hydraulic performance of culverts with safety grates · the texas highway department and messrs....

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1. Report No. 2. Government Accellion No.

FHWA/TX-82/55+30l-IF

4. Title ond Subtitle

HYDRAULIC PERFORMANCE OF CULVERTS WITH SAFETY GRATES

7. Author!.l

Larry W. Mays, Morey E. Walker, Michael S. Bennett, and Randal P. Arbuckle 9. Performing Orgonizotion Name ond Addre ..

Center for Transportation Research The University of Texas at Austin Austin, Texas 78712-1075

TECHNICAL REPORT STANDARD TITLE PAGE

3. Recipient'. Catalog No,

5. Report Dote

March 1983 6. Performing Organi lotion Code

8. Performing Organi lotion Report No.

Research Report 30l-IF

10. Work Unit No.

II. Contract or Grant No.

Research Study 3-5-80-301

r.-;;--;-----:---:----;::---;-:-;-:;-------------------l 13. Type of Report and Period Covered 12. Sponloring Agency Nome ond Addr,,"

Texas State Department of Highways and Public Final Transportation; Transportation Planning Division

P.O. Box 5051 14. Sponloring Agency Code

Austin, Texas 78763 IS. Supplementory Notes

Study conducted in cooperation with the U. S. Department of Transportation, Federal Highway Administration.

Research Study Title: ''Hydraulic Performance of Culverts with Safety Grates" 16. Abstract

The purpose of this research was to establish through an experi~ental study, the hydraulic characteristics of culvert end treatments (safety grates) on both box and pipe culverts. A significant amount of work has been performed in the past to establish the hydraulic characteristics of culverts, but there has been very little effort to study the hydraulics of culverts with grates. A 1:4 scale model was built to simulate flow conditions in a 5 X 8-ft box culvert. Investigators also tested a 1:4 scale model Simulating flow in a 60-in. helical corrugated metal pipe culvert. The slopes of the culverts, the flowrates and the elevations of the tailwater were varied to simulate the various types of flow conditions which can exist in a highway culvert. The box culvert was tested with no safety grates, pipe safety grates and bar safety grates. The pipe culvert was tested with no safety grates and pipe safety grates. A regression analysis of the experimental data was performed so as to relate (1) for outlet control, the various hydraulic parameters to the entrance head loss coefficient, and (2) for inlet control, the headwater depth to the discharge.

17. Key Wordl 18. Diltrlbution Stotement

culverts, box, pipe, safety grates, hydraulic, model, regression

! analysiS

No restrictions. This document is available to the public through the National Technical Information Service, Springfield, Virginia 22161.

19. Securi ty Clolli!. (of thi. report) 20. Security Clo .. lf. (of thi I poge) 21. No. of Pogel 22. Price

Unclassified Unclassified 342

Form DOT F 1700.7 (8-611)

..

HYDRAULIC PERFORMANCE OF CULVERTS WITH SAFETY GRATES

by

Larry W. Mays Morey E. Walker

Michael S. Bennett Randal P. Arbuckle

Research Report Number 301-lF

Hydraulic Performance of Culverts with Safety Grates

Research Project 3-5-80-301

conducted for

Texas State Department of Highways and Public Transportation

in cooperation with the U. S. Department of Transportation

Federal Highway Administration

by the

CENTER FOR TRANSPORTATION RESEARCH

BUREAU OF ENG INEERING RESEARCH

THE UNIVERSITY OF TEXAS AT AUSTIN

March 1983

The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.

There was no invention or discovery conceived or first actually reduced to practice in the course of or under this contract, including any art, method, process, machine, manufacture, design or composition of matter, or any new and useful improvement thereof, or any variety of plant which is or may be patentable under the patent laws of the United States of America or any foreign country.

ii

t

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PREFACE

The research reported herein is a study of the performance of culverts with

and without safety grate end treatments. The experimental work was carried out on 1)

a 2-ft x 1.25-ft box culvert and 2) a l5-inch diameter helical corrugated metal pipe

culvert. Experiments were conducted to determine the effect of safety grate end

treatments on culvert hydraulics.

The study was initiated under an agreement between the State Department of

Highways and Public Transportation, the State of Texas, the Federal Highway

Administration and the Center for Highway Research of the University of Texas,

Austin. Special acknowledgment is made to Messrs. Dwight Reagan and Sam Fox of

the Texas Highway Department and Messrs. Sterling Jones and Dan O'Conner of the

Federal Highway Administration for their valuable suggestions and comments during

the investigation.

Special thanks are also due to the Armco Metal Pipe Corp. for providing the

15-in diameter helical corrugated metal pipe used in this study. The authors also wish

to thank Messrs. Red Worley, J. Pritchard, Delbert Stark, Michael Pepe and J. Paul

Hendrix for their assistance in construction of the models and the collection of the

data. The assistance of Messrs. Nisai Wanakule and Yeou Koung Tung in carrying out

the statistical analysis, was highly appreciated. Finally the authors wish to thank Ms.

Nickla Tayarani for typing the manuscript, and the administrative staff at the Center

for Research in Water Resources for their efforts and support towards completing this

project.

iii

ABSTRACT

The purpose of this research was to establish through an experimental study,

the hydraulic characteristics of culvert end treatments (safety grates) on both box and

pipe culverts. A significant amount of work has been performed .in the past to

establish the hydraulic characteristics of culverts, but there has been very little effort

to study the hydraulics of culverts with grates. A 1:4 scale model was built to

simulate flow conditions in a 5 x 8-ft box culvert. Investigators also tested a 1:4 scale

model simulating flow in a 60-in helical corrugated metal pipe culvert. The slopes of

the culverts, the flow rates and the elevations of the tailwater were varied to simulate

the various types of flow conditions which can exist in a highway culvert. The box

culvert was tested with no safety grates, pipe safety grates and bar safety grates. The

pipe culvert was tested with no safety grates and pipe safety grates. A regression

analysis of the experimental data was performed so as to relate (l) for outlet control,

the various hydraulic parameters to the entrance headloss coefficient, and (2) for inlet

control, the headwater depth to the discharge.

v

T ABLE OF CONTENTS

page

PREFACE iii

ABSTRACT v

LIST OF TABLES xi

LIST OF FIGURES xiii

CHAPTER 1 INTRODUCTION

1.1 Statement Of Problem 1

1.2 Safety Gra te Design 2

1.3 Review Of Previous Studies 6

1.4 Study Objectives 10

1.5 Review Of Culvert Hydraulics For Design 12

1. 5.1 Inlet Control 15

1.5.2 Outlet Control 16

1.6 Flow Regimes 18

1.6.1 Outlet Regimes 18

1.6.2 Inlet Control Regimes 23

CHAPTER 2 EXPERIMENTAL CONSIDERATIONS

2.1 Energy Equation 25

2.2 Hydraulic Similitude 28

2.3 Labora tory F acili ties 29

2.4 Experimental Setup For Box Culvert Tests 32

2.5 Experimental Setup For Pipe Culvert Tests 37

2.6 Instrumentation 37

vii

T ABLE OF CONTENTS (continued)

page

2.7 Model Safety Grates 42

2.8 Measurements For Entrance Headloss 46

2.9 Data Reduction 51

2.10 Summary Of Box Culvert Tests 53

2.10.1 Safety Grate Tests 53

2.10.2 Clogging Tests 55

2.11 Summary Of Pipe Culvert Tests 55

CHAPTER 3 BOX CUL VER T RESULTS

3.1 Entrance Headloss Coefficient With and Without Safety Grates 59

3.2 Headwater-Discharge Relationships 61

3.3 Entrance Headloss Coefficient-Headwater Relationship 63

3.4 Entrance Headloss Coefficient-Discharge Relationship 66

3.5 Headwater-Tailwater Relationships 67

3.6 Regression Equations Considering Regimes 68

3.6.1 Development Of Regression Equations 68

3.6.2 Regression Equations For C e 68

3.7 Regression Equations For Submerged Conditions 70

3.8 Regression Equations For Unsumberged Conditions 74

3.9 Regression Equations For Submerged and Unsubmerged Combined 81

viii

T ABLE OF CONTENTS (continued)

page

CHAPTER 4 CLOGGING TESTS - BOX CULVERT

4.1 Test Procedure For Clogging 95

4.2 Relationship Of Headwater-Percent Clogging 95

4.3 Relationship Of Entrance Headloss Coefficient -Percent Clogging 99

CHAPTER 5 PIPE CUL VER T RESUL TS

5.1 Entrance Headloss Coefficient With and Without Safety Grates 104

5.2 Headwater-Discharge Relationship 104

5.3 Entrance Headloss Coefficient - Headwater Relationship 105

5.4 Entrance Headloss Coefficient - Discharge Relationship 105

5.5 Headwater-Tailwater Relationships 107

5.6 Regression Equations For Submerged Conditions 107

5.7 Regression Equations For Submerged and Un submerged Combined 116

CHAPTER 6 SUMMARY AND CONCLUSIONS

6.1 Conclusions For Box Culvert Model 125

6.1.1 Pipe Safety Grates 125

6.1.2 Bar Safety Grates 127

6.1.3 Summary of Regression Equations for Design 129

6.2 Conclusions For Pipe Culvert Model 131

6.3 Final Discussion 134

LIST OF REFERENCES 135

ix

APPENDICES

A.

B.

C.

D.

E.

F.

G.

TABLE OF CONTENTS (continued)

User's Manual and Fortran Listing For Computer Program Culvert

Graphical Results For Box Culverts

Summary Of Regression Results Box Culvert

Clogging Test Results For Box Culverts

Graphical Results For Pipe Culverts

Data From Box Culvert Experiments

Data From Pipe Culvert Experiments

x

page

139

155

205

217

255

281

303

Table

1.1

1.2

2.1

2.2

2.3

3.1

3.2

LIST OF TABLES

TITLE

Classification of Culvert Hydraulic Controls

Entrance Loss Coefficients

Summary of Box Culvert Tests

Summary of Clogging Tests for Box Culvert

Summary of Pipe Culvert Tests

Regression Equations for Comparing C e

(With and Without Pipe Safety Grates)

Regression Equations for Comparing C e (With and Without Bar Safety Grates)

3.3 Headwater Discharge Relationships for Inlet Control

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

3.12

a.

b.

Pipe Safety Grates

Bar Safety Grates

Regression Coefficient (Pipe Safety Grates)

Regression Coefficients (No Grates'

Regression Coefficients (Bar Safety Grates)

Regression Equations for Ce (No Grates)

Regression Equations for C (Pipe Safety Grates) e Regression Equations for C (Bar Safety Grates) e Summary of Regression Results for Submerged Conditions

Summary of Regression Results for Unsubmerged Conditions

Summary of Regression Results for Submerged and Unsubmerged Conditions Combined

xi

page

14

19

54

56

57

62

62

64

64

69

69

69

71

71

72

73

82

86

LIST OF TABLES (continued)

5.1 Headwater-Discharge Relationships for Inlet Control

a. b.

