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

The Colebrook-White formulation of 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 that more efficiently calculate the friction factor compared with Colebrook-White are presented herein. The aim of this investigation is twofold: to preserve accuracy of estimates while reducing the computational burden (i.e. speed). On 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, 3 strategies for friction factor mapping are proposed which were computed 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. The term “pseudo-polynomial” is referred herein to a class of formulas obtained by adding a number of terms, all based on the same base structure, but not necessarily having integer exponents.