| Description |
1 online resource (xiv, 188 pages) : illustrations (some color) |
| Series |
Advances in geophysical and environmental mechanics and mathematics |
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Advances in geophysical and environmental mechanics and mathematics.
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| Contents |
Preface -- Contents -- Acronyms and Symbols -- 1 Basic Equations for the Gradually-Varied Flow -- 1.1 Introduction -- 1.2 The GVF Equation for Flow in Open Channels -- 1.3 The GVF Equation in Terms of Flow Depth -- 1.3.1 Conveyance and Section Factor of Channel Section -- 1.3.2 Hydraulic Exponents Defined in Relation to Conveyance and Section Factor -- 1.3.3 Role of the Power-Law Flow Resistance Formula in the GVF Equation -- 1.4 The GVF Equation for Flow in Adverse Channels -- 1.5 Classification of Gradually-varied Flow Profiles -- 1.6 Hydraulic Exponents |
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1.7 The Equation for GVF in Non-Prismatic Channels 1.8 Summary -- References -- 2 Conventional Integral Solutions of the GVF Equation -- 2.1 Introduction -- 2.2 GVF Solution in Terms of Varied-Flow Function -- 2.3 GVF Solution by the Bresse Method -- 2.4 GVF Solution by the Bakhmeteff-Chow Procedure -- 2.5 Drawbacks on the VFF Table for GVF Solution -- 2.6 Attempts Made on M and N by Previous Investigators -- 2.7 Previous Studies on Integrating the GVF Equation -- 2.8 Summary -- References |
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3 Normal-Depth-Based Dimensionless GVF Solutions Using the Gaussian Hypergeometric Function3.1 Introduction -- 3.2 Normalization of the GVF Equation -- 3.3 GVF Solutions by Using Gaussian Hypergeometric Functions -- 3.3.1 An Alternative Form of (??) for u> 1 -- 3.3.2 Feasible Arrangement of Two Integrals -- 3.3.3 Gaussian Hypergeometric Functions -- 3.3.4 The GHF-Based Solutions of GVF Equation -- 3.4 Alternative Method to Get the GHF-Based Solutions -- 3.5 Classification of GHF-Based Solutions -- 3.5.1 M, C and S Profiles |
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3.5.2 An Example of GHF-Based GVF Profiles with Specified Hydraulic Exponents3.5.3 N-Values for Fully Rough Flows in Wide Channels -- 3.5.4 GHF-Based Solutions Under Specified Boundary Conditions -- 3.5.5 Examples of GHF-Based GVF Prolfiles with M=3 and N=10/3, Specified λ and BCs -- 3.6 Validation of the GHF-Based Solutions -- 3.6.1 Solving Equation (??) by Use of the ETF -- 3.6.2 Comparison of the GHF-Based and ETF-Based Solutions -- 3.7 Properties of the GHF-Based Solutions -- 3.7.1 Slopes of Flow Profiles Varying with hc/hn and N |
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3.7.2 Singularities of the Rational Function Representing the Slopes of C1 and C3 Profiles3.7.3 Points of Inflection on the M1 and M3 Profiles -- 3.8 Discussion -- 3.8.1 Applicability of the GHF-Based Solutions in Perspective -- 3.8.2 Role of hc/hn in the Domain of the GHF-Based Solution Space -- 3.8.3 Reclassification of the Critical Profiles and Points of Infinite Profile Slopes -- 3.8.4 Identification of Inflection Points on GVF Profiles -- 3.8.5 Curvature of GVF Profiles -- 3.9 Summary -- References |
| Summary |
Gradually-varied flow (GVF) is a steady non-uniform flow in an open channel with gradual changes in its water surface elevation. The evaluation of GVF profiles under a specific flow discharge is very important in hydraulic engineering. This book proposes a novel approach to analytically solve the GVF profiles by using the direct integration and Gaussian hypergeometric function. Both normal-depth- and critical-depth-based dimensionless GVF profiles are presented. The novel approach has laid the foundation to compute at one sweep the GVF profiles in a series of sustaining and adverse channels, which may have horizontal slopes sandwiched in between them |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
English |
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Online resource; title from pdf information screen (Ebsco, viewed March 12, 2014) |
| Subject |
Open-channel flow.
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Hypergeometric series.
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TECHNOLOGY & ENGINEERING -- Hydraulics.
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Sciences de la terre.
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Environnement.
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Hypergeometric series
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Open-channel flow
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| Form |
Electronic book
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| ISBN |
9783642352423 |
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3642352421 |
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3642352413 |
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9783642352416 |
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