Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation

Abstract

Estimating head losses due to friction in closed pipes is an important task in the solution of many practical problems in the different branches of the engineering profession. The hydraulic design and analysis of water distribution systems are two prime examples. Many consider the Darcy–Weisbach equation to be the most fundamentally sound method for evaluating head losses due to friction in closed pipe conduits. The implicit Colebrook–White equation has been widely used to estimate the friction factor for turbulent fluid-flow in Darcy–Weisbach equation. A fast, accurate, and robust resolution of the Colebrook–White equation is, in particular, necessary for scientific intensive computations. For instance, numerical simulations of pipe flows require the computation of the friction coefficient at each grid point and for each time step. For long-term simulations of long pipes, the Colebrook–White equation must therefore be solved a huge number of times and hence this is the main reason for attempting to develop an accurate explicit relationship that is a reasonable approximation for the Colebrook–White equation. This paper examines the potential of genetic programming (GP) based technique in estimating flow friction factor in comparison with the most currently available explicit alternatives to the Colebrook–White equation. The performance of the gene expression programming (GEP), a variant of GP, was compared with most available approximations using some statistic parameters for error estimation. The comparison test results reveal that by using GEP, the friction factor can be identified precisely.