A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels

Marie Sjiernquist Desatnik; Raad Yahya Qassim

doi:doi:10.11648/j.engmath.20170101.12

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A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels

Marie Sjiernquist Desatnik, Raad Yahya Qassim

Published in Engineering Mathematics (Volume 1, Issue 1)

Received: 1 June 2017 Accepted: 22 June 2017 Published: 27 July 2017

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Abstract

One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19^th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel geometries comprising rectangular, trapezoidal, parabolic bottom surfaces and diverse configurations: simple channels, compound channels, and channel networks. The wide rectangular channel case is of particular interest in its own right, as well as serving as a validation benchmark for transient, and multiple dimensional gradually varied flow, the latter normally solved by numerical techniques and therefore requiring calibration. In this paper, a new exact analytical and easy to compute solution is developed. It is shown that this solution possesses the ease of computation as an advantage in comparison with existent exact solutions reported in the literature. As this solution involves a multiple valued function, it is consistent with the nonuniqueness propert of the intial value problem of one dimensional steady gradually varied flow.

Published in	Engineering Mathematics (Volume 1, Issue 1)
DOI	10.11648/j.engmath.20170101.12
Page(s)	7-10
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Gradually Varied Flow, Open Channels, Steady One Dimensional, Exact Solution

References

[1]	Szmkiewicz, R., “Numerical Modeling in Open Channel Hydraulics”, Springer Science + Business Media B. V. (2010). http://doi.dx.org/10.1007/978-90-481-3674-2.
[2]	Jan, C.-D., “Gradually-varied Flow Profiles in Open Channels”, Springer-Verlag Berlin Heidelberg (2014).
[3]	French, R. H., “Open-Channel Hydraulics”, McGraw-Hill Book Company (1985).
[4]	Kumbhakar, M., Ghoshal, K., “Two dimensional velocity distribution in open channels using Renyi entropy”, Physica A, 450 (2016): 546-559.
[5]	Jha, S. K., “Effects of particle inertia on the transport of particle –laden open channel flow”, European Journal of Mechanics B/Fluids, 62 (2017): pp. 32-41.
[6]	Kumar, A., Sairi, R. P., “Performance parameters of Savonius type hydrokinetic turbine – A review”, Renewable and Sustainable Energy Reviews, 64 (2016): 289-310.
[7]	MacDonald, I., Baines, M. J., Nichols, N. K., Samuels, P. G., “Analytic benchmark solutions for open-channel flows”, ASCE Journal of Hydraulic Engineering, 123. 11 (1997): pp. 1041-1045.
[8]	Powell, D. M., Flow resistance in gravel-bed rivers: Progress in research, Earth-Science Reviews, 136 (2014): pp. 301-338.
[9]	Bjierjlie, D. M., Dingman, S. L., bolster, C. H., “Comparison of constitutive flow resistance equations based on the Manning and Chezy equations applied to natural rivers”, Water Resources Research, 42 (2005): pp. W11502-W11509.
[10]	Polyanin, A. D., Manzihrov, A. V., “A Handbook of Mathematics for Engineers and Scientists”, Chapmanand Hall (2007).
[11]	Venutelli, M., “Direct integration of the equation of gradually varied flow”, ASCE Journal of Irrigation and Damage Engineering, 130. 1 (2004): pp. 88-91.
[12]	Vatankhah, A. R., “Exact sensitivity equation for one-dimensional steady-state shallow water flow (Application to model calibration)”, ASCE Journal of Hydrologic Engineering, 15. 11 (2010): pp. 939-945.
[13]	Artichowicz, W., Szymkiewicz, R., “Computational issues of solving the 1D steady gradually varied flow equation”, Journal of Hydrology and Hydromechanics, 62. 3 (2014): pp. 226-233.

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Marie Sjiernquist Desatnik, Raad Yahya Qassim. (2017). A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels. Engineering Mathematics, 1(1), 7-10. https://doi.org/10.11648/j.engmath.20170101.12

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ACS Style

Marie Sjiernquist Desatnik; Raad Yahya Qassim. A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels. Eng. Math. 2017, 1(1), 7-10. doi: 10.11648/j.engmath.20170101.12

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AMA Style

Marie Sjiernquist Desatnik, Raad Yahya Qassim. A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels. Eng Math. 2017;1(1):7-10. doi: 10.11648/j.engmath.20170101.12

