maximum density). In SI units, the density of water is (approximately) 1000 kg/m3 or 1 g/cm3, which makes relative density calculations particularly convenient: the density of the object only needs to be divided by 1000 or 1, depending on the units.

The relative density of gases is often measured with respect to dry air at a temperature of 20 °C and a pressure of 101.325 kPa absolute, which has a density of 1.205 kg/m3. Relative density with respect to air can be obtained by

 
where   is the molar mass and the approximately equal sign is used because equality pertains only if 1 mol of the gas and 1 mol of air occupy the same volume at a given temperature and pressure, i.e., they are both ideal gases. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0 °C and 1 atmosphere whereas carbon dioxide has a molar volume of 22.259 L under those same conditions.

Those with SG greater than 1 are denser than water and will, disregarding surface tension effects, sink in it. Those with an SG less than 1 are less dense than water and will float on it. In scientific work, the relationship of mass to volume is usually expressed directly in terms of the density (mass per unit volume) of the substance under study. It is in industry where specific gravity finds wide application, often for historical reasons.

True specific gravity of a liquid 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 the sample measured in air and   the weight of an equal volume of water measured in air.

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

 

where g is the local acceleration due to gravity, V is the volume of the sample and of water (the same for both), ρsample is the density of the sample, ρH2O is the density of water, WV represents a weight obtained in vacuum,   is the mass of the sample and  is the mass of an equal volume of water.

The density of water varies with temperature and pressure as does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined. It is nearly always the case that measurements are made at 1 nominal atmosphere (101.325 kPa ± variations from changing weather patterns). But as specific gravity usually refers to highly incompressible 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 is being measured. For true (in vacuo) specific gravity calculations, air pressure must be considered (see below). Temperatures are specified by the notation (Ts/Tr), with Ts representing the temperature at which the sample's density was determined and Tr the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, we note that, while SGH2O = 1.000000 (20 °C/20 °C), it is also the case that SGH2O = 0.9982030.999840 = 0.998363 (20 °C/4 °C). Here, temperature is being specified using the current ITS-90 scale and the densities[4] 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 0.9982071 and 0.9999720 respectively, resulting in an SG (20 °C/4 °C) value for water of 0.9982343.

As the principal use of specific gravity measurements in industry is determination of the concentrations of substances in aqueous solutions and as these are found in tables of SG versus concentration, it is extremely important that the analyst enter the table with the correct form of specific gravity. For example, in the brewing industry, the Plato table lists sucrose concentration by weight against true SG, and was originally (20 °C/4 °C)[5] i.e. based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density, ρH2O equal to 999.972 kg/m3 in SI units (0.999972 g/cm3 in cgs units or 62.43 lb/cu ft in United States customary units). The ASBC table[6] in use today in North America, while it is derived from the original Plato table is for apparent specific gravity measurements at (20 °C/20 °C) on the IPTS-68 scale where the density of water is 0.9982071 g/cm3. In the sugar, soft drink, honey, fruit juice and related industries, 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 temperatures of 60 °F 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 above formula:

 

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

Temperature dependence

See Density for a table of the measured densities of water at various temperatures.

The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or masses were determined. It is nearly always the case that measurements are made at nominally 1 atmosphere (101.325 kPa ignoring the variations caused by changing weather patterns) but as relative density usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products) variations in density caused by pressure are usually neglected at least where apparent relative density is being measured. For true (in vacuo) relative density calculations air pressure must be considered (see below). Temperatures are specified by the notation (Ts/Tr) with Ts representing the temperature at which the sample's density was determined and Tr the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures we note that while SGH2O = 1.000000 (20 °C/20 °C) it is also the case that RDH2O = 0.998203/0.998840 = 0.998363 (20 °C/4 °C). Here temperature is being specified using the current ITS-90 scale and the densities[7] 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 0.9999720 resulting in an RD (20 °C/4 °C) value for water of 0.9982343.

The temperatures of the two materials may be explicitly stated in the density symbols; for example:

relative density: 8.1520 °C
4 °C
; or specific gravity: 2.43215
0

where the superscript indicates the temperature at which the density of the material is measured, and the subscript indicates the temperature of the reference substance to which it is compared.

Uses

Relative density can also help to quantify the buoyancy of a substance in a fluid or gas, or determine the density of an unknown substance from the known density of another. Relative density is often used by geologists and mineralogists to help determine the mineral content of a rock or other sample. Gemologists use it as an aid in the identification of gemstones. Water is preferred as the reference because measurements are then easy to carry out in the field (see below for examples of measurement methods).

As the principal use of relative density measurements in industry is determination of the concentrations of substances in aqueous solutions and these are found in tables of RD vs concentration it is extremely important that the analyst enter the table with the correct form of relative density. For example, in the brewing industry, the Plato table, which lists sucrose concentration by mass against true RD, were originally (20 °C/4 °C)[8] that is based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density of ρ(H
2
O
) equal to 0.999972 g/cm3 (or 62.43 lb·ft−3). The ASBC table[9] in use today in North America, while it is derived from the original Plato table is for apparent relative density measurements at (20 °C/20 °C) on the IPTS-68 scale where the density of water is 0.9982071 g/cm3. In the sugar, soft drink, honey, fruit juice and related industries sucrose concentration by mass is taken from this work[3] which uses SG (17.5 °C/17.5 °C). As a final example, the British RD units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).[3]

Measurement

Relative density can be calculated directly by measuring the density of a sample and dividing it by the (known) density of the reference substance. The density of the sample is simply its mass divided by its volume. Although mass is easy to measure, the volume of an irregularly shaped sample can be more difficult to ascertain. One method is to put the sample in a water-filled graduated cylinder and read off how much water it displaces. Alternatively the container can be filled to the brim, the sample immersed, and the volume of overflow measured. The surface tension of the water may keep a significant amount of water from overflowing, which is especially problematic for small samples. For this reason it is desirable to use a water container with as small a mouth as possible.

