Designing Smooth Mixed-Geometry Canal Transition

When a canal’s size or shape changes, usually over a short distance, a section of the channel, known as a transition structure, is needed to connect the waterway’s two stretches. Fifth-degree parametric equations are developed to calculate the cross-section dimensions and bed centerline elevations (thus, the geometric surface coordinates) between the two ends of a warped transition structure in a water-supply canal. The parametric modeling approach provides a smooth representation of the mixed geometry that results from terminal sections having vastly different shapes. A generalized cross-section defined by four parameters enables a straightforward model of various forms ranging from trapezoids to semi-circles. This approach significantly simplifies the interpolation of surface coordinates between the terminal points of a transition structure. It also maintains a smoothness that helps avoid undesirable consequences of channel contractions and expansions. An example is presented that applies the parametric modeling approach to design a significant canal transition where 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.