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 inApplied mathematics letters Vol. 23; no. 9; pp. 1104 - 1108
Main Authors Vatankhah, Ali R., Omid, M.H.
Format Journal Article
LanguageEnglish
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
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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.
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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Issue 9
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
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  start-page: 319
  year: 2003
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  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
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  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:
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– year: 2006
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Snippet The specific force equation has many applications in open channel flow problems. Quantifying of the hydraulic jump phenomenon is an important application of...
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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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