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. 7 relevant sections of the curriculum reform at the Budapest Technical University. In the new curriculum the teaching of hydraulics will be started for the third-year students in hydraulic engineering, in the first semester of the academic year 1976/77. Accordingly, theoretical hydromechanics —hydraulics will be presented in the 5-th semester in 2 + 3 hours per week. The lecture notes of the new subject, theoretical hydromechanics-hydraulics, hereafter Hydromechanics, are already in printing and are expected to become available to the students at the beginning of 1976. The new subject, Hydromechanics differs appreciably from the foregoing. Since it is presented before the so-called practical hydraulics, it deals with the material properties of the fluids, as well as with all basic laws of hydrostatic, kinematics and hydrodynamics. The uniform physical approach is introduced and besides the conventional theoretical methods, the fundamental laws are derived also with the help of the balance equations to test the reponse of the students. Along with each theoretical relationship of hydromechanics the potential practical applications thereof are also indicated. In this way information is presented to the students even at the most abstract theoretical parts on their fields of application. In the 6-th and 7-th semester practical hydraulics — hereafter simply Hydraulics —will be presented in 3 + 3, respectively 2 + 1 hours each week. The subject of the new Hydraulics will be comprised in two volumes scheduled for the end of 1976. The new lecture notes on Hydraulics are founded completely on the theoretical basis laid down in Hydromechanics. With reference to the subject of Hydromechanics the most important t heorems of hydraulics are recalled to the students. This, however, should not be mistaken for repetition on parallelism, since the attention of the students is called to the unity of hydraulics. In the 8-th semester, as an optional subject some parts of hydraulics of eminent practical importance will be presented more in detail with all relevant theoretical and practical implications under the title Applied Hydraulics, in 2 + 2 hours per week. These parts include fluvial hydraulics, sediment transport, similarity theory and model testing, to mention a few only. The students who have decided at the beginning of the 8-th semester to specialise in hydraulics will have to pass an examination on this subject to obtain the State Certificate. The physical approach contemplated in the teaching of hydraulics and in this connection the close interrelation and harmony with hydromechanics will be demonstrated subsequently in detail by two examples. The first example is concerned with the fundamental law of hydrostatics developed by Euler, by which, as will be recalled, the increment pressure dp due to the mass forces T in the fluid space of density q is described along the difference vector dr : dp = pT dr (29) or in scalar form, denoting the three components of the mass forces by T x, T v and T z: T„ = T z — 1 dp . M dx 1 dp . o 9 y ' 1 dp 0 dz (30) The change in pressure is also a phenomenon of physics, which can be described by the balance equations (9). In the hydrostatic "phenomenon " the relevant extensive quantity is momentum. In Eq. (9) the momentum density would be accordingly ví = q \, which, however, will become zero in the stationary fluid where v = 0. For the same reason the surface density of the convective momentum current will also be zero. The conductive surface current of momentum, is a consequence of the hydrostatic pressure force F\ The momentum thereof during the time dt is Pd/ [FT] (31) and the current thereof P [F] (32) The surface density of conductive momentum, current will become, remembering that the pressure force P acts on the area F : F =pe [FL2] (33) where e is the unit vector of the pressure force P, since the force can be defined as the momentum transferred in unit time. Let the mass force acting on unit mass be T, with the components T x, T y, T z. For the mass m and, during the time dt the momentum is mT dt (34) while the momentum source is the share thereof in unit time, thus mT (35) The source density of momentum is qT (36) where q is the density of the fluid. The balance equation of momentum is derived preferably in scalar form. The balance equation should be written accordingly for the component of momentum along x. The surface density of conductive momentum current along x is thus pi (37) where i is the unit vector in the direction x. The source density is then : qT x (38) Thus the balance equation of momentum written for the direction x is div (pi)= eT x (39) On the other hand div ( pi) =<p div i + i grad p since div i = 0 and Ígrad7, = Íí(| Í from Eq. (39) , 9 • , 9 i H JH k dy 9 z m (40) (41) dp dx — oTx (42) Writing the equations for the components along y and z in an analogous manner we obtain 9p dx = 0Ty\ dp 9 z = oT z (43)