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@article{10.11648/j.engmath.20170101.12,
  author = {Marie Sjiernquist Desatnik and Raad Yahya Qassim},
  title = {A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels},
  journal = {Engineering Mathematics},
  volume = {1},
  number = {1},
  pages = {7-10},
  doi = {10.11648/j.engmath.20170101.12},
  url = {https://doi.org/10.11648/j.engmath.20170101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20170101.12},
  abstract = {One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel geometries comprising rectangular, trapezoidal, parabolic bottom surfaces and diverse configurations: simple channels, compound channels, and channel networks. The wide rectangular channel case is of particular interest in its own right, as well as serving as a validation benchmark for transient, and multiple dimensional gradually varied flow, the latter normally solved by numerical techniques and therefore requiring calibration. In this paper, a new exact analytical and easy to compute solution is developed. It is shown that this solution possesses the ease of computation as an advantage in comparison with existent exact solutions reported in the literature. As this solution involves a multiple valued function, it is consistent with the nonuniqueness propert of the intial value problem of one dimensional steady gradually varied flow.},
 year = {2017}
}

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TY  - JOUR
T1  - A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels
AU  - Marie Sjiernquist Desatnik
AU  - Raad Yahya Qassim
Y1  - 2017/07/27
PY  - 2017
N1  - https://doi.org/10.11648/j.engmath.20170101.12
DO  - 10.11648/j.engmath.20170101.12
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 7
EP  - 10
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20170101.12
AB  - One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel geometries comprising rectangular, trapezoidal, parabolic bottom surfaces and diverse configurations: simple channels, compound channels, and channel networks. The wide rectangular channel case is of particular interest in its own right, as well as serving as a validation benchmark for transient, and multiple dimensional gradually varied flow, the latter normally solved by numerical techniques and therefore requiring calibration. In this paper, a new exact analytical and easy to compute solution is developed. It is shown that this solution possesses the ease of computation as an advantage in comparison with existent exact solutions reported in the literature. As this solution involves a multiple valued function, it is consistent with the nonuniqueness propert of the intial value problem of one dimensional steady gradually varied flow.
VL  - 1
IS  - 1
ER  -

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Author Information

Marie Sjiernquist Desatnik

Department of Energy Technology, School of Industrial Engineering and Management, KTH Royal Institute of Technology, Stockholm, Sweden
Raad Yahya Qassim

Department of Ocean Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

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APA Style

Marie Sjiernquist Desatnik, Raad Yahya Qassim. (2017). A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels. Engineering Mathematics, 1(1), 7-10. https://doi.org/10.11648/j.engmath.20170101.12

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ACS Style

Marie Sjiernquist Desatnik; Raad Yahya Qassim. A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels. Eng. Math. 2017, 1(1), 7-10. doi: 10.11648/j.engmath.20170101.12

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AMA Style

Marie Sjiernquist Desatnik, Raad Yahya Qassim. A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels. Eng Math. 2017;1(1):7-10. doi: 10.11648/j.engmath.20170101.12

Copy | Download

@article{10.11648/j.engmath.20170101.12,
  author = {Marie Sjiernquist Desatnik and Raad Yahya Qassim},
  title = {A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels},
  journal = {Engineering Mathematics},
  volume = {1},
  number = {1},
  pages = {7-10},
  doi = {10.11648/j.engmath.20170101.12},
  url = {https://doi.org/10.11648/j.engmath.20170101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20170101.12},
  abstract = {One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel geometries comprising rectangular, trapezoidal, parabolic bottom surfaces and diverse configurations: simple channels, compound channels, and channel networks. The wide rectangular channel case is of particular interest in its own right, as well as serving as a validation benchmark for transient, and multiple dimensional gradually varied flow, the latter normally solved by numerical techniques and therefore requiring calibration. In this paper, a new exact analytical and easy to compute solution is developed. It is shown that this solution possesses the ease of computation as an advantage in comparison with existent exact solutions reported in the literature. As this solution involves a multiple valued function, it is consistent with the nonuniqueness propert of the intial value problem of one dimensional steady gradually varied flow.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels
AU  - Marie Sjiernquist Desatnik
AU  - Raad Yahya Qassim
Y1  - 2017/07/27
PY  - 2017
N1  - https://doi.org/10.11648/j.engmath.20170101.12
DO  - 10.11648/j.engmath.20170101.12
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 7
EP  - 10
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20170101.12
AB  - One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel geometries comprising rectangular, trapezoidal, parabolic bottom surfaces and diverse configurations: simple channels, compound channels, and channel networks. The wide rectangular channel case is of particular interest in its own right, as well as serving as a validation benchmark for transient, and multiple dimensional gradually varied flow, the latter normally solved by numerical techniques and therefore requiring calibration. In this paper, a new exact analytical and easy to compute solution is developed. It is shown that this solution possesses the ease of computation as an advantage in comparison with existent exact solutions reported in the literature. As this solution involves a multiple valued function, it is consistent with the nonuniqueness propert of the intial value problem of one dimensional steady gradually varied flow.
VL  - 1
IS  - 1
ER  -

Copy | Download