Theory of viscous flow in curved shallow channels

The axisymmetrical, viscous flow in curved channels is considered in the case where the hydraulic radius of the cross-section is small with respect to the average radius of curvature of the bend. First Ananyan's theory on this subject is reconsidered, using a regular perturbation method. The results are applied to a specific channel with a shallow rectangular cross-section. This yields solutions for the tangential velocity component, the secondary circulation and the influence of the latter on the former. Second the case of a shallow, rectangular cross-section is treated, using the method of matched asymptotic expansions ..This yields solutions of the velocity components in three separate regions of the cross-section (viz. near each sidewall and near the central axis of the cross-section), which turn out to be sumsHydraulic EngineeringCivil Engineering and Geoscience