Hydraulics of flow over full-cycle cosine and rectangular sharp-crested weirs

Abstract

Laboratory experiments were carried out to investigate the hydraulic characteristics of full-cycle cosine and rectangular sharp-crested weirs in free flow condition. The head–discharge relationships of full-cycle cosine weirs were determined theoretically and the discharge coefficients were correlated with weir geometry for both rigid and erodible bed conditions. The proposed model showed higher discharge coefficients in full-cycle cosine weirs in comparison with rectangular sharp-crested weirs. The three-dimensional velocity profiles of full-cycle cosine and rectangular weirs were measured by an acoustic Doppler velocimeter probe. The effects of weir geometry on mean flow and local erosion upstream of the weirs were studied for two sediment sizes of 0.7 mm and 1.2 mm. The time-averaged velocity profiles exhibited strong three-dimensional flow in full-cycle cosine weirs. The strength of the upper eddy in the crest location of full-cycle cosine weirs decreased by increasing the weir gap opening and the jet stream deflected upward due to uneven eddy sizes. The maximum streamwise velocity of cosine weirs increased by four times the average velocity at the crest level of the weir and the transverse velocity profiles captured strong vortices in the vertical plane closest to the weir. The effect of weir gap opening of full-cycle cosine weirs on the total scour volume was studied for two sediment sizes. It was found that the scour volume in the upstream region of cosine weirs was higher than the scour volume formed upstream of a rectangular weir with the same opening.