OPEN-CHANNEL FLOW
CONTENTS BASIC CONCEPTS INTRODUCTION DE?NITIONS CLASSI?CATION OF FLOWS STEADY AND UNSTEADY FLOWS UNIFORM AND NONUNIFORM ?OWS LAMINAR AND TURBULENT FLOWS SUBCRITICAL, SUPERCRITICAL, AND CRITICAL FLOWS TERMINOLOGY VELOCITY DISTRIBUTION ENERGY COE?CIENT MOMENTUM CE?CIENT EXAMPLE 1-1 PRESSURE DISTRIBUTION STATIC CONDITIONS HORIZONTAL, PARALLEL FLOW PARALLEL FLOW IN SLOPING CHANNELS CURVILINEAR FLOW REYNOLDS TRANSPORT THEOREM COMPUTER PROGRAM SUMMARY REFERENCES CONSERVATION LAWS CONSERVATION OF MASS CONSERVATION OF MOMENTUM EQUATION OF MOTION STEADY FLOW STEADY, UNIFORM FLOW UNSTEADY, NONUNIFORM FLOW SPECI?C ENERGY APPLICATION OF MOMENTUM AND ENERGY EQUATIONS CHANNEL TRANSITION EXAMPLE 2-1 HYDRAULIC JUMP EXAMPLE 2-2 HYDRAULIC JUMP AT SLUICE GATE OUTLET EXAMPLE 2-3 2-10 SUMMARY CRITICAL FLOW RECTANGULAR CHANNEL UNIT DISCHARGE SPECI?C FORCE WAVE CELERITY NON-RECTANGULAR CHANNEL SPECI?C FORCE APPLICATION OF CRITICAL FLOW CONSTANT-WIDTH CHANNEL WITH BOTTOM STEP HORIZONTAL, VARIABLE-WIDTH CHANNEL EXAMPLE 3-1 LOCATION OF CRITICAL FLOW COMPUTATION OF CRITICAL DEPTH DESIGN CURVES TRIAL-AND-ERROR PROCEDURE NUMERICAL METHODS EXAMPLE 3-2 CRITICAL DEPTHS IN COMPOUND CHANNELS GENERAL REMARKS EXAMPLE 3-3 ALGORITHM FOR COMPUTING THE CRITICAL DEPTHS UNIFORM FLOW FLOW RESISTANCE FLOW RESISTANCE EQUATIONS CHEZY EQUATION MANNING EQUATION OTHER RESISTANCE EQUATIONS COMPUTATION OF NORMAL DEPTH EXAMPLE 4-1 EQUIVALENT MANNING CONSTANT COMPOUND CHANNEL CROSS SECTION SUMMARY GRADUALLY VARIED FLOW GOVERNING EQUATION CLASSI?CATION OF WATER-SURFACE PRO?LES SKETCHING OF WATER-SURFACE PRO?LES EXAMPLE 5-1 EXAMPLE 5-2 DISCHARGE FROM A RESERVOIR EXAMPLE 5-3 PRO?LES IN COMPOUND CHANNELS EXAMPLE 5-4 EXAMPLE 5-5 COMPUTATION OF GRADUALLY VARIED FLOW DIRECT-STEP METHOD EXAMPLE 6-1 STANDARD STEP METHOD EXAMPLE 6-2 INTEGRATION OF DI?ERENTIAL EQUATION SINGLE-STEP METHODS EULER METHOD IMPROVED EULER METHOD MODI?ED EULER METHOD FOURTH-ORDER RUNGE-KUTTA METHOD PREDICTOR-CORRECTOR METHODS SIMULTANEOUS SOLUTION PROCEDURE GOVERNING EQUATIONS SINGLE AND SERIES CHANNELS CHANNEL NETWORKS EXAMPLE 6-3 PRACTICAL APPLICATIONS COMPUTER PROGRAMS 6-10 SUMMARY RAPIDLY VARIED FLOW APPLICATION OF CONSERVATION LAWS CHANNEL TRANSITIONS SUBCRITICAL FLOW SUPERCRITICAL FLOW OBLIQUE HYDRAULIC JUMP WEIRS SHARP-CRESTED WEIRS BROAD-CRESTED WEIRS RATIO OF SEQUENT DEPTHS LENGTH OF JUMP JUMP PRO?LE JUMP TYPES ENERGY LOSS JUMP LOCATION CONTROL OF JUMP SPILLWAYS OVER?OW SPILLWAY ENERGY DISSIPATORS STILLING BASINS FLIP BUCKETS ROLLER BUCKETS COMPUTATION OF RAPIDLY VARIED FLOW CHARACTERISTIC DIRECTIONS COORDINATE TRANSFORMATIONS COMPUTATION OF SUPERCRITICAL FLOW FINITE-DI?ERENCE METHODS BOUNDARY CONDITIONS VERI?CATION COMPUTATION OF SUB- AND SUPERCRITICAL FLOWS NUMERICAL SOLUTION SIMULATION OF HYDRAULIC JUMP COMPUTATIONAL PROCEDURE RESULTS CHANNEL DESIGN RIGID-BOUNDARY