Prediction of end-depth ratio in open channels using genetic programming

In this paper, genetic programming (GP) is used as an effective model induction tool to solve a classic problem in open channel flow: the free overfall. By applying GP to experimental data of circular channels with a flat bed and employing a model selection procedure, a reliable expression in the form of h(c) = Ah(e)e(B root S0) is found for calculating the critical depth (h(c)) and end-depth ratio (EDR). Further effort is made to verify the applicability and superiority of this expression for channels with other cross sections. This global expression not only outperforms other expressions in estimating the critical depth, it is also dimensionally correct (unlike some other applications of GP) and can be used for channels with any cross-section and any flow regime.