Abstract:

I-type horseshoe cross-section with flat-bottom is simplified from standard I-type horseshoe cross-section. since the shape and size are easy to control,#em/em# is composed of a flat-bottom and three arc sections. It is commonly applied in hydroelectric engineering. But the critical water depth computation formula is a transcendental equation and has no analytic solution. Mathematics transformation for the critical flow equation was carried out, and the relationship between the dimensionless critical water depth and the relative dimensionless parameters was analyzed. Furthermore, an approximate formula for the calculation of critical water depth for I-type horseshoe cross-section with flat-bottom tunnel was obtained according to the fitting principle. This method overcomes the defects of other iterative trial calculating methods, such as calculation step, dependence on special charts and curves, and serious error. The formula is simple and the maximum error is less than 0.4% under the general engineering design condition (0<h/r≤1.447 1,h/r is the ratio of critical depth to the radius of arch roof). It can be used for engineering design practice and for the compilation of hydraulic structure design handbooks.