Delta-perturbation expansion for critical flow depth problem in trapezoidal channels

Abstract

For man-made and natural channels, the knowledge of the critical depth is an important parameter in the analysis of free surface flow regimes and backwater curves. For trapezoidal channels, a trial and error approach and large sequence computation (iterations or infinitely nested radicals) are needed due to the implicit character of the governing equation. In the present paper, an original analytical solution based on the Delta-perturbation expansion is proposed for the problem of critical depth computation in trapezoidal shaped channels. The obtained explicit analytical expression forms a very precise solution for practical purposes. A series of real canals are treated as examples to illustrate the application of the proposed approach.