For each substance, the density, ρ, is given by

 

When these densities are divided, references to the spring constant, gravity and cross-sectional area simply cancel, leaving

 

Hydrostatic weighing

Relative density is more easily and perhaps more accurately measured without measuring volume. Using a spring scale, the sample is weighed first in air and then in water. Relative density (with respect to water) can then be calculated using the following formula:

 
where
  • Wair is the weight of the sample in air (measured in newtons, pounds-force or some other unit of force)
  • Wwater is the weight of the sample in water (measured in the same units).

This technique cannot easily be used to measure relative densities less than one, because the sample will then float. Wwater becomes a negative quantity, representing the force needed to keep the sample underwater.

Another practical method uses three measurements. The sample is weighed dry. Then a container filled to the brim with water is weighed, and weighed again with the sample immersed, after the displaced water has overflowed and been removed. Subtracting the last reading from the sum of the first two readings gives the weight of the displaced water. The relative density result is the dry sample weight divided by that of the displaced water. This method allows the use of scales which cannot handle a suspended sample. A sample less dense than water can also be handled, but it has to be held down, and the error introduced by the fixing material must be considered.

Hydrometer

 

The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cross-sectional area, as shown in the adjacent diagram.

First the hydrometer is floated in the reference liquid (shown in light blue), and the displacement (the level of the liquid on the stalk) is marked (blue line). The reference could be any liquid, but in practice it is usually water.

The hydrometer is then floated in a liquid of unknown density (shown in green). The change in displacement, Δx, is noted. In the example depicted, the hydrometer has dropped slightly in the green liquid; hence its density is lower than that of the reference liquid. It is necessary that the hydrometer floats in both liquids.

The application of simple physical principles allows the relative density of the unknown liquid to be calculated from the change in displacement. (In practice the stalk of the hydrometer is pre-marked with graduations to facilitate this measurement.)

In the explanation that follows,

  • ρref is the known density (mass per unit volume) of the reference liquid (typically water).
  • ρnew is the unknown density of the new (green) liquid.
  • RDnew/ref is the relative density of the new liquid with respect to the reference.
  • V is the volume of reference liquid displaced, i.e. the red volume in the diagram.
  • m is the mass of the entire hydrometer.
  • g is the local gravitational constant.
  • Δx is the change in displacement. In accordance with the way in which hydrometers are usually graduated, Δx is here taken to be negative if the displacement line rises on the stalk of the hydrometer, and positive if it falls. In the example depicted, Δx is negative.
  • A is the cross sectional area of the shaft.

Since the floating hydrometer is in static equilibrium, the downward gravitational force acting upon it must exactly balance the upward buoyancy force. The gravitational force acting on the hydrometer is simply its weight, mg. From the Archimedes buoyancy principle, the buoyancy force acting on the hydrometer is equal to the weight of liquid displaced. This weight is equal to the mass of liquid displaced multiplied by g, which in the case of the reference liquid is ρrefVg. Setting these equal, we have

 

or just

 

 

 

 

 

(1)

Exactly the same equation applies when the hydrometer is floating in the liquid being measured, except that the new volume is VAΔx (see note above about the sign of Δx). Thus,

 

 

 

 

 

(2)

Combining (1) and (2) yields

 

 

 

 

 

(3)

But from (1) we have V = m/ρref. Substituting into (3) gives

 

 

 

 

 

(4)

This equation allows the relative density to be calculated from the change in displacement, the known density of the reference liquid, and the known properties of the hydrometer. If Δx is small then, as a first-order approximation of the geometric series equation (4) can be written as:

 

This shows that, for small Δx, changes in displacement are approximately proportional to changes in relative density.

Pycnometer

 
An empty glass pycnometer and stopper
 
A filled pycnometer

A pycnometer (from Greek: πυκνός (puknos) meaning "dense"), also called pyknometer or specific gravity bottle, is a device used to determine the density of a liquid. A pycnometer is usually made of glass, with a close-fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus. This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as water or mercury, using an analytical balance.[citation needed]

If the flask is weighed empty, full of water, and full of a liquid whose relative density is desired, the relative density of the liquid can easily be calculated. The particle density of a powder, to which the usual method of weighing cannot be applied, can also be determined with a pycnometer. The powder is added to the pycnometer, which is then weighed, giving the weight of the powder sample. The pycnometer is then filled with a liquid of known density, in which the powder is completely insoluble. The weight of the displaced liquid can then be determined, and hence the relative density of the powder.

A gas pycnometer, the gas-based manifestation of a pycnometer, compares the change in pressure caused by a measured change in a closed volume containing a reference (usually a steel sphere of known volume) with the change in pressure caused by the sample under the same conditions. The difference in change of pressure represents the volume of the sample as compared to the reference sphere, and is usually used for solid particulates that may dissolve in the liquid medium of the pycnometer design described above, or for porous materials into which the liquid would not fully penetrate.

When a pycnometer is filled to a specific, but not necessarily accurately known volume, V and is placed upon a balance, it will exert a force

 
where mb is the mass of the bottle and g the gravitational acceleration at the location at which the measurements are being made. ρa is the density of the air at the ambient pressure and ρb is the density of the material of which the bottle is made (usually glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by Archimedes Principle must be subtracted. The bottle is filled with air but as that air displaces an equal amount of air the weight of that air is canceled by the weight of the air displaced. Now we fill the bottle with the reference fluid e.g. pure water. The force exerted 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 water measurement) we obtain.

 
where the subscript n indicated that this force is net of the force of the empty bottle. The bottle is now emptied, thoroughly dried and refilled with the sample. The force, net of the empty bottle, is now:
 
where ρs is the density of the sample. The ratio of the sample and water forces is:
 

This is called the apparent relative density, denoted by subscript A, because it is what we would obtain if we took the ratio of net weighings in air from an analytical balance or used a hydrometer (the stem displaces air). Note that the result does not depend on the calibration of the balance. The only requirement on it is that it read linearly with force. Nor does RDA depend on the actual volume of the pycnometer.

