The direct solution on normal water depth of I type horseshoe tunnel with flat-bottom

摘要

I type horseshoe with flat-bottom evolved from standard I type horseshoe cross-section. It is composed of a flat-bottom and three arc sections. It is commonly applied in the field of hydroelectric engineering. The normal water depth computation equation for I type horseshoe cross-section with flat-bottom tunnel is a transcendental equation and no analytic solution. In this paper, based on the mathematics transformation for the basis equation and the relationship analysis between the dimensionless normal water depth and the relative parameters, a direct solution is established for the calculation of normal water depth for I type horseshoe cross-section with flat-bottom tunnel according to the fitting principle. This method overcomes the shortage of other iterative trial calculating methods, such as complex calculation step, depend on the special chart and curve, and existed serious error. The formula is simply and the maximum error is less than 0.3% under the general engineering design range (ratio of normal water depth and arch radius is between 0 to 1.4471). it can be used on the engineering designing practice and the edit of the handbook of hydraulic structure design.