Journal of Irrigation and Drainage Engineering

With the increasing trend of replacing barrages in Egypt, especially those built before the High Dam in 1971, there is a need to reduce their construction costs. Barrages/regulators are structures used to control water levels along irrigation canals. The main elements of a barrage/regulator consist of a floor, abutments, piers, and a bridge. The cost of a barrage depends primarily on its floor and secondarily on its abutments, piers, and bridge. There are two methods for designing the barrage floor, including (1) the rigid method, and (2) the flexible method. In this study, two new models are implemented in MATLAB to design barrage elements using both the rigid and flexible methods. The design models are coupled with the shuffled complex evolution algorithm, developed at the University of Arizona (SCE-UA). The developed framework was applied to an existing barrage to demonstrate its efficiency and to obtain the most economical solution. The results proved that using the flexible method provides superior results compared to the rigid method. The developed framework provided good solutions for the studied case using both methods.

Power-law sections provide great flexibility in open channel design. However, in the literature the optimum hydraulic power-law section has been developed for only specific values of the exponent $k$ of the power-law formula. This paper presents a general exact solution of the optimum hydraulic section with $k$ as a parameter based on Gaussian hypergeometric mathematics and the Lagrange multiplier method. The relationships between $k$ and each of the optimum width-depth ratio and the side slope are derived. The explicit exact formulas of the shape factor, normal depth, critical depth, discharge, wetted perimeter, and flow area for different $k$ values are presented. The results show that the discharge of the optimum hydraulic section increases as $k\le 3.3$ and then decreases as $k\ge 3.4$ for a given flow area or wetted perimeter. In addition, a super-best hydraulic power-law section with $k=3.3471$ exists, where the discharge is largest. This super-best section represents a new discovery as it provides the global maximum discharge among all possible power-law section shapes. The characteristics of the super-best section are presented.