New solutions for estimation of critical depth in trapezoidal cross section channel

Critical depth is an important parameter in design of open channels and analysis of gradually varied flow. in trapezoidal channels,the governing equations are nonlinear for computing critical depth. therefore,implicit solution of the equations involves numerical methods. any methods that researchers have suggested for solving these equations are so complex. in this paper,two simple and useful semi-analytical solutions were introduced using data fit software that has minimum errors in calculating the critical depth in trapezoidal channels. in first solutions,equation (20) was obtained based on the equation of degree 6 for trapezoidal channels (equation 4). in second solutions,critical depth equation in trapezoidal channel was developed as the equation (22) using critical depth equation in triangular channel. results show these equations have acceptable accuracy,which relative error of equations (20) and (22) are 1.22% and 1.34% respectively.