In the calculation of the critical depth of trapezoidal open channel with cambered bottom,equations of higher degree needs to be solved. Traditional algorithms and approximation algorithm are complicated with less accuracy,whereas computer programming adopted to solve the equation is inconvenient for on-site application. On the basis of mathematical transformation of the calculation formula,a simplified formula with convenient process is obtained by successive approximation and fitting for engineering practice,with the minimum standard residual difference as objective function. Results of the simplified formula meets the requirements of engineering design,and is worthy of promotion.
TENG Kai
,
ZHANG Li-wei
. Simplified Calculation for the Critical Depth of Trapezoidal Open Channel with Cambered Bottom[J]. Journal of Changjiang River Scientific Research Institute, 2013
, 30(5)
: 60
-63
.
DOI: 10.3969/j.issn.1001-5485.2013.05.014
［1］ 杨 彬. 弧底梯形渠道全断面振捣连续滑膜衬砌机设计研究［J］.陕西水利，2010，（6）：91-92.(YANG Bin. Design of Lining Machine for the Continuous Synovial Membrane for Trapezoidal Channel Section with Cambered Bottom［J］. Shaanxi Water Resources,2010,(6):91-92.(in Chinese))
［2］ 王 虎.不同断面形式防渗渠道的应用效果［J］.防渗技术，2002，（3）：31-33.(WANG Hu. Results of the Application of Anti-seepage Channels with Different Cross-section Patterns ［J］. Technique of Seepage Control,2002，(3): 31-33.(in Chinese))
［3］ 李艳玲. 弧底梯形混凝土衬砌渠道施工技术［J］.山西水利科技，2011，（1）：65-66.(LI Yan-ling. Techniques of Constructing Channels with Trapezoidal Concrete Lining with Cambered Bottom［J］. Shanxi Hydrotechnics,2011,(1): 65-66.(in Chinese))
［4］ 银俊梅.弧底梯形渠的冻胀试验研究［J］.中国农村水利水电，2001，（12）：140-143.(YIN Jun-mei. Frost Heave Test for Trapezoidal Channels［J］. China Rural Water and Hydropower,2001,(12): 140-143.(in Chinese))
［5］ 王正中，李甲林，郭利霞，等. 弧底梯形渠道衬砌冻胀破坏的力学模型研究［J］.农业工程学报，2008，（1）：26-31.(WANG Zheng-zhong,LI Jia-lin,Guo Li-xia,et al. Mechanical Model for the Damage of Trapezoidal Channel with Cambered Bottom Caused by Frost and Heave［J］. Transactions of the Chinese Society of Agricultural Engineering,2008,(1): 26-31.(in Chinese))
［6］ 宋 玲，余书超. 弧底梯形渠道受力特征及设计方法研究［J］.人民黄河，2010，（8）：128-129.(SONG Ling,YU Shu-chao. Forces on and Design Methods of Trapezoidal Channels ［J］. Yellow River,2010,(8): 128-129.(in Chinese))
［7］ 冯金祥，朱勤创. 弧底梯形断面在宝鸡峡灌区应用的效益［J］.防渗技术，2001，（2）：33-35.(FENG Jin-xiang,ZHU Qin-chuang. Application Results of Trapezoidal Section with Spherical bed in the Baojixia Irrigation Area［J］. Technique of Seepage Control,2001,(2): 33-35.(in Chinese))
［8］ 王文龙. 弧底梯形断面在夹马口灌区续改工程中的应用［J］.吉林工程技术学院学报，2004，（3）:56-58.（WANG Wen-long. Application of Trapezoidal Section with Spherical bed in the Improvement Works of Jiamakou Irrigation Area［J］. Journal of Jilin Engineering and Technical College,2004,(3):56-58.(in Chinese))
［9］ 董为民，赵小利，刘卫华，等.底部含圆弧的梯形断面防渗渠道的水力计算［J］.水利与建筑工程学报，2005，（3）：54-57.( DONG Wei-min,ZHAO Xiao-li,LIU Wei-hua,et al. Hydraulic Calculation of Seepage Control Canal with Cross Section of Trapezium with Circular-spherical bed［J］. Journal of Water Resources and Architectural Engineering,2005,(3): 54-57.(in Chinese))
［10］杨茂松，马子普.一种弧底梯形明渠临界水深的快速解法［J］.吉林水利，2011，（11）：21-23.(YANG Mao-song,MA Zi-pu. A Rapid Solution in Calculating Critical Depth for Open Trapezoidal Channel with Cambered Bottom［J］. Jilin Water Resources,2011,(11): 21-23.(in Chinese))
［11］赵 晨.U形及弧底梯形渠道断面水力计算的搜索法与程序［J］.水利与建筑工程学报，2006，（3）：82-84.(ZHAO Chen. Searching method and Procedures of the Hydraulic Calculation for U-shaped and Trapezoidal Channel Cross-section with Cambered Bottom［J］. Journal of Water Resources and Architectural Engineering,2006,(3): 82-84.(in Chinese))
［12］孙铁蕾.EXCEL在常用明渠均匀流水力计算的应用［J］.水利规划与设计，2006，（5）：71-72.(SUN Tie-lei. Application of EXCEL to the Hydraulic Calculation of Common Open Channel with Uniform Flow［J］. Water Resources Planning and Design,2006,(5): 71-72.(in Chinese))
［13］成铁兵. 弧底梯形及弧角梯形断面水力计算电算程序［J］.杨凌职业技术学院学报，2008，（3）：23-25,29.(CHENG Tie-bing. Computer Calculation Procedure for the Hydraulic Calculation of Trapezoidal Cross-section with Cambered Bottom and Arc Angle［J］. Journal of Yangling Vocational and Technical College,2008,(3): 23-25,29.(in Chinese))
［14］王正中，申永康，彭元平,等. 弧底梯形明渠临界水深的直接算法［J］.长江科学院院报，2005,22（3）：6-8.(WANG Zheng-zhong,SHEN Yong-kang,PENG Yuan-ping,et al. Direct Formula Calculating Critical Depth for Open Trapezoidal Channel with Cambered Bottom［J］. Journal of Yangtze River Scientific Research Institute,2005,22 (3): 6-8.(in Chinese))
［15］成都科学技术大学水力学教研室. 水力学［M］.北京：人民教育出版社，1980.(Department of Hydraulics of Chengdu University of Science and Technology. Hydraulics［M］. Beijing: People’s Education Press,1980.(in Chinese))
［16］刘 刚，滕 凯.圆形断面临界水深简化近似计算方法［J］. 水利与建筑工程学报 ，2011，（6）：81-83.(LIU Gang,TENG kai. Simplified Approximate Calculation Method for Critical Water Depth of Circular Section［J］ . Journal of Water Resources and Architectural Engineering,2011,(6):81-83.(in Chinese))
［17］王慧文.偏最小二乘回归法及其应用［M］.北京：国防工业出版社，1999.(WANG Hui-wen. Partial Least Squares Regression Method and Its Application ［M］. Beijing: National Defence Industry Press,1999.(in Chinese))
［18］阎凤文.测量数据处理方法［M］. 北京：原子能出版社，1988.(YAN Feng-wen. Methods of Processing Measurement Data［M］. Beijing: Atomic Energy Press,1988.(in Chinese))
