A novel and exact analytical model for determination of critical depth in trapezoidal open channels

Critical depth is a significant parameter in the designing and management of open channels and related hydraulic structures, understanding the flow characteristics and calculations of varied flows (gradually, spatially, etc.). The trapezoidal cross sections are the most commonly used geometric sections in the network of water transmission and distribution channels, thus discussing its geometrical and hydraulic parameters is inevitable. The used nonlinear and mathematical relationships governing the critical depth problem in the trapezoidal channels are implicit and complex, hence the methods of trial and error, graphical and numerical are used to calculate it. In the present study, new explicit equations are presented based on mathematical analysis of the critical depth problem in the trapezoidal channel. Mathematical analysis has led to completely mathematical and analytical solutions having a definite physical (hydraulic) concept. Having the explicit equations provided by the ease of calculation process with no limitation of the application range and high accuracy are the advantages of this analysis. The accuracy of the presented equations is desired and determined according to the required accuracy. The data used for verification of the results are based on the critical flow condition (Froude number equal to 1), which has been generated in a wide and practical range of the geometric and hydraulic characteristics of the channel. Also, the calculated values are compared with the real values of the considered parameter.