Optimum simple and complex power-law channels

Abstract

This study develops solutions for the hydraulically and most hydraulically efficient power-law sections (simple and complex). For this, the dimensionless objective function is defined as the wetted perimeter to the square root of the flow area. The objective function is then minimized. This study uses a simple procedure to establish the optimum dimensions. In comparison with the Lagrange multiplier method, this approach without any constraints is very simple for implementation. The optimization model of the simple power-law section has two decision variables (dimensionless depth and exponent) while the optimization model of the complex power-law section has three decision variables (dimensionless depth, dimensionless width and exponent). Optimizing all decision variables results in the most hydraulically efficient section (best hydraulic section), while optimizing some of the decision variables results in the hydraulically efficient section. This study presents a novel graphical comparison between simple and complex optimum power-law sections and shows that the dimensionless decision variables are constant for the most hydraulically efficient sections while are not constant for the hydraulically efficient sections. The characteristics of the hydraulically efficient sections are presented in tabular forms and explicit equations. These solutions are easy to use for optimum design of the power-law sections.