New explicit correlations for turbulent flow friction factor

Two new correlations of single-phase friction factor for turbulent pipe flow are shown in this paper. These two formulas are actually explicit approximations of iterative Colebrook's relation for calculation of flow friction factor. Calculated friction factors are valid for whole turbulent flow including hydraulically smooth and rough pipes with special attention on transient zone of turbulence between them. Hydraulically smooth regime of turbulence does not occur only in total absence of roughness of inner pipe surface, but also, four new relations for this theoretical regime are presented. Some recent formulas for turbulent flow friction calculation are also commented.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Standard empirical Colebrook's equation suffers from being implicit in unknown friction factor. ► Two new explicit approximations of Colebrook's equation are with relative error of no more than 2%. ► Hydraulically smooth regime of turbulence does not occur only in total absence of roughness of inner pipe surface, but also, four new relations for this theoretical regime are presented. ► Four new explicit approximations for ideal smooth conditions are with relative error of no more than 0.15%.