No Grates Grates Installed

page

106 106

5.2 Regression Equations for Pipe Culvert Equations 108

5.3 Regression Results for Submerged Conditions, No Grates 109

5.4 Regression Results For Submerged Conditions, Grates Installed 115

5.5 Regression Results for Submerged And Unsuhmerged Conditions Combined, No Grates 117

5.6 Regression Results For Submerged And Unsubmerged Conditions Combined, Grates Installed 117

xii

LIST OF FIGURES

page

Figure TITLE

1.l Pipe Safety Grate, Prototype 3

1.2 Bar Safety Grate, Prototype 4

1.3 Pipe Grate For Pipe Culvert, Prototype 5

1.4 Head-Discharge Relationship 9

1.5 Definition Sketch (from HEC 5) 17

1.6 Flow Regimes (Outlet Control) 20

1.7 Flow Regimes (Inlet Control) 21

2.1 Energy And Hydraulic Gradelines 26

2.2 Schematic Of Hydraulics Laboratory 30

2.3 Overview Of Test Facilities 31

2.4 Experimental Set-up 33

2.5 Outlet Channel 34

2.f1 Schematics Of Experimental Set-up 35

2.7 Box Culvert 36

2.8 Headwall Design And Dimensions 38

2.9 Pipe Culvert Model - Side And Plan Views 39

2.10 Pipe Culvert 40

2.11 Pipe Culvert Headwall Dimensions 41

2.12 Manometers 43

2.13 Stagnation Tubes For Pipe Culvert 44

2.14 Model Safety Grates For Box Culvert 45

2.15 Safety Grates 47

2.16 Pipe Model Safety Grate 48

2.17 Pipe Grates At Inlet 49

2.18 Pipe Grates At Outlet 50

xiii

3.1

3.2

3.3

3.4

3.5

3J;

3.7

3.8

3.9

3.10

3.11

3.12

3.13

3.14

3.15

LIST OF FIGURES (continued)

Entrance Headloss Coefficient For Submerged Conditions, No Grates (Eq. 3.4)

Entrance Headloss Coefficient For Submerged Conditions, Pipe Grates (Eq. 3.5)

Entrance Headloss Coefficient For Submerged Conditions, Bar Grates (Eq. 3.6)

Entrance Headloss Coefficient For Submerged Conditions, No Grates (Eq. 3.7)

Entrance Headloss Coefficient For Submerged Conditions, Pipe Grates (Eo. 3.8)

Entrance Headloss Coefficient For Submerged Conditions, Bar G ra tes (Eq. 3.9)

Entrance Headloss Coefficient For Unsubmerged Conditions, No Grates (Eq. 3.10)

Entrance Headloss Coefficient For Unsubmerged Conditions, Pipe Grates (Eq. 3.11)

Entrance Headloss Coefficient For Unsubmerged Conditions, Bar Grates (Eq. 3. 12)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, No Grates (Eq. 1.13)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, Pipe Grates (Eq. 3.14)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, Bar Grates (Eq. 3.15)

Entrance Headloss Coefficient, ~l 5 = 1.0, BD •

For The Outlet Control ConditlOns, No Grates (Eqs. 3.4, 3.10, 3.13)

Entrance Headloss Coefficient, ~l -5 = 1.0, BD •

For The Outlet Control Condi tlOns, No Grates (Eqs. 3.4, 3.10, 3.13)

Entrance Headloss Coefficient, 0] -5 = 1.0, BD •

For The Outlet Control ConditIons, Bar G rates (Eqs. 3.6, 3.12, 3.15)

xiv

page

75

76

77

78

79

80

83

84

85

88

89

90

91

92

93

3.16

4.1

4.2

4.3

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

5.10

5.11

LIST OF FIGURES (continued)

Entrance Headloss Coefficient, -°1 -5 = 1.0, BD •

For The Outlet Control ConditIons, Bar Grates (Eqs. 3.6, 3. 12, 3.15)

Clogging From Bottom To Top, 15% and 30%



Entrance Headloss Coefficient For Submerged Conditions, No Gra tes (Eq. 5.4)

Entrance Headloss Coefficient For Submerged Conditions, Grates (Eq. 5.5) .

Entrance Headloss Coefficient For Submerged Conditions, Grates And No Grates (Eqs. 5.5, 5.4)

Entrance Headloss Coefficient For Submerged Conditions, Grates and No Grates (Eqs. 5.7, 5.6)

Entrance Headloss Coefficient For Submerged Conditions, Grates And No Grates (Eqs. 5.9, 5.8)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, No Grates (Eq.5.10)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, . Grates (Eq. 5.11)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, Grates and No Grates (Eqs. 5.11, 5.10)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, Grates And No Grates (Eqs. 5.13, 5.12)

Entrance Headloss Coefficient For Submerged And Un submerged Conditions Combined, Grates And No Grates (Eqs. 5.15, 5.14)

Entrance Headloss Coefficient For Submerged And Unsubmerged Conditions Combined, No Grates, (Eqs. 5.12, 5.14,5.16)

xv

page

94

96

97

98

111

112

113

114

115

118

119

120

121

123

124

Figure

A.I

A.2

APPENOIX A

Title

User's Manual For Computer Program "CUL VER T"

Fortran Listing For Computer Program "CULVERT"

xvii

page

139

145

APPENDIX B

page

Figure Title

B.l Comparison of Entrance Headloss Coefficients With And Without Safety Grates, Slope =.0008 155

B.2 Comparison of Entrance Headloss Coefficients With And Without Safety Grates, Slope =.0013 156



B._5 Comparison of Entrance Headloss Coefficients With And Without Safety Grates, Slope =.0128 159




B.9 Headwater vs. Discharge With And Without Pipe Grates, Slope = .0008 163

B.lO Headwater vs. Discharge With And Without Pipe Grates, Slope = .0013 164

B.ll Headwater vs. Discharge With And Without Pipe Grates, Slope = .0062 165

B.12 Headwater vs. Discharge With And Without Pi pe Gra tes, Slope = .0108 166

B.13 Headwater vs. Discharge With And Without Pipe Grates, Slope = .0128 167

B.14 Headwater vs. Discharge With And Without Bar Grates, Slope = .0008 168

B.15 Headwater vs. Discharge With And Without Bar Grates, Slope = .0063 169

B.16 Headwater vs. Discharge With and Wtihout Bar Grates, Slope = .0063 170

xix

APPENDIX B (continued)

page

B.17 Entrance Headloss Coefficient vs. Headwater For Pipe Safety Grates, Slope = .0003 171





B.22 Entrance Headloss Coefficient vs Headwater For Bar Safety Grates, Slope = .0008 176


B.24 Entrance Headloss Coefficient vs. Headwater For Pipe Safety Grates, Slope = .0 1 08 178

B.25 Entrance Headloss Coefficient vs. Discharge For Pipe Safety Grates, Slope = .0008 179



B.28 Entrance Headloss Coefficient vs. Discharge For Pipe Safety Grates, Slope = .0 1 08 182


B.30 Entrance Headloss Coefficient vs. Discharge For Bar Safety Grates, Slope = .0008 184



B.33 Headwater vs. Tailwater For Pipe Safety Grates, Slope = .0008 187

B.34 Headwater vs. Tailwater For Bar Safety Grates, Slope = .0008 188

B.35 Headwater vs. Tailwater For Both Pipe Safety Grates And Bar Safety Grates, Discharge = 8.1 cfs, Slope = .0008 189

xx

APPENDIX B <Continued}

page

B.36 Headwater vs. Tailwater, For Pipe Safety Grates, Slope = .0063 190

B.3? Headwater vs. Tailwater, For Bar Safety Grates, Slope = .0063 191

B.38 Headwater vs. Tailwater, For No Safety Grates, Pipe Safety Grates, And Bar Safety Grates, Discharge = 6.14 cfs, Slope = .0063 192

B.39 Headwater vs. Tailwater, For No Safety Grates, Pipe Safety Grates And Bar Safety Grates, Discharge = 8.12 cfs, Slope = .0063 193

B.40 Headwater vs. Tailwater, For No Safety Grates, Pipe Safety Grates And Bar Safety Grates, Discharge 9.66 cfs, Slope = .0063 194

B.41 Headwater vs. Tailwater, For No Safety Grates, Pipe Safety Grates And Bar Safety Grates, Discharge = 11.81 cfs, Slope = .0063 195

B.42 Headwater vs. Tailwater For Pipe Safety Grates, Slope = .0108 196

B.43 Headwater vs. Tailwater For Bar Safety Grates, Slope = .0108 197

B.44 Headwater vs. Tailwater For No Safety Grates, Pipe Safety Grates And Bar Safety Grates, Discharge 6.14 cfs, Slope = .0108 198

B.45 Headwater vs. Tailwater For No Safety Grates, Pipe Safety Grates And Bar Safety Grates, f)ischarge = 8.12 cfs, Slope = .0108 199

B.46 Headwater vs. Tailwater For No Safety Grates, Pipe Safety Grates And Bar Safety Grates, Discharge = 9.66 cfs, Slope = .0108 200

B.4? Headwater vs. Tailwater For No Safety Grates, Pipe Safety Grates And Bar Safety Grates, Discharge = 11.81 cfs. Slope = .0108 201

xxi

Table

C.2

C.3

C.4

APPENDIX C

Title

Box Culvert Results of Regression Analysis: No Grates

Box Culvert Results of Regression Analysis: Pipe Grates

Box Culvert Results of Regression Analysis: Bar Grates

xxiii

page

211

212

213

APPENDIX D

Figure Title Page

D.l Headwater vs. Percentage Clogging (S = .0008, Q = 9 cfs) 217 0

D.2 Headwater vs. Percentage Clogging (S = .0008, 0 = 9.6 cfs) 218 0

D.3 Headwater vs. Percentage Clogging (S = .0008, Q = 10 cfs) 219 0

D.4 Headwater vs. Percentage Clogging (So = .0008, 0 = 11.2 cfs) 220


D.6 Headwater vs. Percentage Clogging (So = .0063, Q = 9.11 cfs) 222

D.7 Headwater vs. Percentage Clogging (So = .0063, Q = 10.04 cfs) 223

D.8 Headwater vs. Percentage Clogging (So = .0063, 0 = 11.07 cfs) 224

D.9 Headwater vs. Percentage Clogging (S = .0008, Q = 9 cfs) 0

(So = .0128, 0 = 9cfs) 225

D.lO Headwater vs. Percentage Clogging (S = .0063, Q = 9.11 cfs) 0 (S = .0128, 0 = 9.02 cfs) 226 0

D.ll Headwater vs. Percentage Clogging (S = .0008, S = .0063) o 0 227 (S =.0128,O=10cfs) 0

D.12 Headwater vs. Percentage Clogging (So = .0063,0 = 8.12 cfs) 228

D.13 Headwater vs. Percentage Clogging (S = .0063, Q = 9.04 cfs) 0

229


D.L5 Headwater vs. Percentage Clogging (S = .0063, Q = 1 L05 cfs) 0

231

D.16 Headwater vs. Percentage Clogging (So = .0063, 0 = 11. q 1 cfs) 232

D.17 Headwater vs. Percentage Clogging Pipe Safety Grates (So = .0063, Q = 9.11 cfs), Bar Safety Grates (So = .0063, 0 = 9.09 cfs) 233

D.18 Headwater vs. Percentage Clogging, Pipe Safety Grates (S = .0062, Q = 10.04 cfs), Bar Safety Grates (S~ = .0062,0 = 10.l1 cfs) 234

D.19 Headwater vs. Percentage Clogging, Pipe Safety Grates (S = .0063, Q = 11.1 cfs), Bar Safety Grates

0 235 (So = .0063, Q = 11.1 cfs)

D.20 Entrance Headloss Coefficient vs. Percentage Clogging (So = .0008, Q = 9.02 cfs) 236

D.2l Entrance Headloss Coefficient vs. Percentage Clogging (So = .0008, Q = 9.62) 237

xxv

D.22

0.23

0.24

D.25

0.26

D.27

0.28

0.29

0.30

D.31

D.32

D.33

D.34

0.35

APPENDIX 0 (contInued)

Entrance Headloss Coefficient vs. Percentage Clogging (So = .0008, Q = 10.7 cfs)

Entrance Headloss Coefficient vs. Percentage Clogging (So = .0008, Q = 11.2 cfs)

Entrance Headloss Coefficient vs. Percentage Clogging (So = .0063, Q = 8.04, 0 = 9.1, 0 = 10.04, Q = 11.07)

Entrance Headloss Coefficient vs. Percentage Clogging (So = .0008, So = .0128, 0 = 9.02 cfs)

Entrance Headloss Coefficient vs. Percentage Clogging (5 = .0063, Q = 9.11 cfs), (5 = .0128, 0 = 9.02 cfs) o . 0

Entrance Head10ss Coefficient vs. Percentage Clogging (So = .0008, Q = 9.62 cfs), (So = .0063, 0 = .0063, 0 = 10.04 cfs)

(So = .0128, Q = 100 cfs)

Entrance Headloss Coefficient vs. Percentage Clogging (So = .0063, 0 = 10.04), (So = .0128, 0 = 10.0)

Entrance Headloss Coefficient vs. Placement of Clog,ging, So = .0128, 15% clogging

Entrance Headloss Coefficient vs. Placement of Clogging, 5 = .0128, 30% clogging

o Entrance Head10ss Coefficient vs. Placement of Clogging,

50 = .0128, 45% clogging

Entrance Headloss C:oefficient vs. Percentage Clogging. (5 = .0063, 0 = 9.09 cfs, Q = 10.11 cfs, 0 = 11.05 cfs)

o Entrance Headloss Coefficient vs. Percentage Clogging,

Pipe Safety Grates (So = .0063, 0 = 9.11 cfs), Bar Safety Grates (5 = .0063, 0, = 9.09 cfs)


Pipe Safety Grates (So = .0063, Q = 10.04 cfs), Bar Safety Grates (5 = .0063, 0 = 10.11 cfs)


