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The direct solution on critical depth of horseshoe section tunnel

WANG Zhengzhong 1,2,CHEN Tao 1, LU Qin 1, ZHANG Xudong 1(1. School of Water Conservancy and Architectural Engineering, Northwest Sci-tech University of Agriculture and Forestry, Yangling 712100;2. State Key Laboratory of Forzen Soil Engineering, Lanzhou 730000)  
The hydraulic calculation of horse-shoe section tunnel is trouble because of its complex shape.Using the mathematics transformation method and the theory of optimization and regression to deal with the basis equation of the critical depth in horse-shoe section tunnel,a new brief and exact direct formula is presented in the paper,which overcomes the shortage of other methods,such as chart look-up method,trial-and-error method and iterative trial method.The new method has clear physical concept,makes the course straight and short and the max. error is less than 1.6%,so it will be useful in engineering practice and in course of compiling handbook of hydraulic structure design.
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