Further manipulation and finally substitution of RDV, the true relative density (the subscript V is used because this is often referred to as the relative density in vacuo), for ρs/ρw gives the relationship between apparent and true relative density:

 

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

 

Since the density of dry air at 101.325 kPa at 20 °C is[10] 0.001205 g/cm3 and that of water is 0.998203 g/cm3 we see that the difference between true and apparent relative densities for a substance with relative density (20 °C/20 °C) of about 1.100 would be 0.000120. Where the relative density of the sample is close to that of water (for example dilute ethanol solutions) the correction is even smaller.

The pycnometer is used in ISO standard: ISO 1183-1:2004, ISO 1014–1985 and ASTM standard: ASTM D854.

Types

  • Gay-Lussac, pear shaped, with perforated stopper, adjusted, capacity 1, 2, 5, 10, 25, 50 and 100 mL
  • as above, with ground-in thermometer, adjusted, side tube with cap
  • Hubbard, for bitumen and heavy crude oils, cylindrical type, ASTM D 70, 24 mL
  • as above, conical type, ASTM D 115 and D 234, 25 mL
  • Boot, with vacuum jacket and thermometer, capacity 5, 10, 25 and 50 mL

Digital density meters

Hydrostatic Pressure-based Instruments: This technology relies upon Pascal's Principle which states that the pressure difference between two points within a vertical column of fluid is dependent upon the vertical distance between the two points, the density of the fluid and the gravitational force. This technology is often used for tank gaging 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 contact with the fluid of interest. The resonant frequency of the element is measured and is related to the density of the fluid by a characterization that is dependent upon the design of the element. In modern laboratories precise measurements of relative density are made using oscillating U-tube meters. These are capable of measurement to 5 to 6 places beyond the decimal point and are used in the brewing, distilling, pharmaceutical, petroleum and other industries. The instruments measure the actual mass of fluid contained in a fixed volume at temperatures between 0 and 80 °C but as they are microprocessor based can calculate apparent or true relative density and contain tables relating these to the strengths of common acids, sugar solutions, etc.

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

Radiation-based Gauge: Radiation is passed from a source, through the fluid of interest, and into a scintillation detector, or counter. As the fluid density increases, the detected radiation "counts" will decrease. The source is typically the radioactive isotope caesium-137, with a half-life of about 30 years. A key 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.[11]

Buoyant Force Transducer: the buoyancy force produced by a float in a homogeneous liquid is equal to the weight of the liquid that is displaced by the float. Since buoyancy force is linear with respect to the density of the liquid within which the float is submerged, the measure of the buoyancy force yields a measure of the density of the liquid. One commercially available unit claims the instrument is capable of measuring relative density with an accuracy of ± 0.005 RD units. The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage whose magnitude is a direct linear measure of the quantity to be measured.[12]

The relative density in soil mechanics

The relative density   a measure of the current void ratio in relation to the maximum and minimum void rations, and applied effective stress control the mechanical behavior of cohesionless soil. Relative density is defined by

 
in which  , and   are the maximum, minimum and actual void rations.

Examples

Material Specific gravity
Balsa wood 0.2
Oak wood 0.75
Ethanol 0.78
Olive oil 0.91
Water 1
Ironwood 1.5
Graphite 1.9–2.3
Table salt 2.17
Aluminium 2.7
Cement 3.15
Iron 7.87
Copper 8.96
Lead 11.35
Mercury 13.56
Depleted uranium 19.1
Gold 19.3
Osmium 22.59

(Samples may vary, and these figures are approximate.) Substances with a relative density of 1 are neutrally buoyant, those with RD greater than one are denser than water, and so (ignoring surface tension effects) will sink in it, and those with an RD of less than one are less dense than water, and so will float.

Example:

 

Helium gas has a density of 0.164 g/L;[13] it is 0.139 times as dense as air, which has a density of 1.18 g/L.[13]

  • Urine normally has a specific gravity between 1.003 and 1.030. The Urine Specific Gravity diagnostic test is used to evaluate renal concentration ability for assessment of the urinary system.[14] Low concentration may indicate diabetes insipidus, while high concentration may indicate albuminuria or glycosuria.[14]
  • Blood normally has a specific gravity of approximately 1.060.[15]
  • Vodka 80° proof (40% v/v) has a specific gravity of 0.9498.[16]