Pipe Safety Grates (So = .0063, 0 = 11.07 cfs), Bar Safety Grates '5 = .0063,0 = 11.05 cfs) o

xxvi

page

238

239

240

241

242

243

244

245

246

247

248

249

250

251

APPENDIX E

Figure Title Page

E.1 Comparison of Entrance Headloss Coefficients With And Without Safety Grates, Slope = 0.0007 255

E.2 Comparison of Entrance Headloss Coefficients With And Without Safety Grates, Slope = 0.0008 256

E.3 Headwater vs. Discharge With And Without Grates, Slope = 0.0007 257

E.it Headwater vs. Discharge With And Without Grates, Slope = 0.008 258

E.5 Headwater vs. Discharge With And Without Grates, Slope = 0.050 259

E.6 Entrance Headloss Coefficient vs. Headwater, Types 1, 2, itA And itB, With And Without Grates, Slope = 0.008 260

E.7 Entrance Headloss Coefficient vs. Headwater, Tvpe I, With And Without Grates, Slope = 0.008 261

E.8 Entrance Headloss Coefficient vs. Headwater, Type ?, With And Without Grates, Slope = 0.008 262

E.9 Entrance Headloss Coefficient vs. Headwater, Type itA, With And Without Grates, Slope = 0.008 263

E.IO Entrance Headloss Coefficient vs. Headwater, Type itB, With And Without Grates, Slope = 0.008 264

E.11 Entrance Headloss Coefficient vs. Headwater, Types itA And 4B, With And Without Grates Slope = 0.0007 265

E.12 Entrance Headloss Coefficient vs. Headwater ,Type itA, With And Without Grates, Slope = 0.0007 266

E.13 Entrance Headloss Coefficient vs. Headwater, Type itB, With And Without Grates, Slope = 0.0007 267

E.lit Entrance Headloss Coefficient vs. Discharge, Types 1, 2, itA And itB, With And Without Grates, Slope = 0.008 268

E.15 Entrance Headloss Coefficient vs. Discharge, Type 1, With And Without Grates, Slope = 0.008 269

xxvii

APPENDIX E (continUl"d)

page

E.16 Entrance Headloss Coefficient vs. [)ischarge, Type 2, With And Without Grates, Slope = 0.008 270

E.17 Entrance Headloss Coefficient vs. Discharge, Type 4A, With And Without Grates, Slope:: 0.008 271

E.18 Entrance Headloss Coefficient vs. Discharge, Type 4B, With And Without Grates, Slope = 0.008 272

E. 19 Entrance Headloss Coefficient vs. Discharge, Types 4A And 4B, With And Without Grates, Slope = 0.0007 273

E.20 Headwater vs. Tailwater, Grates And No Grates, Slope = 0.0007, Q = 5.6 cfs 274

E.21 Headwater vs. Tailwater, Grates And No Grates, Slope = 0.008, Q = 3.6 through 3.8 cfs 275

E.22 Headwater vs. Tailwater, Grates And No Grates, Slope = 0.008, Q 4.5 cfs 276

E.23 Headwater vs. Tailwater, Grates And No Grates, Slope:: 0.008, Q = 5.6 cfs 277

xxviii

APPENDIX F

Table Title Page

F.I Data, Type l, No Grates 282

F.2 Data, Type 2, Pipe Grates 283

F.3 Data, Type I, Bar Grates 284

F.4 Data, Type 2, No Grates 285

F.5 Data, Type 2, Pipe Grates 286

F.6 Data, Type 2, Bar Grates 287

F.7 Data, Type 3A, No Grates 288

F.8 Data, Type 3A, Pipe Grates 289

F.9 Data, Type 3A, Bar Grates 290

F.IO Data, Type 4A, No Grates 291

F.II Data, Type 4A, Pipe Grates 293

F.12 Data, Type 4A, Bar Grates 296

F.13 Data, Type 4B, No Grates 298

F.14 Data, Type 4B, Pipe Grates 299

F.15 Data, Type 4B, Bar Grates 300

xxix

APPENDIX G

Table Title Page

G.I Data, For Pipe Culvert, Outlet Control, No Grates 304

G.2 Data, For Pipe Culvert, Outlet Control, Pipe Grates 306

G.3 Data, For Pipe Culvert, Inlet Control, No Grates 308

G.4 Data, For Pipe Culvert, Inlet Control, Pipe Grates 309

xxxi

CHAPTER I INTRODUCTION

1.1 Statement of Problem

Culverts are designed to convey flow of stream water both along and

across highway right of ways. If not properly designed, culverts could become

dangerous obstructions to vehicles accidentally driven off a highway. To

minimize the hazard, culverts could be designed so that the inlet and outlet

structures are outside the highway right of way. Another safety feature would

be the installation of guard rails. However, in some instances, the least costly

and most practical safety design could be to install safety grates at the culvert

ends (inlet and outlet structures).

Hydraulic engineers are concerned about the effect that safety

grates have on the hydraulic performance of the culvert. Safety grates can

cause an increase in entrance head losses affecting the culvert hydraulics and

susceptibility to clogging. During flooding conditions, a large amount of debris

(tree branches, trash, etc.) is usually present in the flow. If the debris clogs the

entrance, then the culvert could become hydraulically ineffective and the

possibility of overtopping the hie;hway may exist. This can result in flood

damages to adjacent property, damage to the highway embankment and struc

ture, and increase traffic delays.

The purpose of this experimental study was to determine the effect

of safety grates on the hydraulic performance of both box culverts and

corrugated metal pipe culverts. Specifically studied were the changes in the

entrance head losses for various flow regimes and the effect of clogging on the

1

culvert performance. The results are presented for use in thE" future design of

highway c:ulverts.

1.2 Safety Grate Design

The design of the safety grates is based on two constraints. First,

the grates must have enough structural integrity to support an automobile.

Second, the safety grates should have a minimum amount of materials for least

possible interference of the natural flow. The Texas Transportation Institute

(TTl) at Texas A & M University conducted a series of tests to determine a

safety grate design considering automobile safety. Essentially, automobiles were

driven at varying speeds over safety grates constructed of steel pipes. The

result of the TTl study was a safety grate design constructed of 3-in diameter

pipes placed on 30-in centers. These grates are referred to as "pipe safety

grates" in this study and are illustrated in Fig. 1.1.

These grates are to be installed on highway embankments such that

there are no protrusions above the highway embankments. For a complete

discussion of the TTl study, refer to Texas Highway and Transportation Project

Study No. 2-5-79-280 "Safe End Treatment for Roacside CuI verts."

The experimental study descrihed herein performed hydraulic model

studies of the TTl design using a 1:4 scale model of an 8-ft x 5-ft box culvert.

Also a bar type safety grate was tested using the 1:4 scale box cuI vert.

Prototype dimensions of the bar grates are l/2-in x 2-in placed on 5-in centers

(Figure 1.2). Clogging tests using the box culvert were also performed. Safety

grates for a pipe culvert (Figure 1.3) which had prototype dimensions of 3-in

pipes placed on 24-in centers were also tested. The safety grates are discussed

in detail in Section 2.7. Each of the grates are placed parallel with the highway

embankments so that there are no vertical protrusions above the embankments.

2

k----- 8 t

3" o.D.""!

~ 30" ~

PIPE SAFETY GRATE

Figure 1.1 Pipe Safety Grate, Prototype

3

I ~

2' , x 8" Bar ~

1\

I t

I

I I

1\ " 1 ~

II I

~ ~

J

, J ~ I \

-+ir-S in.

BAR SAFETY GRATE

Figure 1.2 Bar Safety Grate, Prototype

4

21 ' 24"

~~====:::;~l. 25"

~

Figure 1.3 Pipe Grate for Pipe Culvert, Prototype

5

A 4: 1 slope of a highway embankment was used in all the experiments presented in

this report. Results generally can be safely extrapolaterl to other embankment

slopes.

1.3 Review of Previous Studies

Numerous investigators have researched the hydraulic controls and

flow types of culverts. The primary controls of culverts have long been

identified. However, the hydraulic performance of a new culvert design cannot

be theoretically modeled with accuracy, and must be experimentally determined.

A review of previous experiments contributes an understanding of culvert

hydraulic controls and experimental techniques.

Mavis (1942) conducted one of the most comprehensive studies

performed on culvert hydraulics. The culverts tested were 3-in, 4-in, 6-in, and

l2-in diameter pipes. These pipes represented "condui ts of intermediate lengths"

which most field culverts are classified. Short length culverts have been defined

as having negligible frictional resistance, and the discharge depends upon the

geometry of the inlet and on headwater depth r."~avis, 1942). Hydraulically long

culverts have headlosses which are a function of conduit geometry, frictional

forces, flow rate, and Reynold's Number. Mavis determined that intermediate

length culverts operate under five sets of conditions which are:

1. Part-full free outfall

2. Part-full with outfall partially submerged

3. Full with outfall completely submerged

4. Full with outfall partially submerged

5. Full with free outfall.

The study results were charts and nomographs that have been used in a

substantial number of design manuals.

6

Shoemaker and Clayton (1953) performed a series of model studies of

box culverts on steep grades. Objectives of this study were to determine culvert

hydraulics and to improve effectiveness of the Oregon State Highway Standard

inlet. Three inlet types were tested: (l) an inlet with no flare or taper; (2) an

inlet with tapered sidesf and (3) an inlet designed to operate under entrance

control. The investigators observed that a submerged standard inlet operates as

a sluice gate while a tapered inlet allows flow full with no sluice gate

contraction. The increase in culvert capacity due to the tapered inlet resulted

from an increase in flow area by elimination of the sluice gate contraction.

Schiller (1955) conducted a series of tests on circular pipe culvert

inlets. The purpose of the study was to determine efficient inlet designs based

on hydraulic controls. Two inlet designs were compared; (1) a square-edged flush

inlets with flared, straight, and parallel wingwalls; and (2) a mitered sharp-edged

inlet. The square-edged flush inlet performed more efficiently than the mitered,

sharp-edged inlet.

French (1955) presented a discussion of Schiller's works. He noted

that the upstream approach channel characteristics greatly influenced the

efficiency of the inlet. The greater the turbulence in the approach channel, the

larger the amount of separation occurring at the inlet boundary surface. The

ability of the upstream approach channel to control the full capacity was

experimentally shown for culverts placed on steep slopes. French also noted that

the effects of the approach channel would be smaller on larger scale models.

French (1957) also studied the effect of approach channel character

istics on pipe culvert operations. He concluded that general reproducibility of

experimental results to field conditions involves considerable awareness of

approach flow conditions.

7

Bossey (I (1) presented an unpublished paper outlining the hydraulics

of conventional highway culverts. He observerl that two primary factors

controlled culvert capacity - (1) the cross-sectional area of the barrel and (2) the

headwater depth. Secondary factors were: (I) shape of barrel; (2) inlet

geometry; (3) resistance characteristics; (4) length; and (5) slope. The secondary

factors generated an increase in headwater depth as flow contracts into the

culvert.

French (I 966} also conducted an experimental study to determine the

hydraulics of tapered box culvert inlets. Since the box culvert was placed on a

steep slope, the experimental work involved only inlet control conditions. Again,

the hydraulic performance of a highway box cuI vert on super-critical slopes

could be substantially increased by tapering the inlet. Also, the hydraulic

efficiency could be increased by not allowing subatmospheric pressure regions to

form.

Blaisdell (I966) further categorized culvert flow into four regimes:

(I) weir control; (2) orifice control; (3) slug and mixture control; and (4) pipe

control. Weir control was defined for either an unsubmerged entrance geometry

control on steep slopes or barrel geometry control on mild slopes. Orifice

control represents submerged entrance geometry controL Slug and mixture

control describes barrel geometry controlling a flow of water and entrained air.

Pipe control was determined for a full flowing culvert controlled by barrel

characteristics and/or tailwater depth. A graphical representation of the

different flow types can be expressed in a headwater versus discharge plot

(Figure 1.4).

Numerous design manuals exist for step by step selection of a

culvert. Some of the most widely used manuals are listed in the references. In

8

7

6

5

4

3

2

ORIFICE CONTROL

CULVERT FILLS

~-PIPE

CONTROL

~-AREA OF

'" SLUG AND MIXTURE

EFFECT OF VORTICES

CONTROL CONTROL

o ~----~~----~~----~------~------~------~ o 2 4 6 8 10 12

DISCHARGE FACTOR D~:5

Figure 1.4 Head-Discharge Relationship {after Blaisdell (1966)}

9

addition, computer programs have been written to aid in the culvert selection

process. The State Department of Highways and Public Transportation in Texas

uses the Texas Hydraulics System (THYSYS) in culvert design. THYSYS uses

inputted values of the design discharge, the estimated tailwater, the cuI vert

dimension parameters and slope, and determines the appropriate flow

regime, headwater depth, and outlet velocity. THYSYS generally distinguishes

between steep and mild slope regimes and specifically determines other para

meters.

