Accurate gradually varied flow model for water surface profile in circular channels
The paper presents an accurate approximation of the Froude number (F) for circular channels which is part of the gradually varied flow (GVF) equation. The proposed approximation is developed using optimization technique to minimize the relative error between the exact and estimated values, resulting...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2013-12-01
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| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447913000208 |
| _version_ | 1818737659167637504 |
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| author | Ali R. Vatankhah Said M. Easa |
| author_facet | Ali R. Vatankhah Said M. Easa |
| author_sort | Ali R. Vatankhah |
| collection | DOAJ |
| description | The paper presents an accurate approximation of the Froude number (F) for circular channels which is part of the gradually varied flow (GVF) equation. The proposed approximation is developed using optimization technique to minimize the relative error between the exact and estimated values, resulting in a maximum error of 0.6% compared with 14% for the existing approximate method. The approximate F is used in the governing GVF equation to develop an exact analytical solution of this equation using the concept of simplest partial fractions. A comparison of the proposed and approximate solutions for backwater length shows that the error of the existing approximate solution could reach up to 30% for large normal flow depths. |
| first_indexed | 2024-12-18T00:56:33Z |
| format | Article |
| id | doaj.art-f4f130f6ae694f7998121be009a72f60 |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-12-18T00:56:33Z |
| publishDate | 2013-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-f4f130f6ae694f7998121be009a72f602022-12-21T21:26:30ZengElsevierAin Shams Engineering Journal2090-44792013-12-014462563210.1016/j.asej.2013.01.005Accurate gradually varied flow model for water surface profile in circular channelsAli R. Vatankhah0Said M. Easa1Department of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, University of Tehran, P.O. Box 4111, Karaj 31587-77871, IranDepartment of Civil Engineering, Ryerson University, Toronto, Ontario, Canada M5B 2K3The paper presents an accurate approximation of the Froude number (F) for circular channels which is part of the gradually varied flow (GVF) equation. The proposed approximation is developed using optimization technique to minimize the relative error between the exact and estimated values, resulting in a maximum error of 0.6% compared with 14% for the existing approximate method. The approximate F is used in the governing GVF equation to develop an exact analytical solution of this equation using the concept of simplest partial fractions. A comparison of the proposed and approximate solutions for backwater length shows that the error of the existing approximate solution could reach up to 30% for large normal flow depths.http://www.sciencedirect.com/science/article/pii/S2090447913000208Gradually varied flowCircular channelsAnalytical solutionDimensionless variables |
| spellingShingle | Ali R. Vatankhah Said M. Easa Accurate gradually varied flow model for water surface profile in circular channels Ain Shams Engineering Journal Gradually varied flow Circular channels Analytical solution Dimensionless variables |
| title | Accurate gradually varied flow model for water surface profile in circular channels |
| title_full | Accurate gradually varied flow model for water surface profile in circular channels |
| title_fullStr | Accurate gradually varied flow model for water surface profile in circular channels |
| title_full_unstemmed | Accurate gradually varied flow model for water surface profile in circular channels |
| title_short | Accurate gradually varied flow model for water surface profile in circular channels |
| title_sort | accurate gradually varied flow model for water surface profile in circular channels |
| topic | Gradually varied flow Circular channels Analytical solution Dimensionless variables |
| url | http://www.sciencedirect.com/science/article/pii/S2090447913000208 |
| work_keys_str_mv | AT alirvatankhah accurategraduallyvariedflowmodelforwatersurfaceprofileincircularchannels AT saidmeasa accurategraduallyvariedflowmodelforwatersurfaceprofileincircularchannels |