See also

References

  1. ^ Dana, Edward Salisbury (1922). A text-book of mineralogy: with an extended treatise on crystallography... New York, London(Chapman Hall): John Wiley and Sons. pp. 195–200, 316.
  2. ^ Schetz, Joseph A.; Allen E. Fuhs (1999-02-05). Fundamentals of fluid mechanics. Wiley, John & Sons, Incorporated. pp. 111, 142, 144, 147, 109, 155, 157, 160, 175. ISBN 0-471-34856-2.
  3. ^ a b c Hough, J.S., Briggs, D.E., Stevens, R and Young, T.W. Malting and Brewing Science, Vol. II Hopped Wort and Beer, Chapman and Hall, London, 1991, p. 881
  4. ^ Bettin, H.; Spieweck, F. (1990). "Die Dichte des Wassers als Funktion der Temperatur nach Einführung des Internationalen Temperaturskala von 1990". PTB-Mitteilungen 100. pp. 195–196.
  5. ^ ASBC Methods of Analysis Preface to Table 1: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009
  6. ^ ASBC Methods of Analysis op. cit. Table 1: Extract in Wort and Beer
  7. ^ Bettin, H.; Spieweck, F. (1990). Die Dichte des Wassers als Funktion der Temperatur nach Einführung des Internationalen Temperaturskala von 1990 (in German). PTB=Mitt. 100. pp. 195–196.
  8. ^ ASBC Methods of Analysis Preface to Table 1: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009
  9. ^ ASBC Methods of Analysis op. cit. Table 1: Extract in Wort and Beer
  10. ^ DIN51 757 (04.1994): Testing of mineral oils and related materials; determination of density
  11. ^ Density – VEGA Americas, Inc. Ohmartvega.com. Retrieved on 2011-09-30.
  12. ^ Process Control Digital Electronic Hydrometer. Gardco. Retrieved on 2011-09-30.
  13. ^ a b "Lecture Demonstrations". physics.ucsb.edu.
  14. ^ a b Lewis, Sharon Mantik; Dirksen, Shannon Ruff; Heitkemper, Margaret M.; Bucher, Linda; Harding, Mariann (5 December 2013). Medical-surgical nursing : assessment and management of clinical problems (9th ed.). St. Louis, Missouri. ISBN 978-0-323-10089-2. OCLC 228373703.
  15. ^ Shmukler, Michael (2004). Elert, Glenn (ed.). "Density of blood". The Physics Factbook. Retrieved 2022-01-23.
  16. ^ "Specific Gravity of Liqueurs". Good Cocktails.com.

Further reading

  • Fundamentals of Fluid Mechanics Wiley, B.R. Munson, D.F. Young & T.H. Okishi
  • Introduction to Fluid Mechanics Fourth Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald
  • Thermodynamics: An Engineering Approach Second Edition, McGraw-Hill, International Edition, Y.A. Cengel & M.A. Boles
  • Munson, B. R.; D. F. Young; T. H. Okishi (2001). Fundamentals of Fluid Mechanics (4th ed.). Wiley. ISBN 978-0-471-44250-9.
  • Fox, R. W.; McDonald, A. T. (2003). Introduction to Fluid Mechanics (4th ed.). Wiley. ISBN 0-471-20231-2.

