Estimation of flow resistance coefficients in surface water transport pipe with different boundary condition via meta model

An accurate prediction of friction coefficient is one of the most important issues of water engineering. Due to the complexity of hydraulic phenomena and the influence of various parameters in its estimation, it is difficult to determine the governing equations and the classical mathematical models are not sufficiently accurate in this regard. In this research using 300 experimental data, the friction factor of rainwater pipes with different boundary condition (rigid and deposited beds) under three scenarios (first scenario was modeling based on the hydraulic parameters, the second and third scenarios were modeling based on the hydraulic parameters and the sediment particles characteristics without and with considering the sediment discharge as input parameter) was estimated using Gene Expression Programming (GEP) method and the impacts of different employed parameters in each boundary condition was assessed. Also it was observed that for rigid boundary state, the model including parameters of dimensionless sediment discharge, Modified Froude number, dimensionless particle number, and relative flow depth (Cv, Frm, Dgr, d50/y) and for deposited bed state, the model with parameters of relative depth and width of sediment bed, Modified Froude number, and dimensionless sediment discharge (ys/D, Frm, Wb/y0, Cv) led to more accurate outcomes. One of the capabilities of gene expression programming is providing the explicit formula for roughness coefficient. The best results was obtained for deposited bed with values of R=0.9, DC=0.73, and RMSPE=10.9. Therefore, explicit equations were presented for the superior models of the considered scenarios. Also, according to the results of analyzing data series separately lead to more accurate outcomes in compared to the mixed data and combining the data sets reduced the performance of the model.