Optimal design of open channel section incorporating critical flow condition

The flow at critical condition of an open channel is unstable. At critical condition, a small change in specific energy will cause abrupt fluctuation in water depth of the channel. This is because the specific energy curve is almost vertical at critical state. Therefore, if the design depth of the channel is near or equal to critical depth of the channel, the shape of the channel must be altered to avoid a large fluctuation in water depth. In the present study, a nonlinear optimization model is presented for designing an optimal channel section incorporating the critical flow condition of the channel. The optimization model derives the optimal channel section at a desirable difference from the critical condition of the channel so that a small change in the specific energy of the channel will not cause an abrupt change in flow depth. The objective of the optimization model is to minimize the total construction costs of the channel. Manning's equation is used to specify the uniform flow condition in the channel. The developed optimization model is solved by sequential quadratic programming using MATLAB. Applicability of the model is demonstrated for a trapezoidal channel section with composite roughness. However, it also can lie extended to other shapes of channel.