External links

    relative, density, confused, with, specific, density, specific, weight, specific, gravity, ratio, density, mass, unit, volume, substance, density, given, reference, material, specific, gravity, liquids, nearly, always, measured, with, respect, water, densest, . Not to be confused with specific density or specific weight Relative density or specific gravity 1 2 is the ratio of the density mass of a unit volume of a substance to the density of a given reference material Specific gravity for liquids is nearly always measured with respect to water at its densest at 4 C or 39 2 F for gases the reference is air at room temperature 20 C or 68 F The term relative density often abbreviated r d or RD is often preferred in scientific usage whereas the term specific gravity is deprecated Specific gravityCommon symbolsSGSI unitUnitlessDerivations fromother quantitiesS G t r u e r s a m p l e r H 2 O displaystyle SG mathrm true frac rho mathrm sample rho mathrm H 2 O A United States Navy Aviation boatswain s mate tests the specific gravity of JP 5 fuel If a substance s relative density is less than 1 then it is less dense than the reference if greater than 1 then it is denser than the reference If the relative density is exactly 1 then the densities are equal that is equal volumes of the two substances have the same mass If the reference material is water then a substance with a relative density or specific gravity less than 1 will float in water For example an ice cube with a relative density of about 0 91 will float A substance with a relative density greater than 1 will sink Temperature and pressure must be specified for both the sample and the reference Pressure is nearly always 1 atm 101 325 kPa Where it is not it is more usual to specify the density directly Temperatures for both sample and reference vary from industry to industry In British brewing practice the specific gravity as specified above is multiplied by 1000 3 Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines must weight syrups juices honeys brewers wort must etc and acids Contents 1 Basic calculation 2 Temperature dependence 3 Uses 4 Measurement 4 1 Hydrostatic weighing 4 2 Hydrometer 4 3 Pycnometer 4 4 Digital density meters 4 5 The relative density in soil mechanics 5 Examples 6 See also 7 References 8 Further reading 9 External linksBasic calculation EditRelative density R D displaystyle RD or specific gravity S G displaystyle SG is a dimensionless quantity as it is the ratio of either densities or weightsR D r s u b s t a n c e r r e f e r e n c e displaystyle mathit RD frac rho mathrm substance rho mathrm reference where R D displaystyle RD is relative density r s u b s t a n c e displaystyle rho mathrm substance is the density of the substance being measured and r r e f e r e n c e displaystyle rho mathrm reference is the density of the reference By convention r displaystyle rho the Greek letter rho denotes density The reference material can be indicated using subscripts R D s u b s t a n c e r e f e r e n c e displaystyle RD mathrm substance reference which means the relative density of substance with respect to reference If the reference is not explicitly stated then it is normally assumed to be water at 4 C or more precisely 3 98 C which is the temperature at which water reaches its maximum density In SI units the density of water is approximately 1000 kg m3 or 1 g cm3 which makes relative density calculations particularly convenient the density of the object only needs to be divided by 1000 or 1 depending on the units The relative density of gases is often measured with respect to dry air at a temperature of 20 C and a pressure of 101 325 kPa absolute which has a density of 1 205 kg m3 Relative density with respect to air can be obtained byR D r g a s r a i r M g a s M a i r displaystyle mathit RD frac rho mathrm gas rho mathrm air approx frac M mathrm gas M mathrm air where M displaystyle M is the molar mass and the approximately equal sign is used because equality pertains only if 1 mol of the gas and 1 mol of air occupy the same volume at a given temperature and pressure i e they are both ideal gases Ideal behaviour is usually only seen at very low pressure For example one mol of an ideal gas occupies 22 414 L at 0 C and 1 atmosphere whereas carbon dioxide has a molar volume of 22 259 L under those same conditions Those with SG greater than 1 are denser than water and will disregarding surface tension effects sink in it Those with an SG less than 1 are less dense than water and will float on it In scientific work the relationship of mass to volume is usually expressed directly in terms of the density mass per unit volume of the substance under study It is in industry where specific gravity finds wide application often for historical reasons True specific gravity of a liquid can be expressed mathematically as S G t r u e r s a m p l e r H 2 O displaystyle SG mathrm true frac rho mathrm sample rho mathrm H 2 O where r s a m p l e displaystyle rho mathrm sample is the density of the sample and r H 2 O displaystyle rho mathrm H 2 O 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 S G a p p a r e n t W A sample W A H 2 O displaystyle SG mathrm apparent frac W mathrm A text sample W mathrm A mathrm H 2 O where W A sample displaystyle W A text sample represents the weight of the sample measured in air and W A H 2 O displaystyle W mathrm A mathrm H 2 O the weight of an equal volume of water measured in air It can be shown that true specific gravity can be computed from different properties S G t r u e r s a m p l e r H 2 O m s a m p l e V m H 2 O V m s a m p l e m H 2 O g g W V sample W V H 2 O displaystyle SG mathrm true frac rho mathrm sample rho mathrm H 2 O frac frac m mathrm sample V frac m mathrm H 2 O V frac m mathrm sample m mathrm H 2 O frac g g frac W mathrm V text sample W mathrm V mathrm H 2 O where g is the local acceleration due to gravity V is the volume of the sample and of water the same for both rsample is the density of the sample rH2O is the density of water WV represents a weight obtained in vacuum m s a m p l e displaystyle mathit m mathrm sample is the mass of the sample and m H 2 O displaystyle mathit m mathrm H 2 O is the mass of an equal volume of water The density of water varies with temperature and pressure as does the density of the sample So it is necessary to specify the temperatures and pressures at which the densities or weights were determined It is nearly always the case that measurements are made at 1 nominal atmosphere 101 325 kPa variations from changing weather patterns But as specific gravity usually refers to highly incompressible 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 is being measured For true in vacuo specific gravity calculations air pressure must be considered see below Temperatures are specified by the notation Ts Tr with Ts representing the temperature at which the sample s density was determined and Tr the temperature at which the reference water density is specified For example SG 20 C 4 C would be understood to mean that the density of the sample was determined at 20 C and of the water at 4 C Taking into account different sample and reference temperatures we note that while SGH2O 1 000000 20 C 20 C it is also the case that SGH2O 0 998203 0 999840 0 998363 20 C 4 C Here temperature is being specified using the current ITS 90 scale and the densities 4 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 0 9982071 and 0 9999720 respectively resulting in an SG 20 C 4 C value for water of 0 9982343 As the principal use of specific gravity measurements in industry is determination of the concentrations of substances in aqueous solutions and as these are found in tables of SG versus concentration it is extremely important that the analyst enter the table with the correct form of specific gravity For example in the brewing