Optimal Design of Parabolic-Bottomed Triangle Canals

The characteristics of a parabolic-bottomed triangle cross section are introduced. For this geometry the "best" hydraulic cross section is determined by using the undetermined multipliers method of Lagrange. For a given flow, roughness coefficient, and longitudinal slope, the best hydraulic section is the channel section having the least wetted perimeter or cross-sectional area. The cross-sectional parameters of this novel geometry are compared with those of trapezoidal, parabolic, and round-bottomed triangle cross sections. It is shown that for all values of side slopes, the flow area and wetted perimeter in a parabolic-bottomed triangle cross section are less than those of trapezoidal and parabolic cross sections for the same discharge. This indicates that less excavation and linings are involved and therefore implies that the parabolic-bottomed triangle cross section is more economical than trapezoidal and parabolic cross sections.