Optimizing a trapezoidal open-channel for least velocity fluctuation during overflow using mathematical efficiency criterion

Abstract

In open channels, fluid velocity increases with depth of flow. Sewers are particularly susceptible to overwhelming storm water velocities during rains. When flow velocities exceed a certain threshold, damage of channel by scouring may result, or, conversely, siltation of suspended matter. Channel design must optimize dimensions and shapes which both minimize cost, maximizing discharge in normal seasons and regulate the discharge to minimize velocity fluctuations during overflow. Depending on the designer’s objectives, channel design involves numerous parameters, including the characteristics of construction materials and earthwork. Traditional methods such as Langrage multipliers, Sequential Quadratic Programming (SQP), Differential Evolution Algorithm (DEA), genetic algorithms, ant-colony optimization, and lately, metaheuristic algorithms are often used to minimize a cost function subject to channel cross-section. In this paper, using only the mathematical hydraulic efficiency criterion (other factors assumed optimum), a direct integro-differential 6980 John Wahome et al. technique is applied to determine the optimum trapezoidal channel design that additionally minimizes velocity fluctuations during excessive discharge.