# Specific gravity

Last updated

Specific gravity
Common symbols
SG
SI unit Unitless
Derivations from
other quantities
${\displaystyle SG_{\text{true}}={\frac {\rho _{\text{sample}}}{\rho _{\mathrm {H_{2}O} }}}}$

Specific gravity is the ratio of the density of a substance to the density of a reference substance; equivalently, it is the ratio of the mass of a substance to the mass of a reference substance for the same given volume. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance for liquids is nearly always water at its densest (at 4 °C or 39.2 °F); for gases it is air at room temperature (20 °C or 68 °F). Nonetheless, the temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1  atm (101.325 kPa).

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies.

Colloquially, room temperature is the range of air temperatures that most people prefer for indoor settings, which feel comfortable when wearing typical indoor clothing. Human comfort can extend beyond this range depending on humidity, air circulation and other factors. In certain fields, like science and engineering, and within a particular context, room temperature can mean different agreed-on ranges. In contrast, ambient temperature is the actual temperature of the air in any particular place, as measured by a thermometer. It may be very different from usual room temperature, for example an unheated room in winter.

## Contents

Temperatures for both sample and reference vary from industry to industry. In British beer brewing, the practice for specific gravity as specified above is to multiply it by 1,000. [1] 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, hydrocarbons, antifreeze coolants, sugar solutions (syrups, juices, honeys, brewers wort, must, etc.) and acids.

Wort is the liquid extracted from the mashing process during the brewing of beer or whisky. Wort contains the sugars, the most important being maltose and maltotriose, that will be fermented by the brewing yeast to produce alcohol. Wort also contains crucial amino acids to provide nitrogen to the yeast as well as more complex proteins contributing to beer head retention and flavour.

Must is freshly crushed fruit juice that contains the skins, seeds, and stems of the fruit. The solid portion of the must is called pomace and typically makes up 7–23% of the total weight of the must. Making must is the first step in winemaking. Because of its high glucose content, typically between 10 and 15%, must is also used as a sweetener in a variety of cuisines. Unlike commercially sold grape juice, which is filtered and pasteurized, must is thick with particulate matter, opaque, and comes in various shades of brown and purple.

## Details

Being a ratio of densities, specific gravity is a dimensionless quantity. The reason for the specific gravity being dimensionless is to provide a global consistency between the U.S. and Metric Systems, since various units for density may be used such as pounds per cubic feet or grams per cubic centimeter, etc. Specific gravity varies with temperature and pressure; reference and sample must be compared at the same temperature and pressure or be corrected to a standard reference temperature and pressure. Substances with a specific gravity of 1 are neutrally buoyant in water. 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.

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned. It is also known as a bare number or pure number or a quantity of dimension one and the corresponding unit of measurement in the SI is one unit and it is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities to which dimensions are regularly assigned are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.

Surface tension is the tendency of fluid surfaces to shrink into the minimum surface area possible. Surface tension allows insects, usually denser than water, to float and slide on a water surface.

True specific gravity can be expressed mathematically as:

${\displaystyle SG_{\text{true}}={\frac {\rho _{\text{sample}}}{\rho _{\mathrm {H_{2}O} }}}}$

where ρsample is the density of the sample and ρH2O 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:

${\displaystyle SG_{\text{apparent}}={\frac {W_{\mathrm {A} ,{\text{sample}}}}{W_{\mathrm {A} ,\mathrm {H_{2}O} }}}}$

where WA,sample represents the weight of the sample measured in air and WA,H2O the weight of water measured in air.

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

${\displaystyle SG_{\text{true}}={\frac {\rho _{\text{sample}}}{\rho _{\mathrm {H_{2}O} }}}={\frac {\frac {m_{\text{sample}}}{V}}{\frac {m_{\mathrm {H_{2}O} }}{V}}}={\frac {m_{\text{sample}}}{m_{\mathrm {H_{2}O} }}}{\frac {g}{g}}={\frac {W_{\mathrm {V} ,{\text{sample}}}}{W_{\mathrm {V} ,\mathrm {H_{2}O} }}}}$

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

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 [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 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) [3] 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 [4] 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).

The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, kelvin, second, metre, kilogram, candela, mole, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

United States customary units are a system of measurements commonly used in the United States. The United States customary system developed from English units which were in use in the British Empire before the U.S. became an independent country. However, the United Kingdom's system of measures was overhauled in 1824 to create the imperial system, changing the definitions of some units. Therefore, while many U.S. units are essentially similar to their Imperial counterparts, there are significant differences between the systems.

The ASBC is a professional organization of scientists and technical professionals in the brewing, malting, and allied industries. It publishes a journal, the Journal of the American Society of Brewing Chemists, usually four times a year.

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

${\displaystyle {\rho _{\text{substance}}}=SG\times \rho _{\mathrm {H_{2}O} }.}$

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

## Measurement: apparent and true specific gravity

### Pycnometer

Specific gravity can be measured in a number of value ways. The following illustration involving the use of the pycnometer is instructive. A pycnometer is simply a bottle which can be precisely filled to a specific, but not necessarily accurately known volume, V. Placed upon a balance of some sort it will exert a force.