CHANNELS EXAMPLE 9-1 MOST E?CIENT HYDRAULIC SECTION ERODIBLE CHANNELS PERMISSIBLE VELOCITY METHOD EXAMPLE 9-2 TRACTIVE FORCE METHOD EXAMPLE 9-3 ALLUVIAL CHANNELS REGIME THEORY EXAMPLE 9-4 SPECIAL TOPICS 10-1 INTRODUCTION 10-2 FLOW IN A CHANNEL CONNECTING TWO RESERVOIRS A MILD BOTTOM SLOPE B STEEP BOTTOM SLOPE 10-3 AIR ENTRAINMENT IN HIGH-VELOCITY FLOW 10-4 FLOW THROUGH CULVERTS 10-5 FLOW MEASUREMENT VELOCITY-AREA METHOD SLOPE-AREA METHOD FLUMES 10-6 SUMMARY UNSTEADY FLOW 11-1 INTRODUCTION 11-2 DE?NITIONS 11-3 OCCURRENCE OF UNSTEADY FLOW 11-4 HEIGHT AND CELERITY OF A GRAVITY WAVE CONTINUITY EQUATION MOMENTUM EQUATION EXAMPLE 11-1 11-5 SUMMARY GOVERNING EQUATIONS FOR ONE-DIMENSIONAL FLOW 12-1 INTRODUCTION 12-2 ST VENANT EQUATIONS CONTINUITY EQUATION MOMENTUM EQUATION 12-3 GENERAL REMARKS 12-4 BOUSSINESQ EQUATIONS MOMENTUM EQUATION IN Z-DIRECTION MOMENTUM EQUATION IN X-DIRECTION 12-5 INTEGRAL FORMS 12-6 SUMMARY NUMERICAL METHODS 13-1 INTRODUCTION 13-2 METHOD OF CHARACTERISTICS CHARACTERISTICS 13-3 INITIAL AND BOUNDARY CONDITIONS 13-4 CHARACTERISTIC GRID METHOD 13-5 METHOD OF SPECI?ED INTERVALS 13-6 OTHER NUMERICAL METHODS 13-7 SUMMARY FINITE-DIFFERENCE METHODS 14-1 INTRODUCTION 14-2 TERMINOLOGY FINITE-DI?ERENCE APPROXIMATIONS 14-3 EXPLICIT FINITE-DI?ERENCE SCHEMES UNSTABLE SCHEME DI?USIVE SCHEME MACCORMACK SCHEME LAMBDA SCHEME GABUTTI SCHEME 14-4 IMPLICIT FINITE-DI?ERENCE SCHEMES PREISSMANN SCHEME BEAM AND WARMING SCHEME VASILIEVVASILIEV, O F SCHEME 14-5 CONSISTENCY 14-6 STABILITY EXAMPLE 14-1 14-7 SUMMARY TWO-DIMENSIONAL FLOW 15-1 INTRODUCTION 15-2 GOVERNING EQUATIONS 15-3 NUMERICAL SOLUTION 15-4 MACCORMACK SCHEME GENERAL FORMULATION BOUNDARY CONDITIONS 15-5 GABUTTI SCHEME 15-6 ARTI?CIAL VISCOSITY 15-7 BEAM AND WARMING SCHEMES FACTORED SCHEMES IMPLICIT SPLIT-?UX FACTORING 15-8 FINITE-VOLUME SCHEME PREDICTOR PART CORRECTOR PART 15-9 APPLICATIONS PARTIAL BREACH OR OPENING OF SLUICE GATES COMPARISON WITH OTHER METHODS 15-10SUMMARY SEDIMENT TRANSPORT 16-1 INTRODUCTION 16-2 SEDIMENT PROPERTY SEDIMENT SIZE SIZE DISTRIBUTION 16-3 SAND-BED AND GRAVEL-BED STREAMS 16-4 THRESHOLD OF SEDIMENT MOTION CRITICAL SHIELDS STRESS FOR SEDIMENT MIXTURE 16-5 CONDITION FOR SIGNI?CANT SUSPENSION 16-6 SHIELDS DIAGRAM 16-7 THE EXNER EQUATION OF BED SEDIMENT CONSERVATION EXNER EQUATION FOR MULTIPLE SIZE FRACTION 16-8 BED-LOAD TRANSPORT RELATIONS BED LOAD TRANSPORT RELATIONS FOR POORLY SORTED SEDIMENT 16-9 SUSPENDED-LOAD TRANSPORT ENTRAINMENT RELATIONS 16-10RESISTANCE RELATIONS SEPARATION OF FORM DRAG 16-11SUMMARY 17-1 INTRODUCTION 17-2 RATING CURVE 17-3 FLOOD ROUTING 17-4 RESERVOIR ROUTING 17-5 CHANNEL ROUTING 17-6 KINEMATIC ROUTING 17-7 DI?USION ROUTING 17-8 MUSKINGUM-CUNGE ROUTING 17-9 AGGRADATION AND DEGRADATION OF CHANNEL BOTTOM GOVERNING EQUATIONS NUMERICAL SCHEME APPLICATIONS AGGRADATION DUE TO SEDIMENT OVERLOADING KNICKPOINT MIGRATION