Calculation of Multiple Critical Depths in Open Channels Using an Adaptive Cubic Polynomials Algorithm

Abstract

A method for the calculation of multiple critical depths in compound and natural channels, using an adaptive cubic polynomials algorithm (ACPA), is presented in this paper. The algorithm is based on the approximation of the specific energy with multiple cubic polynomials. The roots of these polynomials’ derivatives are determined to calculate all local minima and maxima. These extremities yield the critical depths. Furthermore, the Froude number can be calculated at any elevation by applying a simple formula after calculating the derivative of the corresponding polynomial, which contains the given elevation. The algorithm developed was tested on various compound and natural channels. Its results were then compared with the results provided by the HEC-RAS (Hydrologic Engineering Center – River Analysis System) computer program, proving that in some cases ACPA results were more accurate than those of HEC-RAS. This has to do with the fact that HEC-RAS algorithm determines a single critical depth and is better fitted to simple prismatic channels. On the other hand, the ACPA algorithm is able to calculate all critical depths of a natural or compound channel, providing thus more accurate results.