Temperature

In any form of matter the molecules are continuously moving relative to each other. In gases the molecular motion is a random movement of appreciable amplitude ranging from about 76 x 10-9 m, under normal conditions (that is, at standard sea level pressure and temperature), to some tens of millimeters, at very low pressures. The distance of free movement of a molecule of a gas is the distance it can travel before colliding with another molecule or the walls of the container. The mean value of this distance for all molecules in a gas is called the molecular mean free path length. By virtue of this motion the molecules possess kinetic energy, and this energy is sensed as temperature of the solid, liquid or gas. In the case of a gas in motion, it is called the static temperature. Temperature has units kelvin (K) or degrees celsius (°C), in SI units. For all calculations in this book, temperatures will be expressed in kelvin, that is, from absolute zero. At standard sea level condition, the atmospheric temperature is 288.15 K.

2.2.2 Density

The total number of molecules in a unit volume is a measure of the density p of a substance. It is expressed as mass per unit volume, say kg/m3. Mass is defined as weight divided by acceleration due to gravity. At
standard atmospheric temperature and pressure (288.15 K and 101325 Pa, respectively), the density of dry air is 1.225 kg/m3.

Density of a material is a measure of the amount of material contained in a given volume. In a fluid system, the density may vary from point to point. Consider the fluid contained within a small spherical region of volume SV, centered at some point in the fluid, and let the mass of fluid within this spherical region be Sm. Then the density of the fluid at the point on which the sphere is centered can be defined by:

There are practical difficulties in applying the above definition of density to real fluids composed of discrete molecules, since under the limiting condition the sphere may or may not contain any molecule. If it contains, say, just a single molecule, the value obtained for the density will be fictitiously high. If it does not contain any molecule the resultant value of density will be zero. This difficulty can be avoided over the range oftemperatures and pressures normally encountered in practice, in the following two ways:

1. The molecular nature of a gas may be ignored, and the gas is treated as a continuous medium or continuous expanse of matter, termed continuum (that is, does not consist of discrete particles).

2. The decrease in size of the imaginary sphere may be assumed to reach a limiting size, such that, although it is small compared to the dimensions of any physical object present in a flow field, for example an aircraft, it is large enough compared to the fluid molecules and, therefore, contains a reasonably large number of molecules.