Calculation of stone sill overflowing during low discharges

Abstract

This paper is inspired by a stone sill designed in the channel of the Velika Morava river (near Markovački bridge, Serbia), in order to ensure water supply of the Thermal Power Plant 'Morava' during low flows, and to terminate erosion of the river bed, thus accelerating its stabilization. The impact of extremely high absolute roughness of the sill is particularly strong during low discharges and small water depths, and is manifested by intensive turbulence and air entrainment. Under such flow conditions, the Manning equation for energy loss calculation is not valid. The method by Hartung and Scheuerlein, applied in this case, considers the water-air mixture, and accordingly offers an iterative procedure for estimation of the roughness coefficient value. The Morava river stone sill case study shows that the water surface longitudinal profiles, calculated by the Manning equation, and by the Hartung and Scheuerlein method, differ significantly. Therefore, small depth flows over very rough surfaces are not be calculated in a routine way, but have to be considered as a separate local phenomena.

Ovaj rad je proizašao iz projekta kamenog praga u koritu Velike Morave kod Markovačkog mosta. Svrha praga je da osigura vodosnabdevanje TE 'Morava' u periodu malih voda, zaustavi opštu eroziju korita i time ubrza njegovu stabilizaciju. Uticaj izrazito velike apsolutne rapavosti prelivne konture praga naročito dolazi do izražaja u periodu malih voda - pri malim dubinama prelivnog toka, a ogleda se u intenzivnoj turbulenciji i uvlačenju vazduha. U takvim uslovima, ne važi Maningova jednačina za linijske gubitke energije. Metoda Hartunga i Šerlajna, koja je primenjena u ovom radu, razmatra mešavinu vode i vazduha i shodno tome, omogućava procenu odgovarajuće vrednosti koeficijenta trenja. Primer praga na Moravi pokazuje da se linije nivoa, sračunate pomoću Maningove jednačine i po metodi Hartunga i Šerlajna, značajno razlikuju. To znači da se tanki prelivni tokovi na podlozi velike rapavosti ne smeju računati šablonski, već se moraju hidraulički analizirati posebno, kao lokalni fenomeni.