industry the Plato table lists sucrose concentration by weight against true SG and was originally 20 C 4 C 5 i e based on measurements of the density of sucrose solutions made at laboratory temperature 20 C but referenced to the density of water at 4 C which is very close to the temperature at which water has its maximum density rH2O equal to 999 972 kg m3 in SI units 0 999972 g cm3 in cgs units or 62 43 lb cu ft in United States customary units The ASBC table 6 in use today in North America while it is derived from the original Plato table is for apparent specific gravity measurements at 20 C 20 C on the IPTS 68 scale where the density of water is 0 9982071 g cm3 In the sugar soft drink honey fruit juice and related industries 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 temperatures of 60 F 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 above formula r s u b s t a n c e S G r H 2 O displaystyle rho mathrm substance SG times rho mathrm H 2 O Occasionally a reference substance other than water is specified for example air in which case specific gravity means density relative to that reference Temperature dependence EditSee Density for a table of the measured densities of water at various temperatures The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or masses were determined It is nearly always the case that measurements are made at nominally 1 atmosphere 101 325 kPa ignoring the variations caused by changing weather patterns but as relative density usually refers to highly incompressible aqueous solutions or other incompressible substances such as petroleum products variations in density caused by pressure are usually neglected at least where apparent relative density is being measured For true in vacuo relative density calculations air pressure must be considered see below Temperatures are specified by the notation Ts Tr with Ts representing the temperature at which the sample s density was determined and Tr the temperature at which the reference water density is specified For example SG 20 C 4 C would be understood to mean that the density of the sample was determined at 20 C and of the water at 4 C Taking into account different sample and reference temperatures we note that while SGH2O 1 000000 20 C 20 C it is also the case that RDH2O 0 998203 0 998840 0 998363 20 C 4 C Here temperature is being specified using the current ITS 90 scale and the densities 7 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 9999720 resulting in an RD 20 C 4 C value for water of 0 9982343 The temperatures of the two materials may be explicitly stated in the density symbols for example relative density 8 1520 C4 C or specific gravity 2 432150where the superscript indicates the temperature at which the density of the material is measured and the subscript indicates the temperature of the reference substance to which it is compared Uses EditRelative density can also help to quantify the buoyancy of a substance in a fluid or gas or determine the density of an unknown substance from the known density of another Relative density is often used by geologists and mineralogists to help determine the mineral content of a rock or other sample Gemologists use it as an aid in the identification of gemstones Water is preferred as the reference because measurements are then easy to carry out in the field see below for examples of measurement methods As the principal use of relative density measurements in industry is determination of the concentrations of substances in aqueous solutions and these are found in tables of RD vs concentration it is extremely important that the analyst enter the table with the correct form of relative density For example in the brewing industry the Plato table which lists sucrose concentration by mass against true RD were originally 20 C 4 C 8 that is based on measurements of the density of sucrose solutions made at laboratory temperature 20 C but referenced to the density of water at 4 C which is very close to the temperature at which water has its maximum density of r H2 O equal to 0 999972 g cm3 or 62 43 lb ft 3 The ASBC table 9 in use today in North America while it is derived from the original Plato table is for apparent relative density measurements at 20 C 20 C on the IPTS 68 scale where the density of water is 0 9982071 g cm3 In the sugar soft drink honey fruit juice and related industries sucrose concentration by mass is taken from this work 3 which uses SG 17 5 C 17 5 C As a final example the British RD units are based on reference and sample temperatures of 60 F and are thus 15 56 C 15 56 C 3 Measurement EditRelative density can be calculated directly by measuring the density of a sample and dividing it by the known density of the reference substance The density of the sample is simply its mass divided by its volume Although mass is easy to measure the volume of an irregularly shaped sample can be more difficult to ascertain One method is to put the sample in a water filled graduated cylinder and read off how much water it displaces Alternatively the container can be filled to the brim the sample immersed and the volume of overflow measured The surface tension of the water may keep a significant amount of water from overflowing which is especially problematic for small samples For this reason it is desirable to use a water container with as small a mouth as possible For each substance the density r is given byr Mass Volume Deflection Spring Constant Gravity Displacement W a t e r L i n e Area C y l i n d e r displaystyle rho frac text Mass text Volume frac text Deflection times frac text Spring Constant text Gravity text Displacement mathrm WaterLine times text Area mathrm Cylinder When these densities are divided references to the spring constant gravity and cross sectional area simply cancel leavingR D r o b j e c t r r e f Deflection O b j Displacement O b j Deflection R e f Displacement R e f 3 i n 20 m m 5 i n 34 m m 3 i n 34 m m 5 i n 20 m m 1 02 displaystyle RD frac rho mathrm object rho mathrm ref frac frac text Deflection mathrm Obj text Displacement mathrm Obj frac text Deflection mathrm Ref text Displacement mathrm Ref frac frac 3 mathrm in 20 mathrm mm frac 5 mathrm in 34 mathrm mm frac 3 mathrm in times 34 mathrm mm 5 mathrm in times 20 mathrm mm 1 02 Hydrostatic weighing Edit Relative density is more easily and perhaps more accurately measured without measuring volume Using a spring scale the sample is weighed first in air and then in water Relative density with respect to water can then be calculated using the following formula R D W a i r W a i r W w a t e r displaystyle RD frac W mathrm air W mathrm air W mathrm water where Wair is the weight of the sample in air measured in newtons pounds force or some other unit of force Wwater is the weight of the sample in water measured in the same units This technique cannot easily be used to measure relative densities less than one because the sample will then float Wwater becomes a negative quantity representing the force needed to keep the sample underwater Another practical method uses three measurements The sample is weighed dry Then a container filled to the brim with water is weighed and weighed again with the sample immersed after the displaced water has overflowed and been removed Subtracting the last reading from the sum of the first two readings gives the weight of the displaced water The relative density result is the dry sample weight divided by that of the displaced water This method allows the use of scales which cannot handle a suspended sample A sample less dense than water can also be handled but it has to be held down and the error introduced by the fixing material must be considered Hydrometer Edit Main article hydrometer The relative density of a liquid can be measured using a hydrometer This consists of a bulb attached to a stalk of constant cross sectional area