Turbulent Flow in Smooth and Rough Pipes

Abstract

Fully developed turbulent flow in both smooth and rough-walled pipes is investigated for Reynolds numbers from 30,000 to 480,000. The values of mean velocity, root-mean-square values of the fluctuating velocity components, and cross-correlation values of the fluctuating velocities are presented for flow in a smooth pipe and two sand-roughened pipes, R/ε = 208 and R/ε = 26.4. The quantity R/ε is the ratio of the actual pipe radius to the average sand particle size. The experimental measurements for flow in smooth pipes are in good agreement with those of previous investigations throughout the Reynolds number range considered. Several of the rough pipe turbulence quantities show substantial deviations from the corresponding smooth pipe quantities. For rough pipes, the measured uv cross-correlation values approach those predicted empirically from the Reynolds equations for fully developed, axisymmetric flow as the flow approaches the hydraulically smooth case. However, as the Reynolds number is increased and the flow proceeds through the transition region from smooth to fully rough flow and to the fully rough flow region, the values of the uv cross correlation in rough pipes are significantly lower than the predicted values. This difference between predicted and measured data becomes more pronounced as the Reynolds number is further increased and the flow becomes fully rough. The difference between measured and predicted uv values, and other differences between smooth and rough pipe results, suggests that the accepted reduction of the Reynolds equations for flow in smooth pipes is not valid for flow in rough pipes. Thus, the Reynolds equations are re-examined for flow in rough pipes, and it is shown that these equations can be satisfied by the experimental data if secondary flows and angular variations in the mean velocity are postulated.