Hidrológiai Közlöny 1976 (56. évfolyam)
1. szám - Dr. Bogárdi János: Elmélet, oktatás és gyakorlat a hidraulikában és hidromechanikában
Dr. Bogárdi, L. J.: Theory, education and practice in hydraulics Hidrológiai Közlöny 1976. 1. sz. 5 will become dfa: - ~dT (25) or by dividing by g and introducing the kinematic viscosity v=pIq, the equation written for the component along x becomes dp Av x 1 — jTT~ — 1 % — „ at o Qx + vp'Vx (26) In an analogous manner, for the components along y and z: (27) (28) ~dr~ l y~ dv. Q Qy 3 V , 2 d t 0 dz Eqs. (26), (27) and (28) are indeed the scalar form of the Navier —Stokes equation. The example may appear slightly far-fetched since the Navier —Stokes equations can be applied in very simple cases only to the solution of practical problems. The general applicability of the balance equation under Eq. (9) will however, be demonstrated clearly in the flollowing. The hydrostatic equation of Euler and the energy equation of Bernoulli will be derived subsequently from the balance equation. These latter are commonly used in routine practice. 2. Advanced teaching o! hydraulics The curriculum in hydraulics is subject to continuous changes concerning its contents and methods alike. The changes are controlled primarily by the requirements arising in practice, but evidently the advances in theoretical hydraulics play also an important role. In the Medieval Age a knowledge had to be acquired which could be called water sciences by a comprehensive term. In the 18-th and 19-tli centuries, owing to the different paths of evolution, theoretical fluid dynamics and hydraulics based on experiences and observations were taught separately. Further difficulties were introduced by the relationships of hydrology, evolved from physical geography which were predominantly empirical in character and the regular teaching of which has acquired almost primary importance to meet the requirements of practice. No attempt can be made here at any detailed review of development, since this would lead inevitably to the description of the history of hydraulics. This, however, has been done in several comprehensive works by more competent authors. The present paper will consequently be devoted to the methods of education adopted in the recent past end devek>}>ed in these days. It will be perceived from the foregoing that education based on a physical approach is believed to be most appropriate. This statement is evidently valid, since fluids form an important domain of the material environment, and the exploration of all phenomena related to these belongs to the subject of physics. According to the most conventional classification of physics, the examination of phenomena related to the movement and state of repose of fluids, further the description of relationships and laws prevailing between them, belong to the chapter on fluids in the mechanics of deformable media, namely, the mechanics of fluids. This subjcct, namely hydraulics, hydromechanics, is thus preferably introduced by adopting the physical approach. Accordingly, any moving or stationary fluid, or fluid space is regarded a "system" in the general sense. The physical approach to stationary or moving fluids is conducive to the following statements: — the system consists of elements, — the elements are interrelated, — the system is separated from its environment by a "boundary", — at any instant the system is in a definite state (which is in the exact sense the result of a stochastic process), — the environment may act on^the system across the boundary in different ways, — owing to the environmental effects the state of the system may be changed (owing to mutuality the system may also act on its environment). The state of any system may be described by the points of the so-called state-field. Changes in state are characterized by the series of changes at the individual points. The parameters of the system by which the state is uniquely described are termed the relevant properties of the material. Two states are understood to be equal, if all relevant properties are equal at any particular instant. In principle a change in state is a change in the relevant properties of the material in space and time. These properties are called physical variables. In principle, the number of properties is infinitely large. The term physical variable will, however, be confined to those, which describe the state uniquely. iío description, measurement and computation of processes is possible, unless the physical variables can be characterized uniquely. For this purpose the terms and values of the physical variables must be distinguished. The term implies a qualitative definition unrelated to the actual value. The value is a quantitative definition unrelated to the actual value. The value is a quantitative definition related to an element (a physical quantity) of the physical variable designated by a particular term. The quality of a physical variable is determined — by its relationship to other physical variables, — by its response to the transformation of coordinates and — by their role played in the process. The nature of the relationship with other physical variables is expressed by the dimension. Capital letter symbols are used to indicate the dimensions of the diverse physical variables. For instance L, M, F, T, E and tí are the symbols for length, mass, force (or weight), time, energy, temperature, respectively. The relationship existing between the physical variables can be described by specific expressions, permitting the dimensions of particular variables to be expressed as functions of the others. In other words, adopting some of the physical variables as basic variables, the dimension of all other physical variables can be expressed in a definite manner by the dimensions of the basic variables. The dimensions related to the basic variables are termed primary, while those related to the others are called secondary or derived dimensions. The choice of the basic variables is arbitrary (governed in general by agreement). In hydromechanics and hydraulics the introduction of three fundamental dimensions is in general satisfactory. The so-called technical system involving the length L, the time T and the force F is commonly adopted. In hydroinechanical considerations related to the classic theorem of physics the physical system of dimensions is used, involving the length L, the time T and the mass M. On the other hand, physical laws expressing valid relationships must not depend on arbitrary considera-
