An Improvement in the Calculation of Turbulent Friction in Smooth Concentric Annuli

Abstract

Data for smooth concentric annuli having an overall −25 to +35 percent scattter about the Colbrook prediction for smooth tubes, along with calculation techniques, are reviewed. It is shown that the accepted methods of Meter and Bird [22], and of Rothfus, Monrad, and Senecal [28] deviate substantially from the correct limit for small gaps. Further, neither correctly predicts the data trends with decreasing radius ratio. It is demonstrated that the theoretically determined laminar equivalent diameter which provides similarity in laminar flow for round tubes and concentric annuli also provides similarity in turbulent flow. The resultant equations behave correctly at both circular and flat plate limits. The combined results, when applied to objectively confirmed data, show a reduction in the observed data scatter to approximately ± 5 percent.