New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations

The determination of single-phase friction factor of pipe flow is essential to a variety of industrial applications, such as single-phase flow systems, two-phase flow systems and supercritical flow systems. There are a number of correlations for the single-phase friction factor. It still remains an issue to examine similarities and differences between them to avoid misusing. This paper evaluates the correlations for the single-phase friction factor against the Nikuradse equation and the Colebrook equation, respectively. These two equations are the base for the turbulent portion of the Moody diagram, and are deemed as the standard to test the explicit counterparts. The widely used correlations for smooth pipes, the Blasius correlation and the Filonenko correlation, have big errors in some Re ranges. Simpler forms of the single-phase friction factor covering large ranges are needed. For this reason, two new correlations of single-phase friction factor for turbulent flow are proposed, one for smooth pipes and the other for both smooth and rough pipes. Compared with the Nikuradse equation, the new correlation for smooth pipes has the mean absolute relative error of 0.022%, with the maximum relative error of −0.045% in the Reynolds number (Re) range from 3000 through 108. It is an idea replacement of the correlations of Blasius and Filonenko. The new correlation for both smooth and rough pipes has the mean absolute relative error of 0.16% and the maximum relative error of 0.50% compared with the Colebrook equation in the range of Re = 3000–108 and Rr = 0.0–0.05, which is the most simplest correlation in that error band.