Hydrodynamics, the theory of fluid flow, is a very difficult field of science. The problems it faces are so complex, that in spite of all the effort of generations of scientists, for most practical problems there are no known exact solutions - if they exist at all, solutions are only approximate. This is why there is the necessity of experimental verification or why the solution is sought downright experimentally, even though this requires extremely expensive facilities (wind tunnels, towing tanks, ...) and instrumentation (laser anemometers,...). Because of the subject being so difficult, it is useful in the introduction - which is the subject of the present text - to begin with simplifications. Some of them (one-dimensionality, incompressibility,..) will be observed in the whole of the present text. Others will be gradually removed in the following chapters - after the basic relations will be mastered, it will be useful to look for better approximations to relity or for the possibility to include additional factors. For example, the problem of inevitable losses which occur in fluid flow is, for the time being, postponed here. It will be studied in next Chapter [D]. Although losses cannot be avoided, they are not importand for explanation of some basic phenomena and in the first encounter with the subject it is possible to obtain useful results even when they are neglected. Similarly, postponed to another chapter will be unsteady problems - here we consider only flowsthat are steady, not changing in the course of time.

In the present simplified hydrodynamics of one-dimensional flows (which is particularly useful for study of hydraulics, incompressible fluid flow in pipes and cavities (from Greek "hudor" = water, "aulos" = tube) - it is sufficient for describing the objects of our interest by the Theorem of Bernoullis - the equation for changes of fluid specific energy along the only spatial co-ordinate. In contrast to the form of this conservation equation used so far, in the present chapter, aimed at stidy of one-dimensional lossless steady flows, it will contain an additional term, which represents the fluid kinetic energy. This component of energy is exceptional: its intensity and extensity factor are identical. This exceptional character is the cause of the nonlinear, quadratic (produc of two equal terms) character of solved equations and, in fact, is the root of all the problems of fluid mechanics.
Fig.C-1
Diagram for (rough) estimation of
fluid specific kinetic energy
for a given mass flow rate
and given cross-sectional
area in the case of air
at atmospheric condi-
tions. The diagram is
based upon formula from Fig.A-20.



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This is page Nr. C01 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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