Abstract: In the calculation of the critical depth of trapezoidal open channel with cambered bottom,equations of higher degree needs to be solved. Traditional algorithms and approximation algorithm are complicated with less accuracy,whereas computer programming adopted to solve the equation is inconvenient for on-site application. On the basis of mathematical transformation of the calculation formula,a simplified formula with convenient process is obtained by successive approximation and fitting for engineering practice,with the minimum standard residual difference as objective function. Results of the simplified formula meets the requirements of engineering design,and is worthy of promotion.

Key words: trapezoidal section with cambered bottom , critical water depth , optimization and fitting , approximate calculation