%0 Journal Article
%A ZHANG Zhi-chang
%A JIA Bin
%T Integral Algorithm for Water Surface Profile  of Horseshoe Cross Section of Standard TypeⅡ
%D 2015
%R 10.3969/j.issn.1001-5485.2015.04.012
%J Journal of Yangtze River Scientific Research Institute
%P 59-64
%V 32
%N 4
%X The complex geometrical shape of standard type-II horseshoe cross section makes it difficult to calculate the water surface profile in it. It is necessary to work out a simplified calculation   method for engineering design. According to the geometrical shape, the calculation methods of relative cross section area, relative wetted perimeter, relative hydraulic radius, relative water depth and relative width of   water surface in different areas of standard  type-II horseshoe cross section are given. Furthermore,  according to differential equation of water surface profile   in open-channel with constant non-uniform flow, the trial-and-error method of flow profile  is given. On the basis of least square method, the approximation relationship between <i>j</i>′, <i>Fr</i>′<sup>2</sup> and relative depth <i>h/r</i><sub>1</sub> are given, and according to the relationship, the integral formula of water surface profile   which is an explicit function with convenient calculation and high accuracy is obtained. The  trial-and-error method and  the  integral method are applied to three examples and comparison between the results shows that the calculation accuracy of integral method meets the requirement of engineering design. The maximum error of integral method is 0.965%  compared with the trial-and-error method with 1 mm step high.
%U http://ckyyb.crsri.cn/EN/10.3969/j.issn.1001-5485.2015.04.012