specific gravity

specific gravity

specific gravity, ratio of the weight of a given volume of a substance to the weight of an equal volume of some reference substance, or, equivalently, the ratio of the masses of equal volumes of the two substances.

Relationship Between Specific Gravity and Density

Unlike density, which has units of mass per volume, specific gravity is a pure number, i.e., it has no associated unit of measure. If the densities of the substance of interest and the reference substance are known in the same units (e.g., both in g/cm3 or lb/ft3), then the specific gravity of the substance is equal to its density divided by that of the reference substance. Similarly, if the specific gravity of a substance is known and the density of the reference substance is known in some particular units, then the density of the substance of interest, in those units, is equal to the product of its specific gravity and the density of the reference substance.

The most widely used reference substance for determining the specific gravities of solids and liquids is water. Because the density of water is very nearly 1 g/cm3, the density of any substance in g/cm3 is nearly the same numerically as its specific gravity relative to water. In the English system of units the density of water is about 62.4 lb/ft3, so the near equality between specific gravity and density is not preserved in this system. Specific gravities of gases are often given with dry air as the reference substance. Because the densities of all substances vary with temperature and pressure, the temperature and (particularly for gases) the pressure for both the reference substance and the substance of interest are often included when precise values of specific gravities are given.

Methods of Determining Specific Gravity

A number of experimental methods for determining the specific gravities of solids, liquids, and gases have been devised. A solid is weighed first in air, then while immersed in water; the difference in the two weights, according to Archimedes' principle, is the weight of the water displaced by the volume of the solid. If the solid is less dense than water, some means must be adopted to fully submerge it, e.g., a system of pulleys or a sinker of known mass and volume. The specific gravity of the solid is the ratio of its weight in air to the difference between its weight in air and its weight immersed in water.

Two methods are commonly used for determining the specific gravities of liquids. One method uses the hydrometer, an instrument that gives a specific gravity reading directly. A second method, called the bottle method, uses a "specific-gravity bottle," i.e., a flask made to hold a known volume of liquid at a specified temperature (usually 20°C;). The bottle is weighed, filled with the liquid whose specific gravity is to be found, and weighed again. The difference in weights is divided by the weight of an equal volume of water to give the specific gravity of the liquid. For gases a method essentially the same as the bottle method for liquids is used. Specific gravities of gases are usually converted mathematically to their value at standard temperature and pressure (see STP).

or relative density

Ratio of the density of a substance to that of a standard substance. For solids and liquids, the standard substance is usually water at 39.2°F (4.0°C), which has a density of 1.00 kg/liter. Gases are usually compared to dry air, which has a density of 1.29 g/liter at 32°F (0°C) and 1 atmosphere pressure. Because it is a ratio of two quantities that have the same dimensions (mass per unit volume), specific gravity has no dimension. For example, the specific gravity of liquid mercury is 13.6, because its actual density is 13.6 kg/liter, 13.6 times that of water.

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Specific gravity is defined as the ratio of the density of a given solid or liquid substance to the density of water at a specific temperature and pressure, typically at 4°C (39°F) and , making it a dimensionless quantity (see below). Substances with a specific gravity greater than one are denser than water, and so (ignoring surface tension effects) will sink in it, and those with a specific gravity of less than one are less dense than water, and so will float in it. Specific gravity is a special case of, or in some usages synonymous with, relative density, with the latter term often preferred in modern scientific writing. The use of specific gravity is discouraged in technical use in scientific fields requiring high precision — actual density (in dimensions of mass per unit volume) is preferred.

Specific gravity, SG, is expressed mathematically as:

mbox{SG} = frac{rho_mathrm{substance}}{rho_{mathrm{H}_2mathrm{O}}}

where rho_mathrm{substance}, is the density of the substance, and rho_{mathrm{H}_2mathrm{O}} is the density of water. (By convention ρ, the Greek letter rho, denotes density.) The density of water varies with temperature and pressure, and it is usual to refer specific gravity to the density at 4°C (39.2°F) and a normal pressure of 1 atm. The given temperature and pressure are preferred because it is when water has its maximum density. In this case rho_{mathrm{H}_2mathrm{O}} is equal to 1000 kg·m−3 in SI units (or 62.43 lbm·ft−3 in United States customary units).

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

{rho_mathrm{substance}} = mbox{SG} times rho_{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 not dependent on the system of units used (e.g. slugs·ft−3 or kg·m−3). However, the two densities must of course be converted to the same units before carrying out the numerical ratio calculation.

For information about the measurement of and uses of specific gravity, see relative density.

Examples

  • Balsa wood has a specific gravity of 0.2, so it is 0.2 times as dense as water.
  • Aluminium has a specific gravity of 2.7, so it is 2.7 times as dense as water.
  • Lead has a specific gravity of 11.35, so it is 11.35 times as dense as water.

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

See also

External links

References

  • 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

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