Evaluation of a universal transitional resistance diagram for pipes with honed surfaces

Abstract

A method for evaluating a universal transitional resistance diagram for pipes that relates the pressure drop in the pipe to Reynolds number, as a function of relative surface roughness, is presented. The method assumes a universal wake function, a logarithmic overlap region and a power fit in the viscous and buffer layer. Estimates can be made of the friction factor–Reynolds number relationship for arbitrary relative roughness, based on a given surface geometry. The method is illustrated for a pipe with a honed surface finish and uses data of Shockling (“Turbulent flow in a rough pipe,” MSE dissertation, Princeton University, 2005). Honed roughness demonstrates an inflectional behavior in the transitionally rough regime, much like sand grain roughness [Laws of flow in rough pipes, VDI Forschungsh, 361 (1933), 1292 (NACA TM, 1950)], but the method proposed here can be applied to any given roughness behavior. It is suggested that the critical parameter that determines whether the resistance diagram shows inflectional characteristics is the ratio of roughness height to outer layer scale. Based on analysis of data from previous researchers it is suggested that if the relative surface roughness $k_{\mathrm{rms}}∕D<0.0025$ , where $k_{\mathrm{rms}}$ is the rms amplitude of the roughness and $D$ is the pipe diameter, inflectional relationships should be observed.