Optimizing a Hybrid Round-Bottom Triangular Open-Channel For Storms

Abstract

According to the Fluid Flow Equation, the mass flow rate of a fluid is the product of its density, area and velocity. Fast flowing storm water could therefore cause a sudden increase in fluid velocity and flooding, an increasingly common challenge as the effects of global warming become more pronounced. These might overshoot certain desirable thresholds and damage the channel or canal, by scouring. Similarly, the Continuity Equation guarantees that the velocity of a fluid decreases the closer a location is from the bottom. This implies a converse danger of siltation when the speed of flow is too sluggish. For that reason, channel designers carefully choose shapes with dimensions which maximize discharge, while keeping siltation in check. They also seek to slow down the velocity of the channel’s flow by making it dissipate much of its load in case of an overflow. This can be partially achieved by an appropriate design of the area above the channel. Meta-heuristic, nondominated sorting genetic algorithms, ant-colony optimisation, differential evolution algorithm (DEA), sequential quadratic programming (SQP) and Lagrange multipliers are some of the methods deployed in minimising the cost function subject to the cross-section of a channel. In practice, channel design hydrodynamics and engineering will involve more parameters than those that this paper covers, including the type of construction materials used to line the channel. Several studies have shown that for a given discharge value and for all slopes, the total cost of construction of a compound triangular cross-section with a rounded bottom is always less than the cost of trapezoidal cross-sections. This paper assumes other factors optimum and applies a purely mathematical approach to determine the best round bottomed triangular open channel design which additionally decreases velocity fluctuations during storms.