Novel method for calculating flow depth in open channels combining the iteration theory and the curve-fitting technique

Calculation of critical depth in open channels or closed conduits is a prerequisite for efficient hydraulic design, operation, and maintenance of irrigation channels and drainage ditches. Determination of critical depth in the trapezoidal cross section is of particular significance as it is one of the most widely used channel sections throughout the world, while no closed-form analytical solutions exist. Based on the novel combined iteration-curve-fitting method, the existing equations were unified in the same function model, and two new equations were proposed for directly calculating critical depth in trapezoidal open channels. The maximum absolute relative errors of the two proposed equations are 0.00494% and 0.165%, respectively, in wide application ranges. Comparison and evaluation of the proposed and existing equations for calculating critical depth in trapezoidal open channels were also presented. The introduction and application of the novel method could make the process of function model establishment much more efficient, which provides more insights into the hydraulic calculations of channels and ditches. Moreover, this paper provides reference for the problems related to the empirical equations of high-degree polynomial equations.