The mean velocity profile in turbulent pipe flow

Abstract

An experimental investigation was conducted to determine the mean-flow scaling in a fully-developed, smooth pipe flow. Measurements of the mean velocity profiles and friction factors were performed over a large range of Reynolds numbers (31 × 103 and 35 × 106 based on average velocity and diameter). Analysis of the mean velocity profiles indicate two types of overlap regions; one which scales as a power-law and one which scales as a log-law. The log-law is only evident if the Reynolds number is greater than approximately 300 × 103 which only a handful of other experiments have achieved. A new scaling is proposed that describes this behavior in both overlap regions. The scaling requires a velocity scale for the outer region such that the ratio of the outer velocity scale to the inner velocity scale (the friction velocity) is a function of Reynolds number at low Reynolds numbers, and approaches a constant value at high Reynolds numbers. The outer velocity scale is believed to be the difference between the centerline velocity and the average velocity. This velocity scale is used to normalize the velocity profiles in the outer region and is found to give better agreement between different Reynolds numbers than the friction velocity. At sufficiently high Reynolds numbers, the scaling in the overlap region is found to be logarithmic and the outer velocity scale was found to be proportional to the friction velocity.