Estimation of Drag Coefficient in Open Channel Flows with Submerged Vegetation Using Pareto Analysis and Multi-gene Genetic Expression Programming

Document Type : Research Article


Assistant Professor, Department of Water Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran


The vegetation resistance, drag force and drag coefficient are among the most properties in hydraulic and Eco hydrological studies in rivers. The drag coefficient depends on flow properties, condition of density and distribution of vegetation, and is often estimated by non-accurate empirical equations. In the present study with the aim of improving the accuracy and derivation of optimum equations for drag coefficient in open channel flow with submerged vegetation, the optimal Pareto and multi gene genetic expression programming in combination with maximum dissimilarity classification algorithm is used.  By using the dimensional analysis, the effective parameters derived in non-dimensional form and using 910 data points of drag coefficient and flow with vegetation conditions explicit equations for drag coefficient are developed. Investigating the results of proposed model shows that model with R2=0.9, RMSE=0.41, MPE=10% is more accurate than the empirical equations and its errors are 20% smaller than previous equations, declare the appropriate performance of developed model. Furthermore, the physical meaning of the developed models shows that beyond its simplified form, it has the ability in inferring of physical meaning of drag phenomenon. Therefore, the superiority of proposed model versus previous studies is confirmed. The results of the current model can be used in studies and hydraulic/eco-hydrologic models in rivers and channels having vegetation.


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Volume 7, Issue 4
January 2021
Pages 935-949
  • Receive Date: 11 May 2020
  • Revise Date: 05 September 2020
  • Accept Date: 05 September 2020
  • First Publish Date: 01 December 2020