Density, $\rho$

Density is defined as mass per unit volume of the substance. However, as discussed before, in the spirit of Continuum Hypothesis, it is defined as a limit. If $\delta m$ is the mass of a small volume $\delta \forall$ then

$$\rho = \lim_{\delta \forall \rightarrow \delta \forall_0} {\delta m \over \delta \forall}$$ (1.13)

Unit of density in the SI system is $kg/m^3$ Under ordinary conditions the density of water is $993 kg/m^3$ while that for air at $15^0$C and atmospheric pressure is $1.23 kg/m^3$.

Density of liquids is somewhat insensitive to the changes in pressure and temperature. For gases there is a strong dependence of density on these quantities and is given by the equation of state of the particular gas.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney