The Calculation and Application for Free Flow Tunnel of Normal Depth and Critical Depth

Horseshoe cross-section and circular cross-section are commonly used in water diversion project and water delivery project. It is difficult to calculate hydraulic elements of nonstandard horseshoe shape and circular shape because of their complex section. This article gives the formulas of hydraulic elements and iterative formulas of normal depths and critical depths of horseshoe shape section composed of 6 arcs and 2 kinds of irregular circular shape section by mathematical derivation. And on the basis of the relation with depth, normal depth and critical depth, we can estimate the type of water surface profile. It can be applied in calculation of water surface profile in 81.68 km Qinling tunnel of south water to north project. The formulas of normal depth and critical depth and hydraulic elements can be expected to be used in other similar water delivery project.