Explicit equations for critical depth in open channels with complex compound cross sections

Abstract

Critical depth is an important parameter in the analysis of varied flow in open channels. For many practical sections, the governing equations for critical depth are implicit and no analytical solutions exist. Much work has been done to develop explicit equations for critical depth with various degrees of error in open channels with different shapes, especially in trapezoidal, circular, and horseshoe channels. However, for many other complex compound channel sections, such as quasi-trapezoidal, city-gate, and rounded-bottom trapezoidal sections, there are few studies on explicit equations for critical depth with both simple forms and satisfactory accuracy. This paper presents equations for the geometric elements of these complex cross sections. Based on the principle of gradual optimization fitting and iteration theory, explicit equations were developed for direct computation of critical depth for these three types of compound cross sections. The accuracy of the proposed equations was also evaluated. The proposed equations are suitable for manual calculations with high accuracy.