During heavy rains, open channels are prone to being overrun with storm water. Since the velocity of a flowing fluid increases with   depth, sudden overflows may cause velocities to exceed certain limits. This damages the channel by scouring. On the other hand, siltation of suspended matter occurs in sluggish flow. Channel dimensions and shapes must minimize cost and maximize discharge in normal seasons, while regulating 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 Lagrange multipliers, sequential quadratic programming (SQP), differential evolution algorithm (DEA), genetic algorithms, ant-colony optimization, and lately, meta-heuristic 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 technique is applied to determine the optimum triangular channel design that additionally minimizes velocity fluctuations during excessive discharge. The triangular channel is treated as a special case of a trapezoidal channel.

discharge, wetted perimeter, hydraulic radius, Manning equation, Chézy equation, channel slope.