Optimal Design of Parabolic Canals

Abstract

This paper presents optimality conditions tor a parabolic‐eanal design accounting for freeboard and limitations on velocity and canal dimensions. Freeboard may be based on a design discharge or specified as a function of flow depth, which is more general. The analysis reveals that the side‐slope parameter for the best hydraulic section is 0.514, not 0.7 as reported in the literature for parabolic canals. The aforementioned hydraulic considerations tend to shape the optimal canal narrow and deep. A formulation for the minimization of the sum of excavation and lining costs favors slightly wider canals when the ratio of cost of lining to cost of excavation is high. The necessary conditions for minima are stated analytically. It is shown that the optimal side‐slope parameter of 0.514 sets an upper bound with the implication that no optimal parabola can be wider than the classical best section for a given discharge. Design aids in the form of tables are presented.