Abstract Water normal depth calculation is an important task in the design of an open channel for drainage and irrigation. First, dimensionless variables including channel roughness coefficient, bed slope, geometric parameters, and discharge were introduced for each common section. In order to obtain general equations and evaluate their accuracy, the explicit equations available for water normal depth were expressed by those dimensionless variables. Then, the real ranges of those variables were specified for each common section in applications, the relative errors in the explicit equations that involve the variables were analyzed in the ranges. Also, the global relative error distribution diagrams were plotted to compare the maximum relative error and the global one. According to these analyses, the most appropriate equations, which can explicitly calculate the water normal depth in the channels with five types of common section, were spotted. Finally, based on the best approximations algorithm a new piecewise explicit equation was proposed for the water normal depth in a standard castlegate section. It was shown that the maximum relative errors in all the recommended equations are less than 1％ for the water normal depth in six types of common section. The results in the paper have provided an effective method for designing channels with six types of common section and carrying out hydraulic calculations.
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