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The Development of the VC-Ogee Relationship Which Incorporates Upstream 3-Dimensional Flow Conditions

Author: SJ van Vuuren, GL Coetzee
Conference: 84th Annual Meeting of International Commission on Large Dams
Date: May 15-20, 2016

ABSTRACT
The widely used Ogee relationship is one of the most studied hydraulic relationships in the world (Savage & Johnson, 2001). Various attempts were made to accurately describe the shape of the lower nappe of water flowing over a sharp-crested weir, known as the Ogee profile. The current Ogee profile relationship was formulated from 2-dimensional hydraulic assessments. Recent studies, which included varying upstream geometry layouts, have indicated that the 2-dimensional approach flow conditions may be insufficient and, that 3-dimensional flow should be considered (van Vuuren, et al., 2011). An accurate Ogee flow profile is hydraulically efficiency and minimizes the possible occurrence of sub-atmospheric pressures on the surface of the spillway. An asymmetrical and/or skew approach channel causes 3-dimensional flow over the Ogee spillway that may contribute to the separation of the lower nappe from the surface that was designed with a 2-dimensional flow relationship.

Based on the results obtained from physical model studies and numerical analyses the VC-Ogee relationship was developed to incorporate the upstream 3-dimensional flow conditions. The VC-Ogee relationship utilizes the Hager formula (1987) for the upstream quadrant and the power function of the WES profile for the downstream quadrant. These relationships were extended to include the upstream topography, asymmetricity of the approach channel, orientation of flow relative to the spillway as well as the curvature of the spillway. The VC-Ogee relationship, which incorporates the influence of 3-dimensional flow conditions, reduces the potential of sub-atmospheric pressures and provides a more realistic discharge  relationship.

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