Formula for direct calculation of contracted depth of channel with trapezoidal section

The channel with trapezoidal section is used commonly in practical engineering. To get the contracted depth in the section, high order implicit equation need to be solved. Conventional methods, such as graphic approach and trial calculation method, are complex, inefficient and with large error. So a direct calculation formula with simple form, high efficiency and high precision, is presented in the current work. By introducing a non-dimensional width of water surface, an iterative formula with high efficiency for calculating contracted depth is obtained by identical transformation of the fundamental equation of contracted depth. The reasonable iterative initial value is also given by optimizing the formula form. The non-dimensional contracted depth ranges from 0.01 to 0.5, which satisfies the requirement of practical engineering. Finally, the direct formula for calculating the contracted depth is obtained. Error analysis and a practical engineering example are given to show the advantages of the current direct calculation formula.