Accurate gradually varied flow model for water surface profile in circular channels | Zendy

Ali R. Vatankhah | Zendy; Said M. Easa | Zendy

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Accurate gradually varied flow model for water surface profile in circular channels

Author(s) -

Ali R. Vatankhah,

Said M. Easa

Publication year - 2013

Publication title -

ain shams engineering journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.505

H-Index - 46

eISSN - 2090-4495

pISSN - 2090-4479

DOI - 10.1016/j.asej.2013.01.005

Subject(s) - froude number , approximation error , flow (mathematics) , mathematics , exact solutions in general relativity , surface (topology) , mathematical analysis , mathematical optimization , geometry

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

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