1.4 Study Objectives

As illustrated by the previous review, numerous experimental studies

have been performed on the hydraulics of culverts, \:)ut none have been reported

in the literature on culverts with safety grates. Several objectives included:

1. Perfor m studies using a box cuI vert model to make a direct

comparison of culvert performance l.with and without safety

grates. This included hydraulic tests varying the culvert slope,

discharge, headwater depth, and tail water depth. For each

variation of these parameters experimental r:la ta were collected

without grates, with pipe grates installed, and with bar grates

installed. The results of these tests are summarized in Chapter

3.

2. A second major objective was to determine the hydraulic

effects of various levels of clogging of the safety grates. The

problem of clogging is not addressed in current culvert design

as culverts are presently designed without regard to clogging.

Culverts without safety grates are usually large enough for

trash or debris to pass through. However, from informal field

10

observations, safety grates can retain a significant amount of

debris and can effectively clog the culvert. The effect of

clogging on the entrance headloss coefficient was determ.ined

using various percentages of clogging ranging from 15 to 90

percent. Since the amount of debris collected on a grate

cannot be predicted it would be difficult to develop guidelines

for future culvert design taking into the effect of clogging.

The results of the clogging tests are summarized in Chapter 4.

3. Perform studies using a corrugated metal pipe culvert to make

a direct comparison of culvert performance with grates install-

ed and without safety grates. This included hydraulic tests /

varying the culvert slope, dishcarge, headwater depth, and

tail water depth. For each variation of these parameters,

experimental data were collected with and without safety

grates installed. The results of these tests are summarized in

Chapter 5.

4. For inlet control conditions, headwater-discharge relationships

were developed. Regression equations were derived using the

box culvert results for the situations: (1) no grates; (2) pipe

grates installed; and (3) bar grates installed. Regression

equations were devised using the pipe culvert results for the

situations: (I) no grates; and (2) pipe grates installed.

The results for the box culvert are summarized in Section 3.2

and for the pipe culvert are summarized in Section 5.2.

5. The box culvert results for outlet control were used to derive

regression equations to define the entrance head loss coeffi-

11

cient as a function of the various hydraulic parameters. Sev

eral relationships were derived for each of the following

condi tions:

(a) Each flow regime separately

(b) Submer~ed condi tions of the inlet

(c) Unsubmerged conditions of the inlet

(d) Submerged and unsubmerged conditions combined.

Because either inlet or outlet control in general is considered

in design, the regression equations considering each flow regime

separately may not be of practical use. The results of the

above regression analysis are described in Chapter 3.

6. The pipe culvert results for outlet control were used to derive

regressions to define the entrance head loss coefficient as a

function of the various hydraulic parameters. Several relation

ships were derived for each of the following conditions:

(a) Submerged conditions of the inlet

(b) Submerged and unsubmerged comhined.

7. Another major objective was to put the regression results of the

entrance headloss coefficient (outlet controll for the box cul

vert and pipe culvert, with and without grates, in a graphical

form for easy use by the designer.

1.5 Review of Culvert Hydraulics for Design

Designing culverts involves many factors including estimating flood

peaks, hydraulic performance, structural adequacy, and costs. The design of

culverts, based on the interrelationship of numerous controlling factors is not an

exact scientific procedure. Some of the many factors which control flow

12

through culverts are: (I) discharge; (2) inlet and barrel geometries; 0) frictional

resistance; (4) headwater depth; (5) tailwater depth; and (6) slope. Generally,

only two or three primary factors determine the flow regime through a

particular culvert. For example, the size and shape of the inlet may determine

the capacity of a certain culvert. On the other hand, frictional resistance and

tailwater depth might control the flow in another case. However, the primary

factors are not always identifiable before a design is made. Iterative design

procedures identify the controlling factors for given design parameters.

According to Blaisdell (1966), thirty-eight factors influence the

hydraulic performance of a culvert (Table Ln. The primary controlling factors

can be divided into two main groups: (1) flow with inlet control (steep-slope

regime - S > S ); and (2) flow with outlet control (mUd slope regime - S < S ). 0- c - 0 c

The inlet control group determines the capacity of the culvert based on inlet

conditions, while the outlet control group determines the capacity based on the

barrel and outlet conditions. The outlet control group is a combination of the

outlet control and barrel control groups as defined by Blaisdell.

There have been many reported laboratory tests and field observa-

tions that show the two major types of culvert flow. For each type of control,

different factors and formulas are used to compute the hydraulic capacity of a

culvert. Under inlet control, the cross-section area of the culvert barrel, the

inlet geometry and the amount of headwater or ponding at the entrance are of

primary importance. Outlet control involves the additional consideration of the

elevation of the tailwater in the outlet channel and the slope, roughness and

length of the cuI vert barrel.

Hydraulic computations can be used to determine the probable type

of flow under which a culvert will operate for a given set of conditions. The

13

1.

II.

III.

Table 1.1 CLASSIFICATION OF CULVERT HYDRAULIC CONTROLS

Inlet A.

B.

Barrel A.

Unsubmerged 1. Weir

{after Blaisdell (1966)}

2. Surface profile Submerged

1. Orifice 2. Vortex 3. Full

Length 1. Short 2. Long

B. Slope

C.

Outlet A.

B.

1. Hild

2.

Flow 1. 2. 3.

Part 1. 2.

Full 1. 2.

a.

b.

Steep

Barrel i.

ii. Barrel

i. ii.

a. Barrel i.

ii. b. Barrel

i.

ii.

Part full

slope less than critical slope Part full, normal depth greater than critical depth Full, not applicable slope less than friction slope Part full, depth increases along barrel Full, barrel under pressure

slope steeper than critical slope Part full, normal depth less than critical depth Full, not applicable slope steeper than friction slope Part full, depth decreases along barrel (increases if the inlet causes the depth inside the inlet to be less than the normal depth) Full, barrel under suction

Slug and mixture Full

full Critical depth Taihvater

Free Submereccl

14

Federal Highway Administration (FHW A) in their Hydraulic Engineering Circular

(HEC) No. 5 provide charts for computing headwater depths for both inlet

control and outlet control and then use the higher value to indicate the type of

control and to determine the headwater depth.

1.5.1 Inlet Control

Inlet control means that the discharge capacity of a culvert is

controlled at the culvert entrance by the depth of headwater (HW) and the

entrance geometry, including the barrel shape and cross-sectional area, and the

type of inlet edge. For inlet control the roughness and length of the culvert

barrel and the outlet conditions (including depth of tailwated are not factors in

determining culvert capacity. An increase in barrel slope reduces headwater to

a small degree and any correction for slope can be neglected for conventional or

commonly used culverts flowing with inlet control.

In all culvert design, headwater or depth of ponding at the entrance

to a culvert is an important factor in culvert capacity. The headwater depth (or

headwater HW) is the vertical distance from the culvert invert at the entrance

to the energy line of the headwater pool (depth + velocity head). Because of the

low velocities in most entrance pools and the difficulty in determining the

velocity head for all flows, the water surface and the energy line at the entrance

are assumed to be coincident thus the headwater depths given by the inlet

control charts (in HEC 5) can be higher than may occur in some installations.

For the purposes of measuring headwater, the culvert invert at the entrance is

the low point in the culvert opening at the beginning of the full cross-section of

the culvert barrel.

15

1.5.2 Outlet Control

For outlet control, the conditions downstream of the entrance are the

controlling factors in the culvert hydraulic performance. Either or both the

frictional forces or the tailwater depth directly control the flow through the

culvert. The barrel friction predominates if critical depth occurs at the outlet.

Tailwater controls the flow if the tail water depth is large enough to effect the

headwater depth. Outlet control conditions usually exist in areas of low

topographical relief.

Culverts flowing with outlet control can flow with the culvert barrel

full or part full for part or all of the barrel length. If the entire cross section of

the barrel is filled with water for the total length of the barrel, the culvert is

said to be in full flow or flowing full. The procedures given in HEC 5 provide

methods for the accurate determination of headwater depth for the full flow

conditions. The method given in HEC 5 for the part full flow condition, gives a

solution for headwater depth that decreases in accuracy as the headwater

decreases.

The head, H, or energy required to pass a given quantity of water

through a culvert flowing in outlet control with the barrel flowing full through

out its length is made up of three major parts (Figure 1..5). This energy is

obtained from ponding of water at the entrance and is expressed as

H = H + H + Hf v e 0.1 )

where H is the velocity head, H is the entrance head loss and Hf is the friction v e

loss. A more usable form of the above equation is expressed as y2 y2

HW = d + -2- + C -2- + Hf - S L g ego (1.2)

where HW is headwater depth, d is depth of flow, Y is the mean flow velocity, Ce

is the entrance headloss coefficient, g is acceleration of gravity, Hf is frictional

16

f LSo

Figure 1.5 Definition Sketch (from H.E.C. 5)

17

losses expressed as Hf = Sf . L, Sf is the friction slope, So is the culvert slope,

and L is culvert length; the datum is the elevation of the culvert invert at the

exit.

The FHW A manual (HEC 5) and state highway design manuals specify

that the entrance loss, H depends upon the geometry of the inlet edge. This e

loss is expressed y2

He = Ce 2g

as a coefficient, C , times the barrel velocity head or e

The entrance loss coefficients C for various types of e

entrances when the flow is in outlet control are listed in Table 1.2 which is from

HEC 5.

1.6 Flow Regimes

The Federal Highway Administration (FHW A) and the State Depart-

ment of Highways and Public Transportation in Texas (DHT) distinguishes

between inlet and outlet control for design purposes. DHT (1970) also categor

izes flow into six different regimes (Figures 1.6 and 1.7) which will be used

throughout this report. Four of the flow regimes (t, 2, 4A, and 4B) are

considered outlet control (Fig. 1.6). The other two flow regimes (3A and 3B) are

considered inlet control (Fig. 1. 7).

1.6.1 Outlet Control R~gimes

Type 1 flow conditions (Fig. 1.6) occur when the culvert slope is less

than the critical slope (S < S ), the headwater is less than 1.2 times the culvert o c

height (HW < 1.2D), and the tail water depth is less than the critical depth

(TW < dcL The energy equation is written between the entrance and outlet as

HW = d c

y2 c +--

2g +

y2 c C -

e 2g

18

+ (I.3)

Table 1. 2 - EN'fRANCf: US:::; COKPFICII-:N'IS

Outlet Control, Full or Partly Full

Entro.nce head los~ He Ce

V2

2g

fYpe of Structure and Design of Entrance Coefficient Ce

Plpe, Concrete

ProJect1ng from flll, socket end (groove-end) • Projectlng from flll, sq. cut end •••••• Headvall or headvall and v1ngwnlls

Socket end of p1pe (groove-end) •• Square-edge • • • • • • • • • • • • • Rounded (radtus E 1/120) ••••••••

MItered to conform to fl11 elope ••• *End-Seetion confor.1ng to fill slope ••• • • • •

Beveled edge8, 33.70 or ~5° bevels •••• Side-or slope-tapered inlet • • • • • • • . .

PiP2. or Plpe-Arch. eorrug!ted Metal

0.2 0.5

0.2 0.5 0.2 0.7 0.5 0.2 0.2

ProJecting from fIll (no headwall) •••••••• 0.9 Headvall or headwall and vingvalls square-edge 0.5 M1 tered to conforlll to flll slope, paved or unpaved

slope . . . . . . . . • . • . . . . . . . 0.7 *End-Section conforming to flll slope •• • 0.5

Beveled edges, 33.~ or 450 bevels •••••• 0.2 Slde-or slope-tapered inlet • • • • • • • • • • 0.2

Box, Reinforced Concrete

lfeMW'8.1l parallel to embankment; (no vlngwllD) Square-edged on 3 edges ••••••••• Rounded on 3 edges to radius of 1/12 barrel

dimension, or beveled edges on 3 sides ••• WIngvalls at 300 to 750 to barrel

Square-edged at crown . • • • • • • • • • • • Crovn edge rounded to radius of 1/12 barrel

dimension, or beveled top edge •••• Wingvall at 100 to 250 to barrel

Square-edged at crown • • • • • • • Wlngvall!; IJ(1J'allel (extension of sldes)

Square-edged at crown • • • • SIde-or slope-tapered inlet • • • • • •

0.5

0.2

0.4

o.z

0.5

0.7 0.2

.Note: "End Section conforminl'~ to r111 slope," nnde of either met.al or concrete, are the sections commonly avallable from manufacturers. From limited hydraulIc tests they are equivalent 1n operation to a headvall in both ~ and outlet control. Some end sections, incorporating a elose~ taper in theIr design have ~ superior hydraulic performance.

