Direct solutions for normal and critical depths in standard city-gate sections

Critical and normal depths are important parameters for computing gradually varied flow and for the design, operation, and maintenance of open channels. For many channel sections, the governing equations for critical and normal depths are implicit and no analytical solutions exist. Thus various approximate equations with various degrees of error have been developed for these sections. No explicit equations exist for critical and normal depths of the standard city-gate cross-sections for entire practical range of the water depth. City-gate sections are one of the commonly used cross-sections for water conveyance tunnels. Standard city-gate cross-sections are also used for water conveyance in irrigation and drainage systems. This study proposes explicit equations for critical and normal depths of standard city-gate cross-sections. The proposed equations are simple and valid for entire practical range of the water depth and have maximum relative error less than 0.13% and thus should be useful tools for evaluation and design of the standard city-gate cross-sections.

Graphical AbstractFigure optionsDownload as PowerPoint slideHighlights
► A general mathematical model for numerical inversion procedure with high accuracy.
► New explicit equations for critical depth of the standard city-gate cross sections.
► New explicit equations for normal depth of the standard city-gate cross sections.