American Society of Civil Engineers

Simplified Model of Tractive-Force Distribution in Closed Conduits

by Siow-Yong Lim, (Associate Professor, School of Civil and Environmental Engineering, Nanyang Technological Univ., Singapore 639798. E-mail: and Shu-Qing Yang, (Principal Research Scientist, Maritime Research Center, Nanyang Technological Univ., Singapore 639798. E-mail:

Journal of Hydraulic Engineering, Vol. 131, No. 4, April 2005, pp. 322-329, (doi:

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Document type: Journal Paper
Abstract: A simplified model for the computation of boundary shear stress distributions acting on the flow perimeter of closed ducts is presented. The model assumes that the surplus energy within any control volume in a three-dimensional flow will be transferred towards the nearest boundary to be dissipated. Based on this model, the flow cross sectional area in the closed duct is divided into subflow regions corresponding to the side walls and bed, and the shear distributions over the wetted perimeter within each subflow area are assessed. Analytical equations, valid for all channel aspect ratios, for the prediction of local and mean shear stresses along the bed and side walls in smooth rectangular duct flow are derived. The formulae give good predictions of the shear stress distributions when compared with existing experimental data in the literature. The possible applications of the model to nonrectangular duct flows are also discussed.

ASCE Subject Headings:
Flow resistance
River flow
Turbulent flow
Velocity distribution
Reynolds stress
Hydraulic models