19

HW < - 1.20 L t/W " l [j

s < S o c

~ d';"\... ci ;]

TYPE 1: Free Surface, Outlet Control

TW < d - c

t TW t

d <TW<D H\O; i 1. 2D c

~~---------------------------------.----TlI li

s < S o c

TYPE 2: Free Surface, Outlet Control

TW > 0 or > o+s L o HW ~ 1.20 z:-------;s t t

.. W TW

I \ il

TYPE 4A: Pressure Flow Throughout, Outlet Control

TW < 0 HW> 1.20 z: t

HW

1 [I:

TYPE 4B: Submerged Inlet, Outlet Control

Figure 1.6 Flow Regimes (Outlet Control)

20

s o

> S c

TYPE 3A: Free Inlet, Inlet Control

HW > 1. 2D

HW

1

TYPE 3A: Inlet Submerged, Inlet Control

"'-L ~ t HW

I L

;oJ s > S

0 c

TYPE 3B: Outlet Submerged, Inlet Control

TW

D < TW <

t TW

1

Figure 1.7 Flow Regimes (Inlet Control)

21

O+S L 0

where d is the critical depth, Y is the critical velocity, and Hf is the friction c c

loss. For Type 1 flow conditions, there is a transition from subcritical flow in

the culvert to super critical tail water flow. This situation requires the develop-

ment of an estimate for Sf" In the DHT solution to the energy equation, Sf is

estimated by assuming uniform flow at a constant depth of l.l·d . c

Type 2 Flow Regime

Type 2 flow conditions (Figure 1.6) occur when the entrance is

unsubmerged (HW'::' 1.2D), the slope is less than critical (So < Sc)' and the

tailwater depth is between the critical depth and the culvert height

(d < TW < D). The energy equation is expressed as c

HW = TW +

y2 tw -- +

2g ( 1.4)

where TW is the tail water depth, and Y tw is the outlet velocity. For Type 2 flow

conditions Sf is estimated by assuming uniform flow at a depth equal to TW.

Type 4A Flow Regime

Type 4A flow conditions (Figure 1.6) occur when either the slope is

less than critical (5 < 5 ) and the tail water depth is greater than D (TW > D), or o c

the slope is greater than critical (5 > 5 ) and the tail water depth is greater than o c

slope times length plus D (TW > So· L + D). This type of flow is controlled by

tailwater conditions. The energy equation is expressed as

HW (1.5)

where Y is based on full culvert flow, and Hf is the full pipe flow frictional

losses.

22

Type itB Flow Regime

Type 4B flow conditions (Fig. J .6) occur when the entrance is

submerged (HW > 1.20), tailwater is less than 0, (TW < 0), and the culvert flows

full for part of its length. This type of flow is controlled by the barrel and

tailwater conditions. The culvert hydraulic performance is approximated by

HW 0.6)

where V is based on full culvert flow, P is estimated as (d + 0)/2 when TW < d c c

or is TW when TW > d and Vt is based on d for TW < d or is based on TW for c w c c

TW > dc'

1.6.2 Inlet Control Regimes

Type 3A Flow Regime

Type 3A flow conditions (Fig 1.7) occur when the slope is greater

than or equal to critical (S 2: S ) and tailwater depth is less than the slope times o c

the length (TW < SoL). Critical depth controls at the entrance when the

entrance is unsubmerged and entrance geometry controls when the entrance is

submerged. The culvert hydraulic performance is determined by empirical

curves based on experimental measurements (HEC 5).

Type 3B Flow Regimes

Type 3B flow conditions (Figure 1.7) are similar to the Type 3A flow

conditions, except SoL < TW < SoL + O. The inlet is either submerged or

unsubmerged. Control may be at either the entrance, or the outlet, or may

transfer back and forth as slug flow. Hydraulic performance is predicted from

empirical nomographs or by type itA and 4B hydraulic characteristics.

23

CHAPTER 2 EXPERIMENTAL CONSIDERA nONS

The planning, construction, and hydraulic testing of the model culvert

with safety grates were divided into several stages. First, the physical

parameters effecting the hydraulic performance of a culvert were determined by

examining the energy equation. After identification of the controlling physical

parameters, hydraulic similitude was utilized to express the relationship between

the scale model culvert properties and the full size culvert performance. The

model culvert was then designed and constructed to simulate possible field

condi tions. Finally, numerous hydraulic studies were performed on the culvert

and the resulting experimental data was reduced for analysis.

2.1 Energy Equation

The primary objective of this study was to determine the effect that

safety grates have on the entrance headloss coefficient. Naturally, the entrance

headloss coefficient could not be physically measured, but was determined using

experimentally collected data to solve the energy equation for Ceo Referring to

Fig. 2-1, the energy equation written between points A and C is expressed as:

+ C e

V 2 e 2g

(2.1 )

where HW is the headwater depth, VA is the mean approach velocity, V is the

mean velocity in the culvert, Ce is the entrance headloss coefficient, Hf is the

frictional headloss in the culvert, d is the value of the hydraulic grade line at the

entrance, and V is the mean entrance velocity measured at the entrance, point e

B in Fig. 2.1.

This general form of the energy equation could be solved for the

entrance headloss coefficient if all other terms were physically measured. To

25

IV 0'

E.G.\.·

HW

v2

29

E.G.l. - tAL.

HG.l.

t TW

d CULVERT

8 \.--- Separation ----..\

\ Zone \

-'\

Figure 2.1 Energy and Hydraulic Grade1ines

minimize the number of terms to be measured, the energy equation was

simplified. First, the model culvert approach channel was designed wider than

the model culvert cross-section (velocity assumed to be zero). The approach

velocity head term, V A /2g, was then neglected in the energy equation. Most

culvert design procedures do consider a zero approach velocity. However,

referring to Fig. 2.1, the energy equation between A and B is expressed as:

HW V 2

e 2g

(2.2)

where d is the value of the hydraulic gradeline at the entrance and V is the e

mean velocity at the entrance. The entrance headloss coefficient* can be

expressed as:

c = e

2 (HW - (d + V /2g» e e (2.3)

V2

/2g

A major problem was encountered in measuring the depth of flow at

the entrance because of a large amount of turbulence generated at the entrance.

A separation zone forms along the culvert sides (Fig. 2.1) in which the

streamlines have substantial curvature and, thus, an acceleration component of

flow. The hydrostatic law of pressure distribution cannot be applied to a flow

with a large acceleration component in the cross-sectional plane. In order to

circumvent this problem, piezometers were used in the experimental program to

measure the hydraulic head at intervals along the culvert. From the piezometer

readings and elevation data, the depth of flow and the area of flow were

calculated for each location. The velocity at each piezometer location was

determined from the area of flow and the flowrate; V = Q/ A. The total energy

head at each location equals the velocity head plus the piezometer reading

(adjusted to datum). A least squares, linear fit, of the adjusted piezometer

readings downstream of the separation zone, was utilized to define the hydraulic

*All C evalues were determined using the mean entrance velocity.

27

gradeline. The total energy heads at these locations were similarly linearly

extrapolated to yield the energy gradeline. The calculated hydraulic and energy

gradelines together with the elevation data were used to determine the depth of

flow at the entrance and the entrance velocity.

2.2 Hydraulic Simili tude

Hydraulic model studies are based on the application of the laws of

hydraulic similitude. These laws are derived from the basic relations of fluid

mechanics and express the interrelationship of the various fluid flow parameters,

such as velocity, pressure, and shear, under similar boundary conditions. Simili-

tude requires geometric, kinematic, and dynamic similarity be maintained

between the model culvert and the prototype culvert.

The first condition of geometric similarity is satisfied if the ratio of

all corresponding lengths in the model and prototype are equal. This scale ratio

(LR

) can be expressed as L

m = L

(2.4) p

where Land L are corresponding lengths in the model and prototype, m p

respectively. Geometric similarity does not depend on fluid motion or force.

The second condition of kinematic similarity is satisfied when the

ratio of all corresponding components of velocity and acceleration are equal.

Since the ratio of the components of motion can be written in terms of the scale

ratio, the flow lines will be geometrically similar. The resulting velocity ratio,

VR

, is

where V m

geometric

satisfied.

V m

V R = -V- (2.5) P

and V are velocities in model and prototype, respectively. Once the p

and kinematic similarities are satisfied, dynamic similarity is also

28

In this culvert model study, gravitational forces are the dominant

factors describing flow condition. The inertial, gravitational, and pressure

forces are the major controlling factors affecting the flow in the culvert.

Viscous and surface tension forces do affect the flow, but these effects are

insignificant compared to the magnitude of the inertial, gravitational, and

pressure forces and thus can be neglected.

2.3 Laboratory Facilities

All experimental tests for this study were performed at the Center

for Research in Water Resources (CRWR) hydraulics laboratory at the Balcones

Research Center of the University of Texas at Austin.

Permanent equipment such as pumps, a pipe system, and a return

channel provide a system of recirculating water flow through the model. A

schematic layout of the CRWR hydraulics lab is shown in Fig 2.2. The outdoor

storage reservoir has a diameter of 100-ft and a storage capacity of

approximately 550,000 gallons. Two pumps supplied a range of flows up to a

maximum of approximately 12 cfs through model culverts. Regulating valves

are located between the pumps and the indoor hydraulics laboratory. The supply

piping system consists of 12-in diameter overhead pipes housed in a 97-ft by

IOO-ft room. The 4-ft x 4-ft return channel is located below the floor level of

the laboratory. A sharp crested weir and a Lory Point gage were used to

measure the discharge in the return channel.

A general schematic of the model setup is shown in Fig 2.3. Water

from the supply pipe system enters an 8-ft x 8-ft x 6-ft high head box. This

head box was constructed from 3/4-in thick A-C plywood and set in a metal

frame. All plywood surfaces exposed to water were impregnated with polyester

resin and all joints were reinforced with fiberglass tape. Two sets of baffles

29

w o

Figure 2.2

Regulating valves

Return Flow Channels

Schematic of Hydraulics Laboratory

D F 0==1 H 1~~(2) J

-+

t E )(

-1.

M L of-

II t t LEGEND

w A. Storage Reservior t-' B. Fumps

e, Regulating Valves D. Head Box E. Baffles F. Approach Channel C. eul vert I1llet H. Culvert Model r. eul vert Outlet J. Outlet Channel K. Tailgate L. Return Channel M. Sharp Crested Weir

Figure 2.3 Overview of Test Facilities

were used to reduce the amount of turbulence and were located at the approach

channel entrance. The baffles were constructed of I-in by 2-in vertical slats

placed on alternating sides of a wooden frame. Two large styrofoam pads were

used to decrease the amount of surface turbulence. From the head box the

water flows into an 8-ft wide by 4-ft deep by 20-ft long horizontal approach

channel. The channel was also constructed of 3/4-inch thick A-C plywood and

was placed on a 2-ft high wooden frame. The measurements of headwater depth

were made by two Lory Point gages located in the approach channel. Figure 2.4

shows the head box and approach channel. The water flows from the culvert

model into a discharge channel (Fig. 2.5), also constructed of plywood.

The 8-ft wide by 4-ft high by 9-ft 4-in long outlet or discharge

channel was supported on two stiffened W lO-ft x 12-ft steel beams. Six 5-ton

screw jacks were used to vary outlet channel elevation and culvert slope. An 8-

ft wide by 4-ft 5-in high by 3/l6-in thick sliding steel tailgate was mounted at

the downstream end of the outlet channE'1 in an 8-ft by 7-ft 8-in frame made of

2-in x 2-in angle iron. Tailwater depth was varied by two pulley mechanisms to

raise and lower the tailgate. After passing the tailgate, water flows through a

12-ft wide by 4-ft long by 3-ft la-in deep outfall box made of 3/4-in A-C

plywood. The outfall box was supported bv 2-in x 2-in angle iron and stiffened

with 3/8-in diameter reinforcing steel bars.

