Smooth Mixed-Geometry Transitions in Water-Supply Canals

Abstract

Fifth-degree parametric equations were developed to calculate the cross-sectional dimensions and bed centerline elevations (thus, the geometric surface coordinates) between the two ends of a warped transition in a water-supply canal. A parametric modeling approach provided a smooth representation of the mixed geometry that results from the terminal sections having vastly different shapes. A generalized cross section defined by four parameters enabled a straightforward representation of various forms ranging from trapezoids to semicircles. This approach significantly simplifies the interpolation of surface coordinates between the terminal points of a transition structure. It also maintains a degree of smoothness that helps avoid undesirable consequences of channel contractions and expansions. An example is presented that applies the parametric modeling approach to designing a significant canal transition in which the cross section changes from a standard trapezoidal shape with rounded bottom vertices to a rectangular section in a steeper aqueduct that carries the flow across a broad valley.