Explicit solutions for critical and normal depths in channels with different shapes

Abstract

Critical and normal depths are important for computing gradually varied flow profiles and for the design, operation, and maintenance of open channels. A closed-form analytical equation for the normal depth computation can only be derived for triangular channels. For exponential channels, it is also possible to obtain such equations for the critical depth. This is not possible, however, for other geometries, such as trapezoidal, circular, and horseshoe channels. In these channels, the governing equations are implicit and thus the use of trial procedures, numerical methods, and graphical tools is common. Some channels have explicit solutions for the critical and normal depths, while others do not. This paper presents new and improved explicit regression-based equations for the critical and normal depths of open channels with different shapes. A comparison of the proposed and existing equations is also presented. The proposed equations are simple, have a maximum error of less than 1%, and are well-suited for manual calculations and computer programming.