Boundary Shear in Smooth Rectangular Ducts

Abstract

The results of some laboratory experiments are reported concerning the distribution of boundary shear stresses in smooth closed ducts of a rectangular cross section for aspect ratios between 1 and 10. The distributions are shown to be influenced by the number and shape of the secondary flow cells, which, in turn, depend primarily upon the aspect ratio. For a square cross section with 8 symmetrically disposed secondary flow cells, a double peak in the distribution of the boundary shear stress along each wall is shown to displace the maximum shear stress away from the center position towards each corner. For rectangular cross sections, the number of secondary flow cells increases from 8 by increments of 4 as the aspect ratio increases, causing alternate perturbations in the boundary shear stress distributions at positions where there are adjacent contrarotating flow cells. Equations are presented for the maximum, center line, and mean boundary shear stresses on the duct walls in terms of the aspect ratio.