Vízügyi Közlemények, 1932 (14. évfolyam)
2. füzet - XII. Kisebb közlemények
26 waves (Figs. 12—13). This critical depth may be computed likewise on the basis of the law of momentums by means of the formula : <\ — t a) [h + (to±z)f + 4t 0k„ j + 4t 0*k„ = 0 12. Experiments carried out by the writer in the hydraulic laboratory at Karlsruhe in 1926—27 have shown that dangerous erosions below a dam with an apron placed high can be avoided only when the tail water is so high that the shooting jet on the surface can flow unhindered. (Figs. 15a—b, 16, 17). It is an interesting phenomenon that with dams having an apron placed high — especially with a readily erodible river bed — the water jet periodically changes its position, i. e. at one time it flows along the bottom, where it brings about great erosion, and then, when the hollow lias attained a certain extent, the jet is pushed up again to the surface. Then a flat water cylinder is formed at the bottom, and revolves in such a direction that the former deep hollow is filled up again to a certain point, when the water jet submerges once more and erosion begins anew. This alternative play goes on until there is enough material in the river bed to fill up the erosion. (Fig. 16—17J. With dams where the apron is located at the same elevation as the river bed. or even lower, the erosion depends upon the nature of the hydraulic jump, or upon the relative position of the tail water. At a hydraulic jump without a water cylinder the shooting jet, passing suddenly from the smooth apron to the rough river bed. leaps sharply up at the end of the apron, and then falling down again, still with a fairly high velocity (see Fig. 18a, 19), it causes deep erosion in the immediate vicinity of the dam. With a hydraulic jump having a free top cylinder, the depth of erosion is less, because, as has been shown by experiments, this sort of clow nflow produces the greatest loss of energy (Fig. 186, 20/ With a hydraulic jump having a backed-up cylinder, the erosion is greater again, corresponding to the variations in the depth of tail water, because with this sort of downflow the greater part of the released kinetic energy serves to increase erosion. In this case there may also be observed the phenomenon of periodic variation in the position of the water jet, as described above for the case of dams with a high baffle weir at the end of the apron and placed in a readily erodible river bed. (Fig. 21-—24). Summing up the experimental results obtained at dams of low located apron, we get the curves indicated by full line in Figure 25. These curves represent the correlation between the depth of tail water and that of erosion. It is evident that the downflow forming a free top cylinder is most favourable, because in this case the erosion is the slightest. Recently, on the basis of former experiences and the above experiments, it has been attempted to protect the river bed against erosion and at the same time to protect the dam itself not by lengthening the apron, but by placing it at a proper depth, in order to produce the most favourable downflow, i. e. a hydraulic jump with a free top cylinder, in accordance with the curves shown in Figure 25. The proper location of the apron may be determined as follows : The depth of the tail water in the river bed (t f ) at a certain discharge q is known, and the depth of the water jet in the apron (t 0 ) may be computed from the known head over the danr or from the sluice orifice and the contraction factor ; then the height of the hydraulic jump appropriate to t 0, or the depth of tail water t u, may be determined by formula No. 10(7. Now. if tf > f u. i. e. if the tail water in the river bed is greater than the
