蛋形断面隧洞临界水深的简易算法-河海期刊.PDF

第33卷第6期 水 利 水 电科 技 进 展 2013年11月 Vol.33 No.6 Advances in Science and Technology of Water Resources Nov. 2013 DOI:10.3880/ j.issn.1006 7647.2013.06.007 蛋形断面隧洞临界水深的简易算法 滕摇 凯 (齐齐哈尔市水务局,黑龙江 齐齐哈尔摇 161006) 摘要:蛋形断面临界水深计算需完成表达形式复杂且分3 个区段给出的超越方程求解,针对解析法 无法直接完成求解而采用常规的试算法计算工作量大、效率低、不便实际应用等问题,依据优化拟 合理论,以标准剩余差最小为目标函数,在工程适用参数范围内,经拟合计算得到了一个表达形式 简单直观、计算不分区段、便于实际应用的通用简化公式。 精度分析及实例计算结果表明,该公式 最大计算误差仅为0郾649%,利用该公式完成蛋形断面临界水深计算可大大简化计算过程,提高工 作效率。 关键词:过水隧洞;蛋形断面;临界水深;优化拟合;近似计算 中图分类号:TV131.4摇 摇 摇 文献标志码:A摇 摇 摇 文章编号:1006 7647(2013)06 0037 03 Simple algorithm for the critical depth of an egg鄄shaped section water tunnel/ / TENG Kai(Qiqihar Municipal Water Affairs Bureau,Qiqihar 161006,China) Abstract:Atranscendental equationwhichhasacomplex expressionformneedstobe solvedinthree sub鄄sectionsinorder to calculate the critical depth of an egg鄄shaped cross section. The equation can not be solved directly by an analytical method andtheconventionaltrialmethodhasthedrawbacksof heavy computationaleffort,low efficiency andinconvenience for practical applications. Based on the optimal fitting theory,an objective function was chosen for the smallest standard residual difference. By fitting computation confined to suitable parameters in engineering,a general approximation formula was proposed. The formula has a simple expression, no sub鄄sections for calculation, easy for practical application. Precision analysis andcomputationalresultsshowthatthemaximumfittingerrorisonly0郾649% andtheprocessforcritical depth calculation of an egg鄄shaped cross section can be greatly simplified,and the working efficiency can be improved significantly. Key words:water tunnel;egg鄄shaped cross section;critical depth;optimal fitting;approximate calculation 摇 摇 相比马蹄形、门