Prediction of the friction factor in pipes using model tree

Mohammad Najafzadeh* (Corresponding Author), Jalal Shiri, Gholamabbas Sadeghi, Alireza Ghaemi

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

21 Citations (Scopus)


Prediction of friction factor plays a prominent role in determination of head losses along pipelines or water distribution systems. Numerous traditional equations-based regressive models have been extracted for prediction of the friction factor using experimental and numerical studies. In the present research, a model tree (MT) was developed to present formulations for evaluation of friction factor in pipes. The effective parameters on the friction factor (f), included pipe diameter (D), average flow velocity in pipe (V), kinematic viscosity (ν), and roughness height of the inner surface of pipe (ɛ). Two non-dimensional parameters of the fluid, Reynolds number (Re) and relative roughness (ɛ/D) were employed to improve the proposed model. The training and testing of MT approach were carried out using datasets obtained from the approximate solution. The testing results for the MT were compared with those obtained using gene-expression programming (GEP), evolutionary paradigm regression (EPR), and conventional approaches. Compared to the conventional models and artificial intelligence techniques, MT was manifest that permissible degree of accuracy for evaluation of friction factor was met.
Original languageEnglish
Pages (from-to)9-15
JournalISH Journal of Hydraulic Engineering
Issue number1
Publication statusPublished - 2018
Externally publishedYes


  • Friction factor
  • Model tree
  • Pipe
  • Explicit expressions


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