Hydraulic calculation of horseshoe cross-section with flat-bottom

Abstract: As one of the simplified type of the standard II type horseshoe, the II type horseshoe cross-section with flat bottom is one of the general used shape types for spillway tunnel and irrigation tunnel. However, the hydraulic calculation for this type tunnels has not been reported. Aiming at this problem, a new hydraulic calculation formula was proposed. The II type horseshoe cross-section with flat bottom is consisted of four parts: one flat bottom, two side circular arc arch and one circular arc roof umbrella arch. This simplified horseshoe type is special suitable for the geological conditions with low foundation pressure. The characteristics of hydraulics and mechanics are between horseshoe-shaped and U-shaped arch. Due to the flat bottom, this type can keep a normal water flow regime, and a smoothly connection of the water flow before and behind the tunnel. For obtaining the calculation formula of the normal and critical water depth for II type horseshoe tunnel with flat bottom, its geometrical design of hydraulic tunnel were analyzed. In order to guarantee the status without pressure in a free flow tunnel with changing water level, the free space above the water level was not less than 15 % of the whole cross-sectional areas of the tunnel. The upper limit of dimensionless water depth was 1.41. For most of the application engineering, the lower limit of dimensionless water depth was 0.05. After ascertained the utility range of the formula and based on fundamental equations of uniform flow and critical flow, the interrelation between dimensionless water depth and the dimensionless parameter were analyzed. We used the power function as the formula form, and coefficients of the formula were calculated based on the theory of optimization and regression. The calculation formula for normal water depth and critical water depth were obtained. Results showed that the maximum relative error of normal water depth and critical water depth were 0.41% and 0.20%, respectively. This research indicated that the hydraulic calculation formula could be widely used in engineering design and project management with high accurate and simple form.