Optimal hydraulic section of horizontal-bottom catenary channel

Abstract: A suitable channel section cannot only increase flow capacity of channel, improve efficiency of water resources, and reduce water leakage loss, but also decrease construction cost. This paper proposed a channel section with a horizontal bottom and catenary sides (HBC). The HBC section, on one hand, provided a larger flow capacity, lesser-sharp angles of stress concentration, less leakage, better slope stability and frost heave resistance than trapezoids and rectangles sections. On the other hand, it had lots of advantages of horizontal bottom sections, such as simpler construction, easier leveling and compaction of the foundation, and lesser construction cost. The most important advantage of this section was that the horizontal bottom and sides could be built with different materials or thickness for decreasing the construction cost or other purposes. The shape function for HBC was defined. The formulas for the flow area, wetted perimeter, and water surface width were presented. A simpler iterative algorithm for calculation of the normal depth was developed. The iterative convergence by this algorithm was evidenced. Comparisons showed that this simpler iterative algorithm was better than classic Newton iterative algorithm. The optimal model of the best hydraulic section of HBC was built. The general differential equations for all the sections having horizontal bottomed and curve sides were derived. The best hydraulic section of HBC channel was obtained according to Lagrange multiplier method and its characteristics were presented including shape factor, ratio of horizontal bottom width to shape factor etc. The results showed that the following optimum parameters were constant for the best hydraulic HBC section: bottom width to water depth, water surface width to depth, bottom width to shape factor, water surface width to shape factor, shape factor to water depth equals. The ratio of water surface width for catenary part to shape factor equaled 3.602, the ratio of bottom width to shape factor equaled 0.855, the ratio of bottom width to water depth equaled 0.405, and the ratio of shape factor to water depth equaled 0.474, and the ratio of total water surface width to water depth equaled 2.112. Various explicit formulae to calculate the normal depth, critical depth, shape factor, flow area, wetted perimeter and water surface width of the HBC section were derived for the best hydraulic section for HBC channel. These formulas should make the design of the HBC section easier and promote its practical applications. The optimum parameters of the best hydraulic section for existing horizontal bottom (HB) sections, such as trapezoidal, rectangle, horizontal bottomed parabolic, and horizontal bottomed semi-cubic parabolic were derived. The comparison results showed that the HBC section had larger discharge than those of existing horizontal bottom (HB) sections under the same conditions. In addition, the flow area, wetted perimeter, and water surface of the HBC section were the smallest, which means that earthwork cost, lining cost and land expropriation cost are all decreased, which means HBC section is more economical. Comparison with classic catenary section showed that the discharge of the HBC was larger than that of the classic catenary section under the same conditions. The flow area, wetted perimeter and water surface of the HBC were smaller than these of the classic catenary section, which means the HBC section has better hydraulic characteristics. Its economy was also superior to the traditional catenary section. The results were verified by examples. The proposed section should enrich existing types of open channel sections. The research provides a new practical and flexible channel section for channel design and theoretical support for horizontal-bottom catenary channel design and applications.