Temperature

In any form of matter the molecules are in motion relative to each other. In gases the motion is random movement of appreciable amplitude ranging from about 76 x 10-9 metres under normal conditions to some tens of millimetres at very low pressures. The distance of free movement of a molecule of 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 the molecules in a gas is called the length of mean molecular free path.

By virtue of this motion the molecules possess kinetic energy, and this energy is sensed as the temperature of the solid, liquid or gas. In the case of a gas in motion it is called the static temperature or more usually just the temperature. Temperature has the dimension [0] and the units К or °С (Section 1.1). In practically all calculations in aerodynamics, temperature is measured in K, i. e. from absolute zero.

1.2.2 Density

The density of a material is a measure of the amount of the material contained in a given volume. In a fluid the density may vary from point to point. Consider the fluid contained within a small spherical region of volume 6V centred at some point in the fluid, and let the mass of fluid within this spherical region be dm. Then the density of the fluid at the point on which the sphere is centred is defined by

_ . ..6m.. t.

Density p= km — (1.4)

tfv—►О О V

The dimensions of density are thus ML-3, and it is measured in units of kilogram per cubic metre (kgm-3). At standard temperature and pressure (288 K, 101 325 Nm-2) the density of dry air is 1.2256 kgm-3.

Difficulties arise in applying the above definition rigorously to a real fluid composed of discrete molecules, since the sphere, when taken to the limit, either will or will not contain part of a molecule. If it does contain a molecule the value obtained for the density will be fictitiously high. If it does not contain a molecule the resultant value for the density will be zero. This difficulty can be avoided in two ways over the range of temperatures and pressures normally encountered in aerodynamics:

(i) The molecular nature of a gas may for many purposes be ignored, and the assumption made that the fluid is a continuum, i. e. does not consist of discrete particles.

(ii) The decrease in size of the imaginary sphere may be supposed to be carried to a limiting minimum size. This limiting size is such that, although the sphere is small compared with the dimensions of any physical body, e. g. an aeroplane, placed in the fluid, it is large compared with the fluid molecules and, therefore, contains a reasonable number of whole molecules.