## Dr. SaMeH S. Ahmed

Associate Prof. of Environmental Engineering

# Specific gravity

Specific gravity is the ratio of the density (mass of a unit volume) of a substance to the density (mass of the same unit volume) of a reference substance. 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 is nearly always water for liquids or air for gases. Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm equal to 101.325 kPa. 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.[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, sugar solutions (syrups, juices, honeys, brewers wortmust etc.) and acids.

## Details

Specific gravity, as it is the ratio of densities, is a dimensionless quantity. Specific gravity varies with temperature; reference and sample must be compared at the same temperature, or corrected to a standard reference temperature. Substances with a specific gravity of 1 are neutrally buoyant in water, those with SG greater than one are denser than water, and so (ignoring surface tension effects) will sink in it, and those with an SG of less than one are less dense than water, and so will float. 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, can be expressed mathematically as:

$SG_{true} = frac { ho_{sample}}{ ho_{H_2O}}$

where $ho_mathrm{sample},$ is the density of the sample and $ho_{mathrm{H}_2mathrm{O}}$ 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:

$SG_{apparent} = frac {W_{A_{sample}}}{W_{A_{H_2O}}}$

where $W_{A_{sample}}$ represents the weight of sample and $W_{A_{H_2O}}$ the weight of water, both measured in air.

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

$SG_{true} = frac { ho_{sample}}{ ho_{H_2O}} = frac {(m_{sample}/V)}{(m_{H_2O}/V)} = frac {m_{sample}}{m_{H_2O}} frac{g}{g} = frac {W_{V_{sample}}}{W_{V_{H_2O}}}$

where $g$ is the local acceleration due to gravity, $mathrm{V}$ is the volume of the sample and of water (the same for both), $ho_mathrm{sample},$ is the density of the sample, $ho_{mathrm{H}_2mathrm{O}}$ is the density of water and $W_V$ represents a weight obtained in vacuum.

The density of water varies with temperature and pressure as does the density of the sample so that 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 nominally 1 atmosphere (1013.25 mb ± the variations caused by 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 $(T_s/T_r)$ with $T_s$ representing the temperature at which the sample's density was determined and $T_r$ 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 $SG_{H_2O} = 1.000000$ (20°C/20°C) it is also the case that $SG_{H_2O} = 0.998203/0.999840 = 0.998363$ (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, respectively, 0.9982071 and 0.9999720 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 these are found in tables of SG vs 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, which lists sucrose concentration by weight against true SG, were 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 of $ho_{mathrm{H}_2mathrm{O}}$ equal to 0.999972 g·cm−3 or 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 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·cm−3. 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 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 above formula:

${ ho_mathrm{substance}} = mbox{SG} imes ho_{mathrm{H}_2mathrm{O}}$

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

Specific gravity is, by definition, dimensionless and therefore independent on the system of units used (e.g. slugs·ft−3 or kg·m−3). However, the two densities must be converted to the same units before carrying out the numerical ratio calculation.

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