Vízügyi Közlemények, 2000 (82. évfolyam)
2. füzet - Rátky István: Árvízi hurokgörbék közelítő számítása
258 R àtky István feld in 1985. It was based on the simultaneous measurements of the discharge of the River Tisza at two stations (Tiszapüspöki and Dinnyéshát), where 39 and 36 discharge measurements were made, respectively, in the period 25 March-10 May of 1895. They defined the hysteresis curve in the following, still today acceptable, way of the time of passage of a flood wave: "If one wishes to forecast day-by-day the expectable water stages, one must not only know the arrival of cumulating waters, but also the rate of change of the water stage, whether it is slow or fast. Namely: in our studies it was found that the velocity of progression of a certain water stage depends not only the height of the water level but also on the rate of its change". The analytical solution of the flood-discharge looping curve is given by the author in Eq. 6. Equation 6 cannot be applied in the practice, but in cumbersome way only, since it can only be solved iteratively, using certain approximations. Of the approximate methods those described by equations 7, 8 and 9 (types А, В and C) are the most reliable ones, being also most suitable for practical applications, (notations of the geometry, the surface slope and the additional surface slope are given in Figure 1, while the calculated hysteresis curves are shown in Figure 2.). The author has studied the changes of the hysteresis curve in function of various important hydrological and hydraulic parameters with the help of a ID unsteady flow model (see tables I. and II.). Figure 3 shows the effect of the progressing and flattening of the hydrograph, while figures 4, 5 and 6 those of the intensity of flooding, the change of roughness (smoothness) and the change of bottom slope, respectively. The author has compared the results obtained by the approximate solutions (Eqs. 7., 8., and 9) to those obtained by the ID unsteady flow model. Figure 7 shows the differences in steady and unsteady flow conditions in function of the flow depth. Figure 8 shows the function dQ(h) as obtained by the ID model and the three approximate solutions. It can be seen that approximation С yields practically the same accuracy as approximation B. These proportions will not change with the intensity (Figure 9.) and neither with the changes (within certain domain) of the bottom slope and the roughness. Figure 10 shows the temporal changes of hydraulic parameters used in the approximation of type C. Indication of the effects of all variables was deemed necessary for showing the relationship of the changes of various parameters, with each other. The concrete values or the easy reading of the values are of lesser importance in this case. Figure 10 is also important, as the author claims, that no one has described, illustrated, before the in-time variation of the parameters of the approximate unsteady flow equation during the passage of a flood hydrograph (on the basis of calculations). The graph of Figure 10 can be used for supporting all the important conclusions. Thus, the temporal sequence of occurrence of the maximum values of all hydraulic parameters can be traced: namely, that the rising limb of the flood-hydrograph does not coincide with that part of the hysteresis curve, which is to the right hand side of the steady state curve and that the maximum value of surface slope coincides with the inflexion point of the hydrograph. For illustrating the practical use of the method the author shows the hysteresis curves of the station Remete of the River Fekete-Körös and that of the Makó station of the River Maros, in Figures 11. and 12. respectively, together with the calculated hysteresis curve using the approximation В (based on the instantaneous value of the surface slope). The deviation between calculated and measured curves in negligible. Figure 13 shows the hydraulic conditions of the Körös river system (the rivers FehérKörös, Fekete-Körös, Kettős-Körös, Hármas-Körös and the River Berettyó) and of the emergency flood storage reservoir of Mályvád upon the effect of filling up the latter, as calculated by the 1D unsteady flow model TÁMASZ (Mathematical Simulation of Reservoirs).
