Equations for critical and normal depths of city-gate sections

Abstract

Critical and normal depths are two important parameters in the design of open channels and the analysis of varied flow. For many practical sections, the governing equations for critical and normal depths are implicit and no analytical solutions exist. Various explicit equations have been developed for common open-channel sections. However, there are very limited studies on calculations of critical and normal depths for the city-gate section (CGS), which is one of the frequently used cross-sections for free-water conveyance tunnels. This paper presents equations for the geometric elements of standard CGSs used in water conveyance systems such as for irrigation, drainage and water supply projects. Based on the principle of gradual optimisation fitting, explicit equations for normal and critical depths of standard CGSs were developed for manual calculations with maximum relative errors of less than 1%. The proposed equations have a high accuracy for use in hydraulic design.