as shown in the adjacent diagram First the hydrometer is floated in the reference liquid shown in light blue and the displacement the level of the liquid on the stalk is marked blue line The reference could be any liquid but in practice it is usually water The hydrometer is then floated in a liquid of unknown density shown in green The change in displacement Dx is noted In the example depicted the hydrometer has dropped slightly in the green liquid hence its density is lower than that of the reference liquid It is necessary that the hydrometer floats in both liquids The application of simple physical principles allows the relative density of the unknown liquid to be calculated from the change in displacement In practice the stalk of the hydrometer is pre marked with graduations to facilitate this measurement In the explanation that follows rref is the known density mass per unit volume of the reference liquid typically water rnew is the unknown density of the new green liquid RDnew ref is the relative density of the new liquid with respect to the reference V is the volume of reference liquid displaced i e the red volume in the diagram m is the mass of the entire hydrometer g is the local gravitational constant Dx is the change in displacement In accordance with the way in which hydrometers are usually graduated Dx is here taken to be negative if the displacement line rises on the stalk of the hydrometer and positive if it falls In the example depicted Dx is negative A is the cross sectional area of the shaft Since the floating hydrometer is in static equilibrium the downward gravitational force acting upon it must exactly balance the upward buoyancy force The gravitational force acting on the hydrometer is simply its weight mg From the Archimedes buoyancy principle the buoyancy force acting on the hydrometer is equal to the weight of liquid displaced This weight is equal to the mass of liquid displaced multiplied by g which in the case of the reference liquid is rrefVg Setting these equal we havem g r r e f V g displaystyle mg rho mathrm ref Vg or just m r r e f V displaystyle m rho mathrm ref V 1 Exactly the same equation applies when the hydrometer is floating in the liquid being measured except that the new volume is V ADx see note above about the sign of Dx Thus m r n e w V A D x displaystyle m rho mathrm new V A Delta x 2 Combining 1 and 2 yields R D n e w r e f r n e w r r e f V V A D x displaystyle RD mathrm new ref frac rho mathrm new rho mathrm ref frac V V A Delta x 3 But from 1 we have V m rref Substituting into 3 gives R D n e w r e f 1 1 A D x m r r e f displaystyle RD mathrm new ref frac 1 1 frac A Delta x m rho mathrm ref 4 This equation allows the relative density to be calculated from the change in displacement the known density of the reference liquid and the known properties of the hydrometer If Dx is small then as a first order approximation of the geometric series equation 4 can be written as R D n e w r e f 1 A D x m r r e f displaystyle RD mathrm new ref approx 1 frac A Delta x m rho mathrm ref This shows that for small Dx changes in displacement are approximately proportional to changes in relative density Pycnometer Edit An empty glass pycnometer and stopper A filled pycnometer See also Gas pycnometer A pycnometer from Greek pyknos puknos meaning dense also called pyknometer or specific gravity bottle is a device used to determine the density of a liquid A pycnometer is usually made of glass with a close fitting ground glass stopper with a capillary tube through it so that air bubbles may escape from the apparatus This device enables a liquid s density to be measured accurately by reference to an appropriate working fluid such as water or mercury using an analytical balance citation needed If the flask is weighed empty full of water and full of a liquid whose relative density is desired the relative density of the liquid can easily be calculated The particle density of a powder to which the usual method of weighing cannot be applied can also be determined with a pycnometer The powder is added to the pycnometer which is then weighed giving the weight of the powder sample The pycnometer is then filled with a liquid of known density in which the powder is completely insoluble The weight of the displaced liquid can then be determined and hence the relative density of the powder A gas pycnometer the gas based manifestation of a pycnometer compares the change in pressure caused by a measured change in a closed volume containing a reference usually a steel sphere of known volume with the change in pressure caused by the sample under the same conditions The difference in change of pressure represents the volume of the sample as compared to the reference sphere and is usually used for solid particulates that may dissolve in the liquid medium of the pycnometer design described above or for porous materials into which the liquid would not fully penetrate When a pycnometer is filled to a specific but not necessarily accurately known volume V and is placed upon a balance it will exert a forceF b g m b r a m b r b displaystyle F mathrm b g left m mathrm b rho mathrm a frac m mathrm b rho mathrm b right where mb is the mass of the bottle and g the gravitational acceleration at the location at which the measurements are being made ra is the density of the air at the ambient pressure and rb is the density of the material of which the bottle is made usually glass so that the second term is the mass of air displaced by the glass of the bottle whose weight by Archimedes Principle must be subtracted The bottle is filled with air but as that air displaces an equal amount of air the weight of that air is canceled by the weight of the air displaced Now we fill the bottle with the reference fluid e g pure water The force exerted on the pan of the balance becomes F w g m b r a m b r b V r w V r a displaystyle F mathrm w g left m mathrm b rho mathrm a frac m mathrm b rho mathrm b V rho mathrm w V rho mathrm a right If we subtract the force measured on the empty bottle from this or tare the balance before making the water measurement we obtain F w n g V r w r a displaystyle F mathrm w n gV rho mathrm w rho mathrm a where the subscript n indicated that this force is net of the force of the empty bottle The bottle is now emptied thoroughly dried and refilled with the sample The force net of the empty bottle is now F s n g V r s r a displaystyle F mathrm s n gV rho mathrm s rho mathrm a where rs is the density of the sample The ratio of the sample and water forces is S G A g V r s r a g V r w r a r s r a r w r a displaystyle SG mathrm A frac gV rho mathrm s rho mathrm a gV rho mathrm w rho mathrm a frac rho mathrm s rho mathrm a rho mathrm w rho mathrm a This is called the apparent relative density denoted by subscript A because it is what we would obtain if we took the ratio of net weighings in air from an analytical balance or used a hydrometer the stem displaces air Note that the result does not depend on the calibration of the balance The only requirement on it is that it read linearly with force Nor does RDA depend on the actual volume of the pycnometer Further manipulation and finally substitution of RDV the true relative density the subscript V is used because this is often referred to as the relative density in vacuo for rs rw gives the relationship between apparent and true relative density R D A r s r w r a r w 1 r a r w R D V r a r w 1 r a r w displaystyle RD mathrm A rho mathrm s over rho mathrm w rho mathrm a over rho mathrm w over 1 rho mathrm a over rho mathrm w RD mathrm V rho mathrm a over rho mathrm w over 1 rho mathrm a over rho mathrm w In the usual case we will have measured weights and want the true relative density This is found fromR D V R D A r a r w R D A 1 displaystyle RD mathrm V RD mathrm A rho mathrm a over rho mathrm w RD mathrm A 1 Since the density