Some explicit formulations of Colebrook–White friction factor considering accuracy vs. computational speed

The Colebrook–White formulation of the friction factor is implicit and requires some iterations to be solved given a correct initial search value and a target accuracy. Some new explicit formulations to efficiently calculate the Colebrook–White friction factor are presented herein. The aim of this investigation is twofold: (i) to preserve the accuracy of estimates while (ii) reducing the computational burden (i.e. speed). On the one hand, the computational effectiveness is important when the intensive calculation of the friction factor (e.g. large-size water distribution networks (WDN) in optimization problems, flooding software, etc.) is required together with its derivative. On the other hand, the accuracy of the developing formula should be realistically chosen considering the remaining uncertainties surrounding the model where the friction factor is used. In the following, three strategies for friction factor mapping are proposed which were achieved by using the Evolutionary Polynomial Regression (EPR). The result is the encapsulation of some pieces of the friction factor implicit formulae within pseudo-polynomial structures.