Journal of Hydraulic Structures

Journal of Hydraulic Structures

Application correlation algorithm to create a new critical depth equation for gradually varied flow in trapezoidal channel using teaching–learning and studying

Document Type : Research Paper

Authors
Nguyen Minh Ngoc 1
Le Van Nghi 2
Phạm Hong Cuong 2
1 Department of Environmental Science, Hanoi Architectural University
2 Vietnam Academy for Water Resources, Hanoi, Vietnam.
10.22055/jhs.2020.34372.1141
Abstract
The critical depth is a hydraulic factor of the flow, it plays a particularly important role in studying and designing for open channels, especially during identification of water surfaces and analyzing to determine the phenomenon of a hydraulic jump in open channel. In practice, when calculating the critical depth, only the rectangular and isosceles triangle channels have the theory equation, in other circumstances in calculating by semi empirical equations.
This paper presents the general method to compute the critical depth of trapezoidal channel, the case study methodology was chosen to analyze the application of existing formulas and then offering a new equation to compute the critical depth based on the optimization algorithm in MS Excel software. This new equation will help to obtain more accurate result, which relative error of the equation is less than 0.61%, this equation has a simple structure, easy to calculate with small errors to meet the conditions to quickly calculate the critical depth, this equation is also suitable for teaching–learning and studying in the field of hydraulics.
Keywords
Critical depth
Non-uniform flow
trapezoidal chanel
critical flow
specific energy
  1. Ali R. Vatankhah (2013). Explicit solutions for critical and normal depths in trapezoidal and parabolic open channels. Flow Meas Instrum, 4: p 17–23.
  2. Ivan E. Houk (1918). Caculation of flow in open channel, Miami conserancy District, Technical Report, Pt. IV, Dayton, Ohio.
  3. Horace William King (1954). Handbook of Hydraulics, 4th ed, revised by Ernest F.Brater, McGraw-Hill Book cmpany, Inc, New York.
  4. Havey E. Jobson, David C. Froehlich (1988). Basic hydraulic principles of open-channel flow. Reston, Virginia.
  5. Ven Te Chow (1958). Open-Channel hydraulics. McGraw-Hill.
  6. Vatankhah AR, Kouchakzadeh S (2007). Discussion of exact equations for critical depth in a trapezoidal canal. J Irrig Drain Eng.133(5):508.
  7. Wang, Z and Sha (1995). Inquiry on a formula for calculating critical depth of open-channel flow with trapezoidal cross-section. J. Yangtze River Scientific Res. Inst., Wuhan, China, 12(2): p78-80.
  8. Zhengzhong Wang (1998). Formula for calculating critical depth of trapezoidal open channel. J. Hydraul. Eng.124:p90-91
  9. Vatankhah A.R, Easa S.M (2011). Explicit solutions for critical and normal depths in channels with different shapes. Flow Meas Instrum. 22(1),p43-49.
  10. Vatankhah A. R. (2013), Explicit solutions for critical and normal depths in trapezoidal and parabolic open channels. Ain Shams Engineering Journal. 4: p. 17–23. http://dx.doi.org/10.1016/j.asej.2012.05.002.
  11. Vu Van Tao, Nguyen Canh Cam (2006). Hydraulic – Set 1, Agricultural Publishing House (in Vietnamsese).
  12. Thandaveswara (2018), Hydraulics – Online course of Indian Institute of Technology Madras. Website: www.nptel.ac.in.
  13. H. Arvanaghi, Gh. Mahtabi, M. Rashidi (2015). New solutions for estimation of critical depth in trapezoidal cross section channel. J. Mater. Environ. Sci. 6 (9): p 2453-2460.
  14. Tiejie Cheng, Jun Wang, Jueyi Sui (2018). Calculation of critical flow depth using method of algebraic inequality. J. Hydrol. Hydromech. p316–322.
  15. Swamee, P. K. (1993). Critical depth equations for irrigation canals.J. Irrig. and Drain. Engrg., ASCE, 119(2): p 400–409.
  16. Farzin Salmasi (2020). Critical Depth of Trapezoidal Open Channel Using Explicit Formula and ANN Approach. Iranian Journal of Science and Technology, Transactions of Civil Engineering. DOI:10.1007/s40996-020-00416-7.
  17. Nash, J. E.; Sutcliffe, J. V. (1970). River flow forecasting through conceptual models part I — A discussion of principles. Journal of Hydrology.10 (3): p 282–290. doi:10.1016/0022-1694(70)90255-6.