Effects of Roughness on Liquid Flow Behavior in Ducts

In this paper, liquid laminar flow friction in micro/mini ducts is considered for investigating the effects of roughness. The available research in this field is briefly reviewed, and the results are comprehensively discussed. The flow behavior is theoretically analyzed in the region adjacent to rough wall, and one of roughness effects is considered equivalent to the reduction of flow cross area, which is referred to the constricted flow model. A modified formula and coefficient η are introduced to correct the reduction value of hydraulic diameter. Two important factors, the space of two neighboring roughness elements and the reattachment length, are involved in accounting for the flow cross-section reduction. Eventually, an expression of flow resistance calculation is reduced in terms of relative roughness ε/d, parameter A and Reynolds number Re. Based on the ultimate friction factor formula, the influences of relative roughness ε/d, parameter A and Reynolds number Re on friction coefficient f are discussed by figuring and comparing f variation with those parameters.