Superior cubic channel section and analytical solution of best hydraulic properties

• A new cubic channel section that has superior properties is proposed.
• The theoretical solution of the best hydraulic cubic section is derived.
• An explicit approximate formula for the wetted perimeter is given.

Channel cross section is an important element in water management. Numerous studies regarding parabolic and semi-cubic sections have been published. This paper introduces a new cubic channel section that has superior properties. Section characteristics are formulated and an explicit approximate formula for the wetted perimeter is derived using the Gauss-Legendre integration method. The theoretical solution of the best hydraulic cubic section is derived using the complex function method and the undetermined Lagrange multiplier optimization algorithm. A comparison with four best hydraulic sections (parabolic, semi-cubic, trapezoidal, and catenary) shows that the discharge of the cubic section is the largest, given the same cross-section flow area and/or wetted perimeter. The results also show that the cubic section is the most economic under the best hydraulic condition. Given its simple form and superior properties, the cubic section should be of interest to water resources engineers.