Potential Flow Through Channel Constriction

Abstract

Standard methods for computing backwater at width constrictions of flood plains severely underestimate backwater when the flood plain is wide and heavily vegetated. The energy‐loss term for the approach reach upstream from a constriction depends on the average streamline length in the reach. In standard one‐dimensional step‐backwater procedures, this average streamline length is approximated by the length of the approach reach. Calculation of energy loss in the approach reach can be improved if a more accurate estimate of the average streamline length is used. Potential‐flow streamlines are a reasonable approximation to physical streamlines for convergent flow outside the boundary layer if flood‐plain depth and roughness are fairly uniform. In this paper, potential flow through an eccentric, normal constriction of zero thickness in an infinitely long, straight channel of constant width and unit depth is studied by use of a Schwarz‐Christoffel transformation. The transformation is integrated by a direct approach. Parametric equations for streamlines are obtained and used to compute an average streamline length for a potential‐flow field.