Previous research on compound trapezoidal cross sections has mainly focused on improving the prediction of the discharge (flow rate) because of its inherent challenges. This paper focuses on two other important aspects: Section shape and optimal construction cost. First, the paper proposes a new compound section with third-degree polynomial sides of main channel with horizontal bottom (HB) that allows its top corners to be smooth, called herein compound polynomial section. The special cases of this versatile section include the simple polynomial section, polygonal section, trapezoidal-rectangular section, two-segment linear-side section, and parabolic bottom-trapezoidal section. The simple polynomial section, which is the bank-full part of the compound polynomial section, can further produce parabolic (with or without HB), trapezoidal, rectangular, and triangular sections. Second, an optimization model that minimizes construction cost (excavation and lining) of the compound (or simple) polynomial section is developed. The model includes discharge and physical constraints. Theoretical and empirical methods of discharge prediction were used in the model. The results show that the simple polynomial section was more economical than the popular parabolic section by up to 8.6% when the side slopes were restricted. The new polynomial-based sections not only reduced construction cost, but also improved maintenance and aesthetics. As such, the new sections should be of interest to researchers and practitioners in hydraulic engineering.
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