Direct solution to problems of hydraulic jump in horizontal triangular channels

• Published in: Applied mathematics letters Vol. 23; no. 9; pp. 1104 - 1108
• Main Authors: Vatankhah, Ali R., Omid, M.H.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2010; Elsevier
• Subjects: Analytical solutions; Channels; Computational fluid dynamics; Ditch irrigation; Exact sciences and technology; Exact solutions; Fluid flow; Horizontal; Hydraulic jump; Hydraulics; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Operator theory; Quartic equations; Sciences and techniques of general use; Sequent depth ratio; Triangular channels; Sequent depth ratio; Hydraulic jump; Triangular channels; Ditch irrigation; Analytical solutions; Resolvent; Error estimation; Hydraulicjump; Applied mathematics; Analytical solution; Quartic equation
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/j.aml.2010.04.044

The specific force equation has many applications in open channel flow problems. Quantifying of the hydraulic jump phenomenon is an important application of this equation. This equation has a direct solution only for the rectangular channels. The trial and error procedure as well as the graphical solution are the existing methods of solving hydraulic jump equations. No direct solutions are available in technical literature for sequent depth ratios in horizontal triangular channels because it is presumed that the governing equation is a quintic equation. In the present study, considering physical concepts this quintic equation has been reduced to a quartic equation. In the next step, this quartic equation has been converted to a resolvent cubic equation and two quadratic equations. This research shows these steps clearly to reach an acceptable physical analytic solution for sequent depth ratios in horizontal triangular channels.