Vízügyi Közlemények, 1984 (66. évfolyam)

4. füzet - Varga István: Analitikus megoldások alkalmazása az egydimenziós szabadfelszínű áramlások számításában

Analitikus megoldások alkalmazása az egydimenziós... 571 Analytical solutions in the calculation of one-dimensional open-channel streamflow by Dr. I. VARGA, Civil Engineer, C.Sc. The author presents a special version of the calculation used for open-channel one-dimensional streamflows as part of a broader research effort, the analysis of the dynamics of water diversion and conduct. This special approach is capable to solve the de Saint- Venant equations approximatoely by generalization of the theory of waves with small amplitudes. The base-equations were linearized and inhomogeneous partial differential equations (5) and (6) were solved with aid of the Laplace-transform. Then, the transfer functions were determined characterizing the changes in water level at the border cross-sections of elementary channel sections, (See expressions [12] and [13], and Tables I and If). By use of the boundary value theorem of the Laplace-transform the transition functions indicating the changes in water level in these border cross-sections were calculated, appropriate for the estimation of the needed time-functions (See expressions [14] and [15], and Table III). By use of the transition equations, the base equations of a temporally and spatially discretized streamflow pattern had been obtained, valid for any channel-bed, (See Eqs. [16] and [17]). If these are supplemented by equations of the boundary conditions, the so-called systems-equations may be obtained. Results consist of water levels, and discharges received by solving the system of linear equations in the individual At time intervals. Generalization of use can be demonstrated in a theoretical example. Reliability of the method is characterized by comparison with results obtained by using the method of characteristics. Then, the conditions of use are listed (criteria of stability). The main features of the presented method are the following: - streamflow is discretized in time and space; - relationships between stream characteristics in the border cross-sections of elementary river-sections in a given At interval are described by linear base-equations with constant coefficients; - the coefficients of the base-equations stem from the analytical solution-functions of the linearized de Saint-Venant equations under given conditions; - by the solution of the systems equations stage and discharge values are obtained in selected cross-sections of a river for each time interval; - during calculations there was no stability problem under relatively easy conditions; - due to the fact that the coefficients of the systems equations are analytical solution-functions, accuracy of the calculations was rather insensitive to the selection of time steps and the length of the sections (if these were increased, accuracy has somewhat decreased); - the method is rather simple; if further rational and permissive simplifications are introduced it may be programmed even on pocket-calculators. The present method may be used economically and effectively in the planning and checking of complex water distribution systems and in the analysis of the streaming conditions of natural and canalized rivers. * * *