|
|
|
| Calculation of optimal compound cross-section dimensions channel with flat-bottom and parabolic side walls |
| ZHAI Donghan1, HE Wuquan1,2*, LI Gang1 |
| 1.College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling, Shaanxi 712100, China; 2.Key Laboratory of Agricultural Soil & Water Engineering in Arid and Semiarid Areas, Ministry of Education, Yangling, Shaanxi 712100, China |
|
|
|
|
Abstract To solve a few problems such as great depth and large amount of earthworks occurred when a parabolic cross-section is applied in large- and medium-sized channels, a channel with compound cross-section was proposed, which is subject to a flat bottom and two 2th-order parabolic side walls. Analytical formulas for determining the channel cross-sectional area and wetted perimeter were deduced. Based on the open-channel uniform flow theory, a relationship between flow and water depth was established for the channel when the channel cross-section profile was under optimal hydraulic condition. Additionally, a series of formulas for the optimal width-to-depth ratio, water depth, water surface width, cross-sectional area and wetted perimeter were deduced and programmed by using Mathcad software. It was shown that at flow Q=30 m3/s, the channel had 2.904 m water depth, 6.278 m water surface width and 13.604 m2 cross-sectional area under the optimal hydraulic condition. The channel cross-section area is 1.7% and 0.2% smaller than the channels respectively with ordinary trapezoidal cross-section, arc-bottomed trapezoidal cross-section at the same flow rate. This indicates that the proposed compound cross-section profile is better in hydraulics and earthwork cost in comparison with the two kinds of existing trapezoidal cross-section channels.
|
|
Received: 29 March 2017
|
|
|
|
| [1]RAIKAR R V, REDDY M S S, VISHWANADH G K. Normal and critical depth computations for egg-shaped conduit sections[J]. Flow measurement and instrumentation, 2010, 21(3):367-372.[2]BIJANKHAN M, KOUCHAKZADEH S. Egg-shaped cross section: uniform flow direct solution and stability identification[J]. Flow measurement and instrumentation, 2011,22(6):511-516.[3]魏文礼,杨国丽. 立方抛物线形渠道水力最优断面的计算[J]. 武汉大学学报(工学版),2006,39(3):49-51. WEI Wenli, YANG Guoli. Calculation of optimal hydraulic cross-section for cubic parabola-shape channel[J]. Engineering journal of Wuhan University, 2006,39(3):49-51.(in Chinese)[4]张志昌,刘亚菲,刘松舰.抛物线形渠道水力最优断面的计算[J].西安理工大学学报,2002,18(3):235-237. ZHANG Zhichang, LIU Yafei, LIU Songjian. The calculation of optimal hydraulic cross section of parabola-shape channel[J]. Journal of Xi′an University of Technology, 2002,18(3):235-237.(in Chinese)[5]赵倩辉.复合断面渠道水力最佳断面的选择[J]. 四川水利, 2016(4):65-66. ZHAO Qianhui. Selection of optimal hydraulic section of composite section channel[J]. Sichuan water resources, 2016(4):65-66.(in Chinese)[6]黄朝煊. 梯形断面消力池扩散型消能计算[J]. 水利水电科技进展, 2016,36(5):34-39. HUANG Chaoxuan. Energy dissipation calculation for diffused stilling basin with trapezoidal cross section[J]. Advances in science and technology of water resources, 2016,36(5):34-39.(in Chinese)[7]HAN Yancheng. Horizontal bottomed semi-cubic parabolic channel and best hydraulic section[J]. Flow measurement and instrumentation, 2015,45:56-61.[8]VATANKHAN A R. Semi-regular polygon as the best hydraulic section in practice(generalized solutions)[J]. Flow measurement and instrumentation, 2014,38:67-71.[9]吕宏兴,冯家涛.明渠水力最佳断面的比较[J].人民长江,1994,25(11):42-45. LYU Hongxing, FENG Jiatao. Comparison of optimal hydraulic section of open channel[J]. Yangtze River, 1994,25(11):42-45.(in Chinese)[10]吴持恭.水力学[M]. 3版. 北京:高等教学出版社,2003.[11]STURM T W. Open channel hydraulics[M]. [S.l.]:McGraw-Hill, 2001.[12]SUBRAMANYA K. Flow in open channels[J]. Hamostaseologie, 1997,33(1):43-50.[13]毛建华,华建文. MATHCAD解决工程问题[J]. 计算机应用与软件, 2005,22(12):136-138. MAO Jianhua, HUA Jianwen. Solve engineering computing problems by MATHCAD[J]. Computer applications and software, 2005,22(12):136-138.(in Chinese)[14]荣丰涛.梯形类渠道水力最佳断面统一公式的推求[J].山西水利科技,2003(4):5-7. RONG Fengtao. Derivation of unified equation for best hydraulic section of trapezoid-typed channel[J]. Shanxi hydrotechnics, 2003(4):5-7.(in Chinese) |
|
|
|
