# Relative density (specific gravity)

In general, relative density means the ratio of the mass of the body under examination to that of a body taken as a reference, for given temperature and pressure. Relative density is often defined as the ratio of the density of the body under test to that of pure water at a temperature of 4 °C and a pressure of 1 bar, or equivalently as the ratio of the mass of the body under test to that of an equal volume of pure water (distilled or deionized) at a temperature of 4 °C and a pressure of 1 bar.

$RD=\dfrac{\rho_{sample}}{\rho_{reference}}$

Relative density can be determined in several ways. Solid bodies that have a density greater than that of water are weighed first in air and then in water under fully immersed conditions. Relative density is obtained by dividing the weight in air by the decrease in weight of the immersed body (see Archimedes’ principle). To determine the relative density of fluids, special instruments called densimeters are used. If very accurate measurements are required, we proceed by determining the mass of a known volume of liquid or gas under controlled temperature conditions.

Specific gravity SG usually means relative density with respect to water. It is a dimensionless quantity.

$SG=\dfrac{\rho_{sample}}{\rho_{water}}$

The choice of the reference substance is arbitrary: it is also possible to define the specific gravity with reference to other substances, but specifying the conditions of temperature and pressure since the density of the material varies with temperature and pressure. This physical quantity is of fundamental importance in the context of fluid statics and in particular in the formulation of Archimedes’ law, which explains the floating of bodies in a fluid.

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