Exact solution of optimum hydraulic horizontal-bottomed power-law section with general exponent parameter

Abstract Horizontal-bottomed power-law sections (HBP sections) are new composite channel sections, which provide more adaptability and flexibility for optimal section design than power-law sections (PL sections). Analytical solutions for wetted perimeters with general exponent parameter m are difficult to obtain, except for several definite sections, such as a horizontal-bottomed parabolic section and a horizontal-bottomed half-cubic parabola section. Therefore, there has been no detailed investigation of the general form of the HBP section. This paper present a group of general exact solutions (ratio of water surface width of PL section to water depth, and ratio of channel bed width to water depth) of the optimum hydraulic HBP section with exponent m as a parameter based on Gauss Hyper geometric mathematics and Lagrange multiplier. Many explicit exact formulas for various hydraulic parameters (flow discharge or water depth) under the condition of optimum hydraulic HBP section are also given. Error analysis shows the proposed explicit exact formulas are accurate. Next, by comparing several sections, the results indicate the cross area and wetted perimeter of horizontal-bottomed cubic sections are smaller than those of other sections for a given flow discharge. This finding means that the least amount of excavation and lining is required for construction. Therefore, the horizontal-bottomed cubic parabola section is the most economical section among the typical sections (PL sections, Rectangular, Triangular, Trapezoid, semi-cubic section and other HBP sections). This study sheds new light on a general and concise hydraulic calculation method for any HBP section with general exponent parameter m .