Hidrológiai Közlöny 1976 (56. évfolyam)

1. szám - Dr. Bogárdi János: Elmélet, oktatás és gyakorlat a hidraulikában és hidromechanikában

6; Hidrológiai Közlöny 1976. 1. sz. Dr_ Bogárdi, L. J.: Theory, education and practice in hydraulics lions, their form being identical in any system of the basic variables. In other words, the physical laws are invariant, i.e. unaffected- by any transformation of dimensions. Consequently, no equation describing objective laws must contain terms of different dimensions, the equations must be dimensionally homogeneous. It should be noted here, that distinction must be made between physical variables of identical kind and of identical name. Physical variables having identical dimensions are of same kind, thus for instance energy, heat and work are of identical kind but of different names. Depending on their response to a transformation of coordinates, different tensorial ranks of the physical variable may be distinguished, such as scalar-, vectorial", and tensorial quantities. The system of coordinates is adopted arbitrarily, governed in general by practical considerations. On the other hand, physical laws expressing valid relationships must not depend on arbitrary considerations, their form being identical in any (so called inertial) system of coordinates. In other words: the physical laws are invariant, i.e. uneffected by any transformation of coordinates. Depending on their role played in the process, flowing quantities and physical variables determining the direction and rate of flow are distinguished. This classification is completely competible with the transport theory describing engineering processes. Those mentioned first are quantities proportionate to extension (the variables of size character are the extsnsive quantities), whereas the latter are the intensive quantities unrelated to extension. In their majority, extensive variables represent permanent properties. Objective laws must not conflict with the laws of conservation. Knowledge of the names of the physical variables and of the relationships existing between them is sufficient for writing the equations or expressions describing phenomena. In computations or measurements the magnitudes of physical quantities (some value of the physical variables) are involved, so that quantitative terms are also needed. For the determination of a quantity a particular value of the physical variable is adopted and the other values are related thereto. This particular element is understood as the unit of measurement defined on the population of the physical variable. In principle, any physical variable could be given its particular unit of measurement. Remembering, however, the statement made in connection with the fundamental (primary) and derived (secondary) dimensions, some of the units of measurement are considered fundamental, the others as derived units of measurement. By adopting the fundamental units a particular set of units of measurement is uniquely defined. Hereafter, any element of the physical variable (the physical quantities having the same name) can be characterised by a single number, indicating in general the ratio of the element to the unit of measurement. This number is referred to as the measure. The above review of the familiar theorems has been presented with the sole intention of emphasizing more clearly the importance of the physical approach. It is fully realised that the physical approach is not novel to the teaching of hydraulics. All laws of hydraulics have been derived by starting from physical foundations. The very same approach is adopted by contemporary research workers. That these problems must still be dealt with is due to the lack of the uniform phylosophy. It must be admitted, that no method of hydraulics teaching has been developed so far enabling the student to recognise readily the theorem closely interrelated to each other. The problem, however, is not confined to what, to what extent and how should be taught under what uniform approach, but the sequence of acquiring knowledge is also essential. Thus in teaching hydraulics, four essential circumstances must be taken into consideration. The first is the uniform physical approach, which is unquestionably the only possible procedure. The acceptance thereof is inevitable, and its correctness is demonstrated convincingly by the foregoing logics. The second is the method of teaching, which may already include a wider variety. The balance equations describing various engineering phenomena and founded on the transport theory are recommended. The introduction of this method is under way, if only with an experimental character, for the time being. The experiences gained so far are favourable. The third problem is concerned with what .and to what extent should be taught in hydraulics, bearing the steadily growing volume of information in mind. This most difficult problem in teaching hydraulics is closely related to the method of teaching. If we succeed in composing the proper method, many details confusing the students can be omitted without causing a lack of essential information. The work involved is very exacting and considerable time is required before a method can be elaborated completely. The results, however are likely to compensate the teacher and student alike. The "common language", namely the balance equations of the transport theory are believed to meet the above requirements. This will be demonstrated by examples. The fourth question is related to the sequence of acquiring knowledge. The theoretical fundamentals should be presented first, or the so-called practical hydraulics? A few decades ago, sequence presented no particular problems. Theoretical hydraulics (hydromechanics) was but loosely related to practice. Its inclusion into the curriculum amounted to preparation only for the post-graduate education of future engineers. For this reason, it was in general presented after practical hydraulics only. The students were evidently uncapable of integrating the two subjects. The change in the sequence of presentation of the two subjects was logically of little help. Nevertheless, this was the starting base for uniform teaching which has been demonstrated to be very favourable by the experience gained during the past four-five years at the Budapest Technical University. The simultaiieous introduction of teaching by the uniform physical approach

—as mentioned already

—has contributed to success. Besides the foregoing four considerations, other conditions are also recognised to influence successful teaching of hydraulics. The problem has received international attention. The relevant problems were discussed at a seminar during the XVI Sao Paulo Congress in 1975 of the International Association for Hydraulic Research (IAHR). A great number of interesting and useful proposals and comments have been made, which are likely to contribute to the solution of this important educational problem. Before embarking on examples related to the teaching of hydraulics, it may be of interest to review in brief the