of dry air at 101 325 kPa at 20 C is 10 0 001205 g cm3 and that of water is 0 998203 g cm3 we see that the difference between true and apparent relative densities for a substance with relative density 20 C 20 C of about 1 100 would be 0 000120 Where the relative density of the sample is close to that of water for example dilute ethanol solutions the correction is even smaller The pycnometer is used in ISO standard ISO 1183 1 2004 ISO 1014 1985 and ASTM standard ASTM D854 Types Gay Lussac pear shaped with perforated stopper adjusted capacity 1 2 5 10 25 50 and 100 mL as above with ground in thermometer adjusted side tube with cap Hubbard for bitumen and heavy crude oils cylindrical type ASTM D 70 24 mL as above conical type ASTM D 115 and D 234 25 mL Boot with vacuum jacket and thermometer capacity 5 10 25 and 50 mLDigital density meters Edit Hydrostatic Pressure based Instruments This technology relies upon Pascal s Principle which states that the pressure difference between two points within a vertical column of fluid is dependent upon the vertical distance between the two points the density of the fluid and the gravitational force This technology is often used for tank gaging 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 contact with the fluid of interest The resonant frequency of the element is measured and is related to the density of the fluid by a characterization that is dependent upon the design of the element In modern laboratories precise measurements of relative density are made using oscillating U tube meters These are capable of measurement to 5 to 6 places beyond the decimal point and are used in the brewing distilling pharmaceutical petroleum and other industries The instruments measure the actual mass of fluid contained in a fixed volume at temperatures between 0 and 80 C but as they are microprocessor based can calculate apparent or true relative density and contain tables relating these to the strengths of common acids sugar solutions etc Ultrasonic Transducer Ultrasonic waves are passed from a source through the fluid of interest and into a detector which measures the acoustic spectroscopy of the waves Fluid properties such as density and viscosity can be inferred from the spectrum Radiation based Gauge Radiation is passed from a source through the fluid of interest and into a scintillation detector or counter As the fluid density increases the detected radiation counts will decrease The source is typically the radioactive isotope caesium 137 with a half life of about 30 years A key 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 11 Buoyant Force Transducer the buoyancy force produced by a float in a homogeneous liquid is equal to the weight of the liquid that is displaced by the float Since buoyancy force is linear with respect to the density of the liquid within which the float is submerged the measure of the buoyancy force yields a measure of the density of the liquid One commercially available unit claims the instrument is capable of measuring relative density with an accuracy of 0 005 RD units The submersible probe head contains a mathematically characterized spring float system When the head is immersed vertically in the liquid the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall effect linear displacement sensors The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage whose magnitude is a direct linear measure of the quantity to be measured 12 The relative density in soil mechanics Edit The relative density D R displaystyle D mathrm R a measure of the current void ratio in relation to the maximum and minimum void rations and applied effective stress control the mechanical behavior of cohesionless soil Relative density is defined byD R e m a x e e m a x e m i n 100 displaystyle D mathrm R frac e mathrm max e e mathrm max e mathrm min times 100 in which e m a x e m i n displaystyle e mathrm max e mathrm min and e displaystyle e are the maximum minimum and actual void rations Examples EditMaterial Specific gravityBalsa wood 0 2Oak wood 0 75Ethanol 0 78Olive oil 0 91Water 1Ironwood 1 5Graphite 1 9 2 3Table salt 2 17Aluminium 2 7Cement 3 15Iron 7 87Copper 8 96Lead 11 35Mercury 13 56Depleted uranium 19 1Gold 19 3Osmium 22 59 Samples may vary and these figures are approximate Substances with a relative density of 1 are neutrally buoyant those with RD greater than one are denser than water and so ignoring surface tension effects will sink in it and those with an RD of less than one are less dense than water and so will float Example R D H 2 O r M a t e r i a l r H 2 O R D displaystyle RD mathrm H 2 O frac rho mathrm Material rho mathrm H 2 O RD Helium gas has a density of 0 164 g L 13 it is 0 139 times as dense as air which has a density of 1 18 g L 13 Urine normally has a specific gravity between 1 003 and 1 030 The Urine Specific Gravity diagnostic test is used to evaluate renal concentration ability for assessment of the urinary system 14 Low concentration may indicate diabetes insipidus while high concentration may indicate albuminuria or glycosuria 14 Blood normally has a specific gravity of approximately 1 060 15 Vodka 80 proof 40 v v has a specific gravity of 0 9498 16 See also EditAPI gravity Baume scale Buoyancy Fluid mechanics Gravity beer Hydrometer Jolly balance Plato scaleReferences Edit Dana Edward Salisbury 1922 A text book of mineralogy with an extended treatise on crystallography New York London Chapman Hall John Wiley and Sons pp 195 200 316 Schetz Joseph A Allen E Fuhs 1999 02 05 Fundamentals of fluid mechanics Wiley John amp Sons Incorporated pp 111 142 144 147 109 155 157 160 175 ISBN 0 471 34856 2 a b c Hough J S Briggs D E Stevens R and Young T W Malting and Brewing Science Vol II Hopped Wort and Beer Chapman and Hall London 1991 p 881 Bettin H Spieweck F 1990 Die Dichte des Wassers als Funktion der Temperatur nach Einfuhrung des Internationalen Temperaturskala von 1990 PTB Mitteilungen 100 pp 195 196 ASBC Methods of Analysis Preface to Table 1 Extract in Wort and Beer American Society of Brewing Chemists St Paul 2009 ASBC Methods of Analysis op cit Table 1 Extract in Wort and Beer Bettin H Spieweck F 1990 Die Dichte des Wassers als Funktion der Temperatur nach Einfuhrung des Internationalen Temperaturskala von 1990 in German PTB Mitt 100 pp 195 196 ASBC Methods of Analysis Preface to Table 1 Extract in Wort and Beer American Society of Brewing Chemists St Paul 2009 ASBC Methods of Analysis op cit Table 1 Extract in Wort and Beer DIN51 757 04 1994 Testing of mineral oils and related materials determination of density Density VEGA Americas Inc Ohmartvega com Retrieved on 2011 09 30 Process Control Digital Electronic Hydrometer Gardco Retrieved on 2011 09 30 a b Lecture Demonstrations physics ucsb edu a b Lewis Sharon Mantik Dirksen Shannon Ruff Heitkemper Margaret M Bucher Linda Harding Mariann 5 December 2013 Medical surgical nursing assessment and management of clinical problems 9th ed St Louis Missouri ISBN 978 0 323 10089 2 OCLC 228373703 Shmukler Michael 2004 Elert Glenn ed Density of blood The Physics Factbook Retrieved 2022 01 23 Specific Gravity of Liqueurs Good Cocktails com Further reading EditFundamentals of Fluid Mechanics Wiley B R Munson D F Young amp T H Okishi Introduction to Fluid Mechanics Fourth Edition Wiley SI Version R W Fox amp A T McDonald Thermodynamics An Engineering Approach Second Edition McGraw Hill International Edition Y A Cengel amp M A Boles Munson B R D F Young T H Okishi 2001 Fundamentals of Fluid Mechanics 4th ed Wiley ISBN 978 0 471 44250 9 Fox R W McDonald A T 2003 Introduction to Fluid Mechanics 4th ed Wiley ISBN 0 471 20231 2 External links EditSpecific Gravity Weights Of Materials Retrieved from https en wikipedia org w index php title Relative density amp oldid 1129829804, wikipedia, wiki, book, books, library,

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