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 scour-
ing 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 construc-
tion materials and earthwork. Traditional methods such as Langrage multipli-
ers, Sequential Quadratic Programming (SQP), Differential Evolution Algo-
rithm (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 ef-
ficiency criterion (other factors assumed optimum), a direct integro-differential technique is applied to determine the optimum trapezoidal channel design that
additionally minimizes velocity fluctuations during excessive discharge
