Direct calculation method for normal depth of arched section tunnel

The arched section is one of the usually adoptive section shapes in flood discharge tunnels and irrigation tunnels, but the analytic expression of normal water depth for this section is not explicit. Though the conventional trial and error method or the graph method can be implemented, it is time-consuming and imprecise. The uniform was transformed flow equation into its equivalence, and then the relationship between the relative normal water depth and the introduced dimensionless parameter was analyzed. Finally, by fitting the relationship based on the theory of optimization and regression, a direct expression for calculating the normal water depth of arched section channel was proposed. The practical example and error analysis illustrated the validity and effectiveness of the proposed direct expression. The absolute value of the maximum relative error was not greater than 0.24 percent among the utility range of engineering (the ratio of normal water depth to arch radius was from 0.20 to 1.55). The proposed method is clear in course, simple in calculation, and can be regarded as a useful supplement to the engineering design and the compilation of the hydraulic structure design handbook.