2.4 Experimental Set up for Box Culvert Tests

Schematics (side view and plan view) of the experimental set up for

the box culvert tests are shown in Fig. 2.6. The box culvert was constructed of

3/4-in plywood with l/2-in plexiglass installed on one side (Fig. 2.7). The

plexiglass enabled visual observation of the different flow regimes. The

dimension of the culvert were 2-ft wide by 1.25-ft high by 27 -ft long. The

32

a. Headbox and Approach Chtmne 1

b. Entrance to the Culvert

Figure 2.4 Experimental Set-Up

33

Figure 2.5 Outlet Channel

34

Supply Pipe

21ft " Slide II Gate

T I I

1 I II ~Baffles 'I I, I

6ft I I I, ~ 4 ft ~'"

1 I I II I' ,I 2 If'lt- 20ft

II ~ I I ~ II

... lJ ~

..... ..... ..... V ..... ++--4ft

I--- 8ft~ '\

variable

(a) SIDE VIEW

W \JI

'" i'

co

" Head Approach D t C] Outlet Return

0 ....... .

Box Culvert N

Boy. Channel ., t Channel Channel

.. I

f

I .l

PLA.'>; VIEW

Figure 2.6 Schematics of Experimental Setup

F i. gure 2.7 Box Culvert

36

culvert was supported on two W 12 x 22 steel beams to keep deflections in the

culvert to a minimum. Four 5-ton screw jacks were used to change the culvert

slope and support the culvert. The slope of the culvert was set by the use of a

Dumpy level. The headwalls to the box culvert were constructed of plywood on a

4 to 1 slope with a wingwall flare of 4 to 1. Figure 2.8 is a schematic of the box

culvert headwalls. Figure 2.4 (b) shows water entering the box culvert.

2.5 Experimental Set Up for Pipe Culvert Tests

Schematics (side view and plan view of the pipe culvert model) are

shown in Fig. 2.9. The pipe culvert is a 15-in diameter, ~-in by 2-3/4-in helical

corrugated metal pipe* (Fig. 2.10). Two sections of pipe were connected by a

bolt lock collar. The pipe was mounted on two stiffened W 10 x 12 steel beams.

Five 5-ton screw jacks provided culvert support and slope variability.

The headwalls of the pipe culvert were constructed of 3/4-in A-C

plywood (Fig. 2.11). The headwalls were mounted on a 4:1 sloping 2-in by 4-in

wood frame. Polyester resin sealant, fiberglass tape, rubber stripping, metal

plates, and sheet metal screws were used to waterproof the headwall.

2.6 Instrumentation

Discharge was measured with a sharp crested weir and depths were

measured using Lory point gages, stagnation tubes, an open air manometer, and

piezometers. The discharge was measured with a Lory point gage and a sharp

crested weir, located in the return channel. Headwater depth was measured in

the approach channell O-ft upstream of the culvert entrance with two Lory point

gages. The tailwater depths were measured with a piezometer, located in the

outlet channel floor. The piezometers were connected by "Tygon" tubing to its

separate, graduated, open air manometer. The slope of the culvert was measured

with a Dumpy level.

*Donated to the project by Armco, Inc., Middletown, Ohio.

37

38

co N

W \0

12" •

T 4"0"

1;"0'

_J,ll.,1 IldA~

I 8"0"

_I

0-~ --

5',0" -1-0 -19"0,,-1 ~ • I- l-:)',0'

Figure 2.9

1"3" •

j.

T 3'-10"

E3 "J\ 1\ 1\ !

Side View

· • · · · 12'-0"

J · --..---. ·

--~ · · •

· · ,I. . I

25'·1" 7r

Plan View

Pipe Culvert Model - Side and Plan Views

Figure 2.10 Pi.pe Culvert

~ 111.._------- 8ft

8ft

.... -----5tl

TOP VIEW

4

1 I ~-::::_-___ +-_____ _ --------=--------~-- - ----- ~I---------...;~ 1.25 ft •

SIDE VIEW

Figure 2.11 Pipe Culvert Headwall Dimensions

41

For the box culvert model the piezometric depths were measured by

twelve piezometers located along the culvert centerline. The piezometers were

connected by Tygon tubing to l/2-in diameter open air manometers shown in Fig

2.12. Another manometer tube was placed at the downstream end of the box

culvert for the 12th piezometer.

For the pipe culvert, hydraulic depths were measured by eight

stagnation tubes and open air manometers. Eight 1-1/8-in diameter holes were

drilled at approximately 3-l/2-ft intervals along the pipe. The stagnation tubes

(Fig. 2.13) were set in rubber stoppers and mounted in the holes with silicon

sealant, rubber gaskets, steel plates, and sheet metal screws. The stagnation

tubes were connected by "Tygon" tubing to the 1/2-in diameter open air

manometers (Fig. 2.12).

2.7 Model Safety Grates

Safety grates for the box culvert model included 1:4 scale model

grates of the prototype grates (3-in diameter on 30-in centers) determined by the

Texas Transportation Institute (TTI) study (I 979). The model safety grate of the

TTl design is shown in Fig. 2.14(a). These grates are referred to as the pipe

safety grates for the purpos~ of this report. These model pipe grates were

constructed of 3/4-in O.D. pipe conduit and were placed on 7.5-in centers as

illustrated in Fig. 2.14(a).

In addition to using the model pipe grates, tests were also performed

for prototype grates that have been used in the field. These prototype grates are

constructed of 1/2-in x 2-in flat iron bars and are placed on .5-in centers: These

grates are referred to as "bar grates" for the purpose of this report. The model

bar grates are shown in Fig. 2.14(b). These model grates which are also a 1:4

scale model are 1/8-in x 1/2-in flat iron bars placed on 1.25-in centers. Figures

42

I 10 q • 8 T 6!J

Figure 2.12 Manometers

43

Figure 2.13 Stagnation Tubes For Pipe Culvert

.l:V!

2 It. ~ O.D. Pipe

1/2 by 2 in. Bar

/

1 I

J

4

J

,

I

J I

-I 7.S.n. f.- --+if---1.25.n.

(a) Pipe Safety Grate (b) Bar Safety Grate

Figure 2.14 Model Safety Grates For Box Culvert

~

" \ 1\

1\

~

~

1\

~ \

2.15(a) and (b) show the pipe and bar safety grates installed on the headwalls of

the box culvert model.

The safety grates for the corrugated metal pipe culvert are shown in

Fig. 2.16. these grates have a somewhat different design than either of the two

box culvert grates. These grates were constructed of 3/4-in diameter conduits

placed on 6-in centers; they simulate 3-in diameter conduits placed on 24-in

centers and are shown in Fig. 2.16. Figure 2.17 shows the pipe grates installed at

the pipe culvert inlet and Fig. 2.18 shows the grates installed at the outlet.

2.8 Measurements For Entrance Headloss

Several flow parameters were measured in both free outfall and

tailwater tests: (}) slope; (2) discharge; 0) headwater depth; (4) tail water depth;

and (5) hydraulic depths. Measurements were taken for three different situa-

tions: (}) no safety grate at the inlet or outlet; (2) a safety grate at the inlet

only; and (3) safety grates at both the inlet and the outlet. A range of discharges

were considered. This testing procedure enabled a direct comparison of the

effect of safety grates on the entrance headloss coefficient.

For the pipe culvert tests, free outfall and tall water test trials were

performed for only two situations: (I) no safety p,rate treatment of inlet or

outlet; and (2) safety grate installation on both inlet and outlet.

Free Outfall Tests

Free outfall conditions occur when the tall water depth is less than

the critical depth at the outlet. The general procedure to take free outfall test

measurements was as follows:

1. The discharge was determined from the weir reading once the flow was stabilized (generally, a period of 10 minutes).

2. The headwater depth was measured with the two Lory Point gages in the approach channel.

46

(a) Pipe Saf~ty Grates Installed

(b) Bar Safety GrRtes Installed

Figure 2.15 Safety Grates

47

r Ir·3" 6"

~=====~..L

Scale: 1"= I'

Figure 2.16 Pipe Model Safety Grate

48

• •

•

•

• PI,. Cr.teo ~t 'Dl.,

..

Figure 2 . 18 Pipe Grate s At Outlet

50

3. The hydraulic grade line in the cuI vert was measured.

4-. Steps 2 and 3 were repeated. (a) No grates in place. (0) Grate at the inlet only. (Box culvert only) (c) Grates at both the inlet and outlet.

5. Steps 1, 2, 3 and 4- were repeated for different discharges.

Tailwater Test

The general procedure for taking measurements for the tail water

tests (when tailwater is greater than critical depth at the outlet) were as

follows:

1. A constant flow rate was established in the culvert and weir readings were taken for determining the discharge.

2. A free outfall test (TW< dc) was run for the constant discharge.

3. An initial tail water depth was established by lowering the discharge channel gate.

4-. After the flow stabilized, the two upstream point gages, the cuI vert piezometers, and the discharge channel piezometer were read and the values recorded.

5. The tail water depth was increased in increments of TW = 0.1

and Step 4 was repeated. The tail water depth was IPmited to TW D = 1.8.

2.9 Data Reduction

The experimental data from the test measurements were converted

into actual values of headwater depths, tail water depths, entrance flow depths,

and entrance velocity head. The data reduction was accomplished by using

computer programs developed only for this purpose.

The computer program, CULVERT, was developed by the authors. A

Fortran listing of the program and a user's manual is provided in Appendix A.

CUL VER T was used to reduce raw data into flow parameters and the

51

entrance coefficient. Routines within the program computed the following

quanti ties:

1.

2.

3.

4.

5.

6.

7.

8.

headwater depth,

tail water depth,

hydraulic and energy grade lines,

velocity head at the culvert entrance,

entrance loss coefficient, Ce (based on Eq. 2.3),

tail water depth divided by culvert diameter T;

headwater depth divided by culvert diameter H6' '

discharge factors 3_ for the box culvert and DQ2 .5 for the BD1.5

pi pe cuI vert.

9. culvert slope.

Headwater Depth Determination

The headwater depth was measured by two Lory point gages 1. O-ft

upstream from the culvert entrance. The gages were placed far enough

upstream to minimize effects of the entrance turbulence but close enough to the

entrance to keep frictional losses at a minimum. The difference in elevation

between the culvert entrance invert and the pointer tip at the zero mark was

added to the Lory gage readings to determine the headwater depth.

Hydraulic Head and Velocity Head at Entrance

The determination of the hydraulic head and velocity head at the

entrance involves several steps:

a. The piezometer readings (or the stagnation tube readings for the pipe) were converted into elevations above the inlet invert. The conversion is the difference in elevation between the inlet invert and the manometer zero point. A linear extrapolation of the converted instrument readings gives the approximate hydraulic grade line, from which the hydraulic head at the

52

entrance is obtained.

b. The velocity head (using average velocities) at each piezometer (stagnation tube) location was added to the hydraulic head to obtain the energy head. The velocities were determined by dividing the discharge by the corresponding flow area at each piezometer location. The approximate energy grade line was determined by linear extrapolation of the energy head values at each instrument location.

c. The velocity head (y2/2g) at the entrance is obtained by subtracting the value at this location of the hydraulic grade line from the value of the energy grade line.

Tailwater Depth Determination

The tail water depth was measured by a piezometer located in the

middle of the outlet channel. An open air manometer was used to determine the

hydrostatic pressure measured by the piezometer. To calibrate the piezometer

to measure tail water depth, the difference in elevation between the culvert

outlet invert and the zero mark on the manometer was added to the manometer

readings.

2.10 Summary of Box Culvert Tests

2.10.1 Safety Grate Tests

The tests were designed to provide adequate data for evaluating the

hydraulic effects, of pipe or bar safety grates, for both entrance and outlet

control, so as to include the six basic flow regimes of culvert flow. A summary

of the tests are given in Table 2.1. The box culvert was tested for each of five

slopes, ranging from 0.008 to 0.0128. A series of flowrates were run, either with

no safety grates in place or with pipe safety ~rates on both upstream and

downstream ends. The tail water depth was increased for four specified values of

flowrate, at each of three slopes. The tailwater gate was lowered such that the

value of TW was increased, in increments of approximately 0.1, for each o

flowrate up to 1.8. The bar safety grates were simlliarly tested for three slopes.

