Velocity distribution and the boundary layer at channel bends

Abstract

An analysis of the accelerating forces available within a relatively wide shallow channel bend shows that the existence of higher velocities near the outside bank requires, in addition to the helical flow pattern commonly observed, that the outward flowing upper layers be unaffected by bed shear. Velocity measurements made in a model channel bend at a point unaffected by entry conditions have confirmed this requirement, indicating that the inward flowing bottom layers move within a boundary layer similar to those found near the surface of airfoils. The parameter (r/v) dv/dr, which should have the value −1 for free vortex flow and +1 for flow with constant angular velocity, exceeded +4 in these experiments and was found to be directly proportional to the friction factor. Theory developed indicates that this parameter is directly proportional to the width‐radius ratio also in those regions beyond the effect of entry conditions.