Optimal Hydraulic Section of Ice-Covered Open Trapezoidal Channel

Previous studies have focused on the optimal hydraulic section for ice-free channels only. This paper presents the optimal trapezoidal section and its characteristics under ice-covered conditions. Using the Lagrange multiplier optimization method, formulas for the dimensions of the optimal hydraulic trapezoidal section are derived. The results show that the optimal hydraulic section under ice-covered conditions is different from that under ice-free conditions. The optimal width-to-depth ratio depends not only on the side slope, but also on the roughness coefficients of the ice cover and channel bed (bottom and sides). The ratio of bed roughness (or ice-cover roughness) to composite roughness is another key parameter in determining the shape of the optimal section. The comparison with the ice-free section shows that the optimal hydraulic section under ice-covered conditions is relatively narrow and deep, which helps reduce the heat loss at the water surface. Practical aspects of the optimal hydraulic section under ice-covered conditions are addressed.