Full Equations Utilities (FEQUTL) Model for the Approximation of Hydraulic Characteristics of Open Channels and Control Structures During Unsteady Flow

By DELBERT D. FRANZ, Linsley, Kraeger Associates and
CHARLES S. MELCHING, U.S. Geological Survey


Water Resources Investigations Report 97-4037

Prepared in cooperation with the


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Table of Contents

1. Introduction
1.1 Purpose and Scope

1.2 Look-Up Tables
1.2.1 Look-Up Tables for Channel Cross Sections

1.2.2 Look-Up Tables for Hydraulic Control Structures
1.2.3 Table Look-Up Procedure
1.3 Procedure for Computation of Function Tables for Use in Simulation of Unsteady Flow Using the Full Equations Model

2. Table Types Generated in the Full Equations Utilities Model
2.1 One-Dimensional Function Tables
2.1.1 Type 2 Tables

2.1.2 Cross-Section Function Tables
2.2 Two-Dimensional Function Tables
2.3 Three-Dimensional Function Tables

3. Approximation of Hydraulic Characteristics of Open Channels
3.1 Characteristics of a Cross Section for a Branch
3.1.1 Static Characteristics and Simple Dynamic Characteristics

3.1.2 Improved Flux Coefficients and Critical Flow
3.1.3 Correction Coefficients for Channel Curvilinearity
3.1.4 Interpolation of Cross Sections
3.2 Channel Expansions and Contractions
3.2.1 Governing Equations for Expansions and Contractions

3.2.2 Expansion-Contraction Losses
3.2.3 Mean Conveyance for the Expansion or Contraction
3.2.4 Outline of Solution Process for Expansions and Contractions
3.3 Channel Ratings for Bypass Channels
3.3.1 Governing Equation for Channel Ratings

3.3.2 Outline of Solution Process for Channel Ratings

4. Approximation of Hydraulic Characteristics of Control Structures
4.1 Bridges

4.2 Culverts
4.2.1 Additional Flow Types

4.2.2 General Routing Methodology for Culvert Flow
4.2.3 Routing Methodology for Culvert-Flow Type 5
4.2.4 Transitions Between Flow Types
4.2.5 Departure-Reach Losses
4.2.6 Outline of Solution Process for Culvert Flow
4.2.7 Momentum Flux for Flow Over the Roadway
4.2.8 Special Losses
4.2.9 Summary of the CULVERT Command
4.3 Embankments and Weirs
4.4 Closed Conduits
4.5 Generalized Ritter Dam-Break Solution
4.6 Critical-Flow Function
4.7 Floodway Delineation
4.8 Underflow Gates
4.8.1 Free-Orifice Flow

4.8.2 Free-Weir Flow
4.8.3 Submerged-Orifice Flow
4.8.4 Submerged-Weir Flow
4.8.5 Outline of Solution Process for Underflow Gates
4.8.6 Interpolation for Flows at Nontabulated Gate Openings

5. Input Description for the Full Equations Utilities Model:Version 4.0
5.1 Standard Header Block

5.2 Channel Command
5.3 Chanrat Command
5.4 Critq Command
5.5 Culvert Command
5.6 Embankq Command
5.7 Expcon Command
5.8 Feqx Command
5.9 Feqxext Command
5.10 Feqxlst Command
5.11 Finish Command
5.12 Floodway Command
5.13 Ftabin Command
5.14 Gritter Command
5.15 Hec2x Command
5.16 Mulcon Command
5.17 Mulpipes Command
5.18 Qclimit Command
5.19 Sewer Command
5.20 Ufgate Command
5.21 Wsproqz Command
5.22 Wsprot14 Command
5.23 Wsprox Command
5.24 Xsinterp Command
References Cited
Appendix 1: List of Notation
Appendix 2: Dimensions of Arrays and Specification of Fortran Unit Numbers in the Full Equations Utilities Model
Appendix 3: Full Equations Utilities Model Error Messages and Warnings: Version 4.0
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