Computing conjugate depths in trapezoidal channels

• Published in: Proceedings of the Institution of Civil Engineers. Water management Vol. 165; no. 9; pp. 507 - 512
• Main Authors: Liu, Jiliang, Wang, Zhengzhong, Fang, Xing
• Format: Journal Article
• Language: English
• Published: London Telford 01.10.2012; ICE Publishing
• Subjects: Applied fluid mechanics; Applied sciences; Buildings. Public works; Channels; Computational fluid dynamics; Conjugates; Critical depth; Exact sciences and technology; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Hydraulic constructions; Hydraulic design; Hydraulic jump; Hydraulics; Hydrodynamics, hydraulics, hydrostatics; Iterative methods; Mathematical analysis; Mathematical models; Momentum equation; Open channels; Physics; Hydraulics; Open channel flow; Iterative method; Numerical simulation; Trapezoidal shape; Hydraulic jump; Modeling
• ISSN: 1741-7589; 1751-7729
• DOI: 10.1680/wama.11.00014

Accurate calculation of conjugate depths in a hydraulic jump is important to hydraulic design in open channels. Iterative formulae for calculating conjugate depths in hydraulic jumps in trapezoidal open channels were developed using mathematical transformation of the momentum equation. Two formulae that are adjusted from the critical depth of trapezoidal channels were proposed to compute the initial values for iterative formulae. The iterative formulae described here can be used for computer program development to find accurate solutions of conjugate depths. Because the appropriate initial values were selected to accelerate the convergence rates of iteration procedures, the output from the first iteration can be treated as a reliable estimate of conjugate depths with the relative error less than 0.8% in most cases. The approximation formulae are well-suited for manual calculations.