Fig.A-9 Typical surface of equilibrium states:
Solid, liquid, as well as gaseous phase exist only within a given range
of state parameters. Values of two parameters (e.g. temperature
and pressure) determine in a unique manner the third one. There is
an additional degree of freedom in phase transition regions (melting,
evaporation, sublimation).
information about the mean free path of their motion between successive mutual collisons. This is - under the common laboratory temperature and pressure conditions - only (= sixty millionths of a millimetre).

Note.: There is an extraordinary part of fluid mechanics, called superaerodynamics - aero-
dynamics of very dilute gases (the name was introduced by Tsien 1946). There the concept of continuum is not applicaple. It is, of course, a highly special matter, which finds application e.g. in solutions of return of rockets and other space objects into atmosphere, in the outer layers of which the mean free path as as long as hundreds of meters. Criterion of the necessity of applying the laws of superaerodynamics is the je Knudsen Number

... where l is the characteristic length of the object (dimensions of the satellite or orifice diameter in a vacuum aparatus).

It is necessary to emphasize that fluids are very complicated objects of study and, as a consequence, it is almost always necessary to work with certain simplified fluid models. Such a model usually neglects properties (such as taste, smell, color, pH value, ...) not important in mechanical connotations. It is important, however, that in order to obtain mathematical simplifications, many models often neglect even mechanical properties as long as they are of secondary consequences for a phenomenon under study. We shall work here with the model of the incompressible fluid and at the beginning we shall actually introduce also a model of nonviscous fluid. The axiom in this respect is always to use as simple model as possible and to apply a more complicated one only when absolutely necessary.

Fig.A-10
Division of fluid mechanics into
particular branches according to
the value of Mach numbers, en-
countered in a given branch.
Mach number expresses the
relative influence of compressibility.
The incompressible fluid model brings really substantial simplification and we shall use it in the whole of the present textbook. Of course, any fluid is, in reality, more or less compressible, i. e. exhibits volume variations as a response to pressure changes. This effect is particularly large in gases. The volume changes are, however, associated with unavoidable thermal changes - tempreture increases when gas is compressed and decreases when gas expands. The thermal effects make the energetic budget of the change much more complex - and intractable for those, who did not so far study the subject "Thermodynamics". The incompressible fluid model may be successfully used for computing flow of liquids (it is, in fact, nearly perfect there): in the typical example of dependence between pressure and volume in Fig.A-9 (let us e.g. assume a process with negligible temperature change) we may note the steep, almost vertical shape of the equilibrium surface in the liquid region (water is, for example, only about 100-times more compressible than steel). On the other hand, the gas phase has not only much larger v (volume increases by nearly 3 decimal orders during evaporation) but the slope of the surface is much lower. Compressibility of gases is usually -times larger than that of liquids. In spite of this, methods of hydromechanics (= mechanics of liquids, from Greek "hudor" = water) which operates with the basic assumption v = konst may solve many problems of gas flow, which is otherwise a subject of interest in aerodynamics (Greek "aeros" = air, "dynamikos" = force ) - it is evidently possible as long as the changes of pressure are only small, at least relative to absolute values (which are large - let us not forget that air in the atmosphere



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