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.
Highlights
A flow in an open channel may be either deep with low velocity or shallow with high velocity
Calculation of the critical depth is very important, as an open channel should be protected from erosive conditions caused by unstable critical flow or high velocity supercritical flow
The critical depths calculated through adaptive cubic polynomials algorithm (ACPA) were 1, 3, 5 or 7 for each section
Summary
A flow in an open channel may be either deep with low velocity or shallow with high velocity. Specific energy curve positive, thethe flow is is subcritical, The specific energy in simple prismatic channels (i.e. rectangular, trapezoidal) for a given discharge negative slope indicates supercritical flow. The specific energy in simple prismatic channels (i.e. rectangular, trapezoidal) foronly a given critical depth channels for only every discharge value. There is through numerical modelling, that in open channels with overbanks (compound channels), more than only one critical depth in such channels for every discharge value. The specific energy at these depths has more local and critical through numerical modelling, that in open channels overbanks (compound channels), minima, maydepth have. Exact positions where the minima and maxima of the specific energy occurs, they didn’t provide a Blalock and Sturm [2] defined a Froude number for compound channels, which correctly solid procedure to calculate the critical depths related.
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