Gradually-varied flow profiles in open channels [electronic resource] : analytical solutions by using Gaussian hypergeometric function /
Jan, Chyan-Deng.author.
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.
""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""
""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""
""3 Normal-Depth-Based Dimensionless GVF Solutions Using the Gaussian Hypergeometric Function""""3.1 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""
""3.5.2 An Example of GHF-Based GVF Profiles with Specified Hydraulic Exponents""""3.5.3 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 Î» 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""
""3.7.2 Singularities of the Rational Function Representing  the Slopes of C1 and C3 Profiles""""3.7.3 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""
""4 Critical-Depth-Based Dimensionless GVF Solutions Using the GHF""
Includes indexes.
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.
Continuum physics.
Mechanics.
Classical and Continuum Physics.
Classical Mechanics.