${\displaystyle F_{\mathrm {b} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}\right)}$

where mb is the mass of the bottle and g the gravitational acceleration at the location at which the measurements are being made. ρa is the density of the air at 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, for example pure water. The force exerted on the pan of the balance becomes:

${\displaystyle F_{\mathrm {w} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}+V\rho _{\mathrm {w} }-V\rho _{\mathrm {a} }\right).}$

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

${\displaystyle F_{\mathrm {w,n} }=gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}$

where the subscript n indicates 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:

${\displaystyle F_{\mathrm {s,n} }=gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}$

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

${\displaystyle SG_{\mathrm {A} }={\frac {gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}{gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}}={\frac {\rho _{\mathrm {s} }-\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }-\rho _{\mathrm {a} }}}.}$

This is called the Apparent Specific Gravity, 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 SGA depend on the actual volume of the pycnometer.

Further manipulation and finally substitution of SGV, the true specific gravity (the subscript V is used because this is often referred to as the specific gravity in vacuo), for ρs/ρw gives the relationship between apparent and true specific gravity.

${\displaystyle SG_{\mathrm {A} }={\frac {{\frac {\rho _{\mathrm {s} }}{\rho _{\mathrm {w} }}}-{\frac {\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }}}}{1-{\frac {\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }}}}}={\frac {SG_{\mathrm {V} }-{\frac {\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }}}}{1-{\frac {\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }}}}}}$

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

${\displaystyle SG_{\mathrm {V} }=SG_{\mathrm {A} }-{\frac {\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }}}\left(SG_{\mathrm {A} }-1\right).}$

Since the density of dry air at 101.325 kPa at 20 °C is [5] 0.001205 g/cm3 and that of water is 0.998203 g/cm3 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 of water (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 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 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 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 specific gravity 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 specific gravity and contain tables relating these to the strengths of common acids, sugar solutions, etc. The vibrating fork immersion probe is another good example of this technology. This technology also includes many coriolis-type mass flow meters which are widely used in chemical and petroleum industry for high accuracy mass flow measurement and can be configured to also output density information 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 a detector which measures the acoustic spectroscopy of the waves. Fluid properties such as density and viscosity can be inferred from the spectrum.
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 cesium-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. . [6]
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 specific gravity with an accuracy of ±0.005 SG 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 an output voltage whose magnitude is a direct linear measure of the quantity to be measured. [7]
Inline continuous measurement
Slurry is weighed as it travels through the metered section of pipe using a patented, high resolution load cell. This section of pipe is of optimal length such that a truly representative mass of the slurry may be determined. This representative mass is then interrogated by the load cell 110 times per second to ensure accurate and repeatable measurement of the slurry.[ citation needed ]

## Examples

• Helium gas has a density of 0.164 g/L; [8] it is 0.139 times as dense as air.
• Air has a density of 1.18 g/L. [8]
MaterialSpecific gravity
Balsa wood 0.2
Oak wood0.75
Ethanol 0.78
Water 1
Table salt 2.17
Aluminium 2.7
Cement 3.15
Iron 7.87
Copper 8.96
Mercury 13.56
Depleted uranium 19.1
Gold 19.3
Osmium 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 approximately 1.060.
• Vodka 80 proof has a specific gravity of 0.9498. [9]

## Related Research Articles

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Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in scientific usage. It is defined as a ratio of density of particular substance with that of water.

In fluid mechanics, a fluid is said to be in hydrostatic equilibrium or hydrostatic balance when it is at rest, or when the flow velocity at each point is constant over time. This occurs when external forces such as gravity are balanced by a pressure-gradient force. For instance, the pressure-gradient force prevents gravity from collapsing Earth's atmosphere into a thin, dense shell, whereas gravity prevents the pressure gradient force from diffusing the atmosphere into space.

The Grashof number (Gr) is a dimensionless number in fluid dynamics and heat transfer which approximates the ratio of the buoyancy to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number. It's believed to be named after Franz Grashof. Though this grouping of terms had already been in use, it wasn't named until around 1921, 28 years after Franz Grashof's death. It's not very clear why the grouping was named after him.

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Terminal velocity is the highest velocity attainable by an object as it falls through a fluid. It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration.

Alcohol by volume is a standard measure of how much alcohol (ethanol) is contained in a given volume of an alcoholic beverage. It is defined as the number of millilitres (mL) of pure ethanol present in 100 mL of solution at 20 °C (68 °F). The number of millilitres of pure ethanol is the mass of the ethanol divided by its density at 20 °C, which is 0.78924 g/mL. The ABV standard is used worldwide. The International Organization of Legal Metrology has tables of density of water–ethanol mixtures at different concentrations and temperatures.

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Vertical pressure variation is the variation in pressure as a function of elevation. Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these variations have relevance in the context of pressure gradient force and its effects. However, the vertical variation is especially significant, as it results from the pull of gravity on the fluid; namely, for the same given fluid, a decrease in elevation within it corresponds to a taller column of fluid weighing down on that point.

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## References

1. 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
2. Bettin, H.; Spieweck, F.: "Die Dichte des Wassers als Funktion der Temperatur nach Einführung des Internationalen Temperaturskala von 1990" PTB-Mitteilungen 100 (1990) pp. 195–196
3. ASBC Methods of Analysis Preface to Table 1: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009
4. ASBC Methods of Analysis op. cit. Table 1: Extract in Wort and Beer
5. DIN51 757 (04.1994): Testing of mineral oils and related materials; determination of density
6. Density – VEGA Americas, Inc. Ohmartvega.com. Retrieved on 2011-11-18.
7. Process Control Digital Electronic Hydrometer. Gardco. Retrieved on 2011-11-18.