Page 25 - Aerodynamics for Engineering Students

8 Aerodynamics for Engineering Students

1.2.4 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
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 [e] and the units K or "C (Section 1.1). In practically all calculations in
aerodynamics, temperature is measured in K, i.e. from absolute zero.

1.2.5 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 SV centred 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 centred is defined by

Sm
Density p = lim -
6v+O SV

The dimensions of density are thus ML-3, and it is measured in units of kilogram per
cubic metre (kg m-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.

1.2.6 Viscosity
Viscosity is regarded as the tendency of a fluid to resist sliding between layers or,
more rigorously, a rate of change of shear strain. There is very little resistance to the
movement of a knife-blade edge-on through air, but to produce the same motion