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Tunnel spillways are widely used in medium-and high-pressure hydraulic works. It is therefore an important and pressing task to improve the constructions used in these types of spillways and to develop optimal and reliable spillway structures.With this in mind, we would like to turn the reader's attention to essentially novel (i.e., in terms of configuration and operating conditions) vortex spillways which utilize vortex-type flows [1, 2, 3, 4]. On the one hand, these types of spillways make possible large-scale dissipation of the kinetic energy of the flow on the initial leg of the tailrace segment, and, as a consequence, flow rates of slightly vortex-type and axial flows through the subsequent legs that do not produce cavitation damage. On the other hand, the dangerous effect of high flow rates on the streamlined surface decreases over the length of the initial tailrace leg as a consequence of the increased pressure on the wall caused by the effect of centrifugal forces.A number of structural studies of tunnel spillways for hydraulic works such as the Rogunskii, Teri, Tel'mamskii, and Tupolangskii hydraulic works based on different operating principles have now been completed. These constructions may be divided into the following basic groups:-vortex-type (or so-called single-vortex type) spillways with smooth dissipation of the flow energy throughout the length of the tunnel when L r > (60 --80)hT or (60 --80)dT (where dT and hT are the diameter and height of the tunnel; cf. Fig. 1), while the cross-section of the tunnel is either circular or near-circular throughout its length.-vortex-type spillways with increasingly greater dissipation of the energy of the vortex-type flow over a shorter length Lr -< (60 --80)hT of a noncircular section river diversion tunnel (horseshoe-shaped, square, triangular) which is connected to the eddy chamber either by means of an energy-dissipation (expansion) chamber (Fig. 2) [5, 6] or by means of a smooth transition leg [7]; -spillways with two or more interacting vortex-type flows in energy-dissipation discharge chambers [8] or in special energy dissipators that have been termed "counter-vortex energy dissipators" [2, 4].The terminal portion of the tailrace tunnel of a vortex spillway may be constructed in the form of a ski-jump bucket, a stilling basin, or special structures depending on the flow rate at the exit from the tunnel and on the conditions in the channel downstream. The hydraulic system used to link the flow to the tailrace canal may involve the use of either overflowtype or free-fall type structures.Vortex spillways with smooth or accelerated [7] dissipation of energy over the entire length of the water conduit represent the simplest and most promising types of hydraulic structures.Techniques of designing vortex spillways have now been developed and published in numerous studies [2, 7, 8]; in particular, techniques are now available for calculating the hydraulic resistance of individual legs of a route and the flow rates and pressures in vortex-type flow. Howeve...

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