53

Table 2.1 Summary of Box Culvert Tests

Tests for TW< Tailwater Tests. TW>

Grates Range of Grates Range of TW

Slopes Tested Discharges. (cfs) Tested Discharges D

No Grates No Grates 6.14,8.12,10.4, 11.8 0.0008 Pipe 3.3 to 11.7 cfs Pipe same as for no grates 0.4 to 1.8

Bar in 0.8 increments Bar 4.0, 6.5, 8.1, 11.0 increments of 0.1

V1 +:- No Grates 5.0 to 11.7 cfs None

0.00 13 Pipe in 0.7 increments

No Grates No Grates 0.0063 Pipe 3.0 to 11.7 cfs Pipe 6.14,8.12,9.66, 11.8 0.5 to 1.8

Bar in 0.8 increments Bar increments of 0.1

No Grates No Grates 0.0108 Pipe 3.0 to 11.7 cfs Pipe 6.14, 8.12, 9.66, 11.8 0.4 to 1.8

Bar in 0.8 increments Bar increm ents of 0.1 ---.-

No Grates 3.0 to 11.7cfs 0.0128 Pipe in 0.8 increments None

2.10.2 Clogging Tests

Clogging tests were performed in order to evaluate the hydraulic

effects of various degrees of debris blockage as could be caused by the safety

grates. The pipe grates were tested using 3 slopes and 4- discharge for each

slope. The bar grates were tested at one slope using 5 different discharges. In

each case, the percentage of the entrance that was blocked, was increased from

bottom to top in increments of 15% of the total available from a to 90 percent

blockage. The tests were then repeated, beginning at the top of the entrance

and increasing toward the bottom, until 90% blockage was achieved. A sum mary

of the tests are given in Table 2.2.

2.11 Summary of Pipe Culvert Tests

The tests as summarized in Table 2.3, were designed to provide

adequate data for evaluating the hydraulic effects of pipe grates on culvert flow,

for both entrance and outlet control, so as to include the six basic flow regimes.

For each of three slopes (0.0007, 0.008, and 0.05), a series of flowrates, in

increments of approximately 0.3 cfs were run. Tailwater tests were made for S o

= 0.0007 and S = 0.008, at flow rates of 3.5, 4-.5 and 5.5 cfs, and a range of TW o -D

up to 1.9 in increments 0.1. All tests were performed with no safety grates and

then with pipe safety grates at both upstream and downstream ends. Clogging

tests were not performed on the pipe culvert.

55

Table 2.2 Summary of Clogging Tests for Box Culvert

Grates Range of Slopes Tested Discharges. (cfs) Percent Clogging

----U1 0.0008 Pipe 9, 9.6, 10.0, 11.2 cr-

All tests for clogging 0% to 90% in

increm ents of 15% 0.0063 Pipe 8.04,9.11,10.04,11.17

Bar 8.12,9.09,10.1,11.05,11.91

0.028 Pipe 9.0, 10.0

Table 2.3 Summary of Pipe Culvert Tests

Tests for TW< d c Tailwater Tests. TW >dc

Range of TW Range of D

VI Slopes Discharges Discharges -....J ----

0.0007 2.0 to 8.0 cfs 0.0 to 1.9 3.5

0.008 in increm ents in increments 4.5 of 0.3 cfs. of 0.1

5.5

0.05 2.3 to 9.6 cfs No Tests No tests

in increments of 0.3 cfs ._-----------

CHAPTER 3 BOX CULVERT RESULTS

The experimental tests using the pipe and bar safety grates for the

box culvert model are presented and analyzed in this chapter. Figures are

presented to compare the hydraulic effect with and without the pipe and bar

safety grates under different combinations of slopes, discharges, headwater

depths, and tail water depths. For comparison, the experimental tests without

safety grates are also included on selected figures. Discussion of the tests are

presented describing the change in the hydraulics due to the safety grates. In

addi tion, regression equations are presented for predicting entrance headloss

coefficients for different conditions for outlet control. Also, regression equa-

tions are presented for determining headwater-discharge relationships for inlet

control.

3.1 Entrance Headloss Coefficients With and Without Safety Grates (Mild

Slopes)

The box cuI vert was tested under numerous possible condi tions

including low to high flow rates, mild to steep slopes, and free outfall to high

tail water. The effect of the pipe and bar safety grates on the entrance headloss

coefficient, C , is illustrated by graphs of C for the safety grates installed e e

versus C without the safety grates installed. e

Figures B.l through B.6 (Appendix B) show the entrance head loss

coefficients with pipe safety grates installed versus the entrance headloss

coefficients without safety grates installed. The entrance head loss coefficients

with the bar safety grates installed versus the entrance headloss coefficients

wi thout safety grates installed are shown in Figures B.7 through B.9.

59

On Figs. B.I through B.9, a line intersecting the origin was drawn at a

lf5 degree angle with the abscissa. If either the safety grates increased the

entrance headloss coefficient then the corresponding data points would plot

above this line. If the entrance headloss coefficient decreased with the safety

grates then the data points would plot below this line.

Types 1 and 2 flow regimes had a slight increase in the entrance

headloss coefficient with pipe safety grates for slopes .0008 and .0063 (Fig. B. I

and B.3) and a slight decrease for slope .0013 (Fig. B.2). These two flow regimes

had the lowest entrance headloss coefficients for outlet control condi tions.

The Type If A flow regime (Figs. B.l through B.5) had the highest

entrance headloss coefficients for both inlet and outlet control conditions. For

this flow regime, the C values with and without pipe safety grates had a large e

amount of variability. For Type If A flow regime, very general conclusions are

that the pipe safety grates had little or no effect on the entrance headloss

coefficient for slopes .0008 and. 0063 (Figs. B.I and B.3) and slightly decreased

the C values on slopes .0013, .0108, and .0128 (Figs. B.2, B.lf, and B.5). Again it e

should be noted, for Type If A flow regime, the change in the entrance headloss

coefficients with the pipe safety grates were not consistent and the conclusions

should be viewed judiciously.

For the Type lfB flow regime, the entrance headloss coefficients

increased with the pipe safety grates for slopes .0008 and .0063 (Figs. B.l and

B.3) and decreased for the slope .0013 (Fig. B.2).

The entrance headloss coefficients with the bar safety grates were

generally higher than without safety grates (Fig. B.6 through B.8). For slopes

.0008 and .0108 (Fig. B.6 and B.8), the increase in C with the bar safety grate e

was obvious for all flow regimes. For slope .0063 (Fig. B.7), the increase in the

60

entrance headloss coefficient was evident for flow regimes 2 and 4B. For flow

regime 1, the C with and without the bar safety grates were sim Bar for slope e

.0063. Similar to the pipe safety grates, the Type 4A flow regime for slope .0063

(Fig. B.7) had a large variability in the entrance coefficient with and without the

bar safety grates and the effect of the bar safety grates on the entrance

headloss coeficient was not clearly evident.

For each slope, linear regression analyses were performed for each

flow regime using collected data points. The linear regression analysis determin-

ed the coefficients for the following equation:

C (with grates) = A C (without grates) + B e e

(3.1)

where A and B are the slope and y-intercept, respectively. Tables 3.1 and 3.2

are the linear regression analysis results performed for each slope and flow

regime for the pipe and bar safety grates, respectively.

3.2 Headwater-Discharge Relationships (Inlet Control)

A unique relationship exists between the headwater and the discharge

for inlet control. Inlet control should have only one headwater value for each

discharge. Figures B.IO through B.17 are the relationships of Hri vs ---!t.5 for

inlet control. For each discharge, the headwater depth was measured with and

without the safety grates. Figures B.IO through B.14 are results for the pipe

safety grate tests and Fig. B.15 through B.17 are results for the bar safety grate

tests.

For the pipe safety grate testing program (Fig. B.IO through B.14),

the pipe safety grates had no effect on the headwater depth. Noting that the

plots are for hydraulic tests with "clear" water (debris free), the test data with

and without the pipe safety grates were identical. No noticeable increases in

61

Table 3.1 Regression Equations for Comparing C e

(With and Without Pipe Safety Grates)

S o = .0008 So = .0013 So = .0063

Flow Regime A* B* R** A B R A B R

1.348 -.062 .869 1.036 -.022 .832 .983 .140 .993

2 1.285 -.066 .992 2.416 -.203 .802

4A 2.36 -.981 .423 1.138 -.109 .87

4B .957 .001 .%1 -3.704 -1.06 -.115

All 1.086 -.045 .915 .978 -.025 .952 .961 .0185 .967 ----

*A and B are defined in Eq. 0.1) **Coefficient of determination of the regression equation

Table 3.2 Regression Equations for Comparing Ce

(With and Without Bar Safety Grates)

S o = .0008 So = .0063 S = .1080 0

Flow Regime A B R A B R A B R

1.059 .063 .988 .041 .844 .904

2 1.351 -.030 .396 .192 .176 .225

4A .914 .904 .819 .696 .198 .731 .095 .7J8 .174

4B 2.525 -.204 .303

All 1.029 -.065 .981 .834 .103 .859 .972 .065 .935 ---

62

headwater depth due to the pipe safety grates were indicated for either outlet

control conditions (Fig. B.IO through B.12) or inlet control conditions (Fig. B.l3

and B.14). Referring to Figs. B.12 and B.l3, differences in headwater depths

with and without safety grates were noted at the higher discharges. Not enough

data was taken at these higher discharges to determine if the differences were

due to the safety grates or were due to uncertainties in the measuring devices.

For the bar safety grate tests (Fig. B.15 and B.Il), the headwater

depth did increase with the bar safety grates. The bar safety grate test data

plotted slightly above the test data without the safety grates. The increase in

headwater was not constant but varied with discharge.

Headwater-discharge equations were determined by using all data

points for inlet control conditions. Type 3A flow regime is inlet controlled, and

the hydraulic capacity of a culvert depends upon the entrance geometry.

Empirical curves which determine the culvert hydraulic performance are in the

form

HW D = + ••• +

where a , aI' ••• , a are the regression coefficients. The equations used o n HW as the dependent variable and ? 5 as the independent variable. The ---0 BD •

results of the regression analysis are summarized in Table 3.3. Because the pipe

grates made no significant hydraulic effect, the results are presented as with and

without pipe safety grates in Table 3.3a. The regression results for the bar

grates are presented in Table 3.3b.

3.3 Entrance Headloss Coefficient - Headwater Relationship

Figures B.18 through B.25 are plots of the entrance headloss coeffici-

ents versus measured headwater depth. Each figure was for a constant slope

63

Table 3.3 Headwater Discharge Relationships For Inlet Control

(a) With And Without Pipe Safety Grates

a a1 a2 a3 a4 a5 R

0

1 .1395 .3141 .98

2 .3624 .1270 .0349 .99

3 -.0587 .6814 -.1897 .0281 .99

4 -.0934 .7534 -.2349 .4000 -.0011 .99

5 1.8880 -3.7450 3.6310 -1.5390 .3071 -.0231 .99

(b) Bar Safety Grates

a a1 a2 a3 a4 a5 R 0

1 .1190 .3291 .98

2 .3827 .1090 .0403 .99

3 .0433 .5655 -.1450 .0231 .99

4 -.5938 1. 7280 -.8811 .2170 -.0181 .99

5. 1.3236 -2.661 2.9070 -1. 3330 .2843 -.0226 .99

64

where the discharge and tail water were varied. The corresponding flow regime

was identified for each data point. The pipe safety grate tests are shown in Figs.

B.18 through B.25 and the bar safety grates are shown in Figs. B. 23 and B. 25.

For outlet control conditions (Figs. B. 18 through B.20) and Type 4A

flow regime (Figs. B.21 through B.22), the pipe safety grate tests data points are

approximately grouped together according to the appropriate flow regime. The

lowest average entrance headloss coefficients were measured for the Type 1

flow regime. Type 4A flow regime had the highest average entrance headloss

coefficients. As a general trend, the entrance headloss coefficient increased

with an increase in headwater. The Ce values did appear to reach a limit at

HW /D greater than 1.5.

For the inlet control conditions (Figs. B.21 and B.22), the entrance

headloss coefficients also increased with an increase in the headwater depth.

The increase in the C value was very obvious for Type 3B flow regime for a e

slope .0108 (Fig. B.21). The maximum entrance headloss coefficient occurred at

HW /D greater than 1.5.

Similarly, the bar safety grates data tended to group together

according to flow regime (Figs. B.23 through B.25). For outlet control, the

lowest and highest average entrance coefficients were for Types 1 and 4A flow

regimes, respectively. For inlet control, Type 3A flow regime had the lowest

average entrance coefficients. The entrance headloss coefficient had an obvious

increase with an increase in headwater for slopes .0008 and .0063 (Fig B. 23 and

B.24). The C values reached a maximum at HW /D greater than 1.5. e

No direct evidence as to the effect of either pipe or bar safety grates

can be inferred from the entrance headloss coefficient versus headwater

relationships (Figs. B.18 through B.25). The changes in the entrance headloss

65

coefficient were not necessarily caused only by the pipe or bar safety grates.

The entrance headloss coefficient actually depended upon the headwater which

was in turn affected by the discharge, slope, tail water , etc.

3.4 Entrance Headloss Coefficient - Discharge Relationship

Figures B.26 through B.24 are plots of entrance headloss coefficient

versus the discharge factor (~1 5). Each data point was identified as to the BD •

corresponding flow regime. For each plot, the slope remained constant while the

discharge and tail water were varied. Figures B.26 through B.30 are for the pipe

safety grates. Figures B.31 through B.34 are for the bar safety grates. For Figs.

B.26 through B.28, and B.30 through B.32, designated discharges were held

constant and the tail water depth was varied. The different C values for the e

same discharge resulted from changes in tail water depth.

For the pipe safety grates (Figs. B.26 through B.30), the lower

entrance head loss coefficients were for Type land 3A flow regimes and the

higher C values were generally for Type 4A flow regime. From the figures, the e

entrance headloss coefficients varied with discharge and different flow regimes.

Types I and 3A flow regimes had the lowest variability of entrance headloss

coefficients wi th discharge.

For the bar safety grates (Fig. B.26 through B.30), the lower entrance

headloss coefficients were for Types I and 3A flow regimes and the higher C e

values were generally for Type 4A flow regime. From the figures,the entrance

headloss coefficients varied with discharge and different flow regimes. Type 1

and 3A flow regime had the lowest variability of entrance headloss coefficients

with discharge.

For the bar safety grates (Figs. B.31 through B.33), the entrance

headloss coefficients also varied with discharge and flow regime. Types 1 and

66

3A flow regimes had the lowest C values and the smallest range in values. e

Again, Type 4A flow regime had the largest entrance headloss coefficients.

3.5 Headwater - Tail water Relationships

For the tailwater tests, the tailwater was increased from free outfall

condi tions to full flow. The measured headwater versus the measured tail water

for pipe, bar, and no safety grates are shown in Figs. B.37 through B.48. On each

plot, the calculated discharges were identified for the tested slopes. For Figs.

B.36, B.39 through 41, and B.45 through 48, the measured data for the pipe, bar,

and no safety grates were presented on the same plots. For these plots, using

the same discharge, the headwaters with the pipe and bar safety grates were

compared to the headwater without safety grates.

The plots of headwater versus tailwater have two distinct parts. In

the first part, the headwater was not affected by the tail water and the data

points plotted horizontal. In the second part, the headwater increased with an

increase in tail water depth. For outlet control conditions, the tailwater did not

affect the headwater until the tailwater depth was greater than critical depth.

For inlet control conditions, the tail water was greater than the slope times the

length plus the critical depth when the tailwater affected the headwater.

For slopes of .0063 and .0108, seven different tests were run using

four different discharges (Fig. B.38 through B.49). As evident, the data points

from the pipe safety grates tests were approximately identical with the data for

no safety grates tests. The effect of the pipe safety grates was less than the

accuracy at which the tests were run. The bar safety grate tests did indicate an

increase in the headwater depth for the lower tailwater (Figs. B.40 through B.41

and B.45 through B.48) but indicated little increase for the higher tail water.

67

Large deviations in headwater depths between the pipe, bar, and no safety grate

tests were noted for a slope of .0063 and a discharge of 11.81 cfs in Fig. B.42.

3.6 Regression Equations Considering Flow Regimes

3.6.1 Development of Regression Equations

Present engineering practice normally has a single entrance headloss

coefficient for each culvert entrance design. However, based upon this

experimental study, the entrance headloss coefficient varies with different flow

conditions. Using a constant C value, the culvert could be under-designed for a e

given flow regime. To aid in the design of culverts with and without safety

grates, several regression equations were determined which can be used to

predict the entrance headloss coefficient based on (combinations of) design

discharge, headwater, tail water and/or slope. In this study, equations were

derived for each of the four flow regimes under outlet control.

The regression equations for outlet control can be expressed in the

general form

(3.3)

where Y is the dependent variable to be estimated, XI 2 are the , , ... n

independent variables, and B , Bl , ... B are the regression coefficients. For this o n

study, the dependent variable was the entrance headloss coefficient, C • e

3.6.2 _R--,e:......g,.;;.r...:.e-,-ss.:,...i_o_n_E_9 ..... u_a_t_i_o_n_s _f_or_C e

The different equations used for the theoretical models and the

general models are listed in Table C.l. Equations 1 through 7 in Table C.l are

theoretical regression models, and Eqs. 8 through 19 are the general models. The

regression results (best fit models) for the pipe grates, no grates and bar grates

are listed in Tables 3.4, 3.5, and 3.6, respectively. The equations are presented

68

Table 3.4 Regression Coefficients (Pipe Safety Grates)

Regime Equation B Bl B2 B3 B4 R 0

13 .203 2.258 -.651 -.084 34.185 .918

2 8 .387 1.450 -.321 .944

3A (; .205 -.472 .655

4A 9 .365 J;88 -.036 -.498 .591

4B 11 -.610 2.321 -.479 -105.65 .945

Table 3.5 Regression Coefficients (No Grates)

Regime Equation B B1 B2 B3 B4 R 0

13 .210 2.956 -.8~2 -.112 42.682 .884

2 8 -.333 1.3{)7 -.309 .958

3A .344 -2.823 1.154 .586

4A 9 .003 .. 525 .014 -.153 .653

4B 11 -.354 -1.664 .~27 -41.{)57 .779

Table 3.6 Regression Coefficients (Bar Safety Grates)

Regime Equation BO B1 B2 B3 B4 R --.----- _.

13 -.091 1.581 -.196 -.108 16.073 .919

2 8 -.269 1.782 -.4702 .941

3A 6* .543 -.608 .818

4A 2 .747 5.091 -3.648 - 3.081 .700

4B 13 -8.193 -.689 4.210 -.421 -12.012 .980

69

in Tables 3.7 through 3.9. The information presented on the best fit models

includes the appropriate regime, the model equation, the regression coefficients,

and the coefficient of determination. A complete listing of each regression

equation analyzed is presented in Appendix C.

Equations 13 and 8 (Table C.l) were the best fit equations for Type

and 2 flow regimes, respectively. For the pipe safety grates, and no safety

grates, the best regression equations for flow regimes 4A and 4B are Eqs. 9 and

11, respectively (Table C.O. For the bar safety grates, Eq. 2 (Table C.O for

flow regime 4A and Eq. 13 (Table C.1) for flow regime 4B had the lowest

coefficients of determination. The highest coefficients of determination were

for the pipe and bar safety grate regression equations for flow regime 4B.

3.7 Regression Equations for Submerged Conditions

The regression equations developed for submerged inlet, unsubmerged

inlet and combined submerged and unsubmerged inlet conditions, all with outlet

control are developed for use in design. From the viewpoint of design

considerations, regression equations should be in the simplest form with the least

number of independent variables. The suggested or recommended equations may

not necessarily be the best fit (largest coefficient of determination) because of

the number of independent variables considered.

For submerged inlet conditions, HW --o~1.2, (flow regimes 4A and

4B), regression equations were developed using the data for all slopes and

discharges in these regimes. A summary of the regression equations and the

results are presented in Table 3.10. One set of best fit regressions are as follows

(Eq. 8, Table C.l):

No Grates

C e HW ~ = -0.061 + 0.519 (-D-) - 0.049 (BD1.5)

70

(3.4)

Table 3.7 Regression Equations for C e (No Grates)

Regime 1

Ce

0.210 + 2.956 (HWl_ 0.842 (3_) - 0.112 <_Q __ )2 + 42.682 5 o B01.5 B01.5 0

Regime 2

Regime 4A

Ce

= 0.003 + 0.525 (HW) + 0.014 (~1 5) - 0.153 ( TOW) o BO •. ,

Regime 4B

HW 0 Ce = -0.354 - 1.664 (0) + 0.827 (B01.5) - 41.657 So

TABLE 3.8 Regression Equations for Ce (Pipe Safety Grates)

Regime 1

HW 2 ( 0 Q 2 Ce = 0.203 + 2.258 (-0) - 0.651 ~1 5) - 0.084 <-1-5) + 34.185 5 BO • BO • 0

Regime 2

HW Q Ce = -0.387 + 1.450 (D) - 0.321 (Bo I3)

Regime 4A

HW 0 TW C e 0.365 + 0.688 ( ) - 0.036 (SO 1.5) - 0.498 ( 0)

Regime 4B

Ce 0.610 + 2.321 ( ~W) - 0.479 (B~1.5) - 105.650 So

71

Table 3.9 Regression Equations for C e (Bar Safety Grates)

Regime J

HW 2 0 Q 2 C = -0.091 + 1.581 ( ) - 0.196 (~1-5) - 0.108 (~1-5) + 16.073 S

e BO' BO • 0

Regime 2

HW Q C = -0.269 + 1.782 (-0 ) - 0.470 (-1-5)

e BO •

Regime 4A

_ q (HW) ( Q ,-2 ( Q )-2 ( TW) ( Q )-2 C - + 0.747 + 5.0-,1 \ -0 '~1-5 - 3.tl48 --1-5 - 3.081 -0 - -1--5 e BO • BO •. BO •

Regime 4B

HW 2 0 0 2 C = 8.193 - 0.689 (-0 ) + 4.210 (-"1-5) - 0.421 (-~l 5) - 12.012 S e BO " BO' 0

72

Table 3.10 Summary of Regression Results for Submerged Condition

Type Of B B1 B2 B3 B4 Equation Number Grates 0 R

No 2 Grates 0.820 -1.838 -4.279 3.932 0.64 8 -0.061 0.519 -0.049 0.56 9 -0.055 0.073 0.072 0.260 0.70

11 -0.067 0.519 -0.048 0.759 0.56 13 -0.163 0.162 0.292 -0.054 1. 755 0.57 16 0.670 -0.270 1.740 0.10 21 421 0.102 -0.348 0.65

Bar

"" 2 Grates 0.814 -1.421 -6.070 5.032 0.71

w 8 -0.023 0.595 -0.086 0.63 9 -0.064 0.130 0.032 0.318 0.76

11 -0.061 0.600 -0.086 4.900 0.64 13 -0.118 0.180 0.258 -0.052 6.28 0.64 16 0.920 -0.088 6.800 0.25 21 0.616 0.063 -0.433 0.67

Pipe 2 Grates 0.785 -1.379 -2.896 2.779 0.45 8 -0.023 0.595 -0.086 0.38 9 0.216 -0.029 0.067 0.199 0.50

11 0.241 0.267 -0.005 -5.730 0.40 13 0.223 0.075 0.157 -0.025 -5.410 0.38 16 0.660 0.000 -7.530 0.14 21 0.470 .080 -0.250 0.47

Pipe Safety Grates

C ::: 0.21 + 0.269 ( HW ) - 0.003 (~) e 0 B01.5

(3.5)

Bar Safety Grates

HW ~ C ::: -0.023 + 0.595 (-0-) -0.086 ( ) e B01.5

(3.6)

The coefficients of determination for Eqs. 3.4, 3.5, and 3.6 are 0.56, 0.38 and

0.63, respectively. Figures 3.1, 3.2, and 3.3 are the respective graphs of Eqs.

3.4, 3.5 and 3.6.

Another set of best fit regression equations for submerged conditions

are as follows (Eq. 21, Table C.l):

No Grates

Ce

= 0.421 + 0.102 (~) _ 0.348 (HW-TW) B01.5 0

(3.7)

Pipe Safety Grates

~ HW-T~ C ::: 0.474 + 0.080 ( 1 5) - 0.254 ( 0 e SO •

(3.8)

Bar Safety Grates

Ce

::: 0.616 + 0.063 (~) - 0.433 (HW-TW) B01.5 0

(3.9)

The coefficients of determination for Eqs. 3.7, 3.8, and 3.9 are 0.65, 0.47 and

0.67, respectively. Figures 3.4, 3.5 and 3.6 are the respective graphs of Eqs. 3.4,

3.5, and 3.6.

3.8 Regression Equations for Unsubmerged Conditions

For unsubmerged inlet conditions, ~ < 1.2, (flow regimes 1 and 2)

regression equations were developed using the data for all slopes and discharges

74

'-I U1

Ce

2.2. , i I

1.8

1.4

0.6

0.4

(lr~ 1 ( Q 1 Ce -0.061 + 0.519 l-'o ! - 0.049 l--- J

) BDL 5

Q BD l • 5

.5 1.5 2.5 3.5 4.5

2,4 2.8

0.01 I O~ I 3.6 0.4 0.8 2.0 1.2 1.6 3.2

H~I

D

Figure 3.1 Entrance Head10ss Coefficient for Submerged Conditions, No Grates (Eq.3.4)

Ce

-....J 0\

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.2

Ce 0.21 + 0.269 (HW] - 0.003 (-----.Sl_] lQ lBD1.S

Q BDl.