Direct solution to problems of hydraulic jump in horizontal triangular channels
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 so...
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Published in | Applied mathematics letters Vol. 23; no. 9; pp. 1104 - 1108 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
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Elsevier Ltd
01.09.2010
Elsevier |
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Abstract | 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. |
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AbstractList | 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. 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. |
Author | Vatankhah, Ali R. Omid, M.H. |
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Cites_doi | 10.1080/00221680309499976 |
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Keywords | Sequent depth ratio Hydraulic jump Triangular channels Ditch irrigation Analytical solutions Resolvent Error estimation Hydraulicjump Applied mathematics Analytical solution Quartic equation |
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References | Chaudhry (b1) 2006 Beyer (b5) 1987 Subramanya (b7) 1986 P.A. Argyropoulus, The hydraulic jump and the effect of turbulence on hydraulic structure, in: Proc. IAHR, Dubrovnik, Yugoslavia, 1961, pp. 173–183. Achour, Debabeche (b2) 2003; 41 Beyer (b6) 1987 Abramowitz, Stegun (b4) 1972 Beyer (10.1016/j.aml.2010.04.044_b6) 1987 Achour (10.1016/j.aml.2010.04.044_b2) 2003; 41 Subramanya (10.1016/j.aml.2010.04.044_b7) 1986 Chaudhry (10.1016/j.aml.2010.04.044_b1) 2006 Abramowitz (10.1016/j.aml.2010.04.044_b4) 1972 10.1016/j.aml.2010.04.044_b3 Beyer (10.1016/j.aml.2010.04.044_b5) 1987 |
References_xml | – volume: 41 start-page: 319 year: 2003 end-page: 325 ident: b2 article-title: Control of hydraulic jump by sill in triangular channel publication-title: J. Hydraul. Res. contributor: fullname: Debabeche – year: 1987 ident: b6 article-title: Handbook of Mathematical Sciences contributor: fullname: Beyer – year: 2006 ident: b1 article-title: Open-Channel Flow contributor: fullname: Chaudhry – year: 1972 ident: b4 article-title: Handbook of Mathematical Functions contributor: fullname: Stegun – year: 1987 ident: b5 article-title: CRC Standard Mathematical Tables contributor: fullname: Beyer – year: 1986 ident: b7 article-title: Flow in Open Channels contributor: fullname: Subramanya – year: 1987 ident: 10.1016/j.aml.2010.04.044_b5 contributor: fullname: Beyer – volume: 41 start-page: 319 issue: 1 year: 2003 ident: 10.1016/j.aml.2010.04.044_b2 article-title: Control of hydraulic jump by sill in triangular channel publication-title: J. Hydraul. Res. doi: 10.1080/00221680309499976 contributor: fullname: Achour – year: 1972 ident: 10.1016/j.aml.2010.04.044_b4 contributor: fullname: Abramowitz – year: 2006 ident: 10.1016/j.aml.2010.04.044_b1 contributor: fullname: Chaudhry – ident: 10.1016/j.aml.2010.04.044_b3 – year: 1986 ident: 10.1016/j.aml.2010.04.044_b7 contributor: fullname: Subramanya – year: 1987 ident: 10.1016/j.aml.2010.04.044_b6 contributor: fullname: Beyer |
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SubjectTerms | 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 |
Title | Direct solution to problems of hydraulic jump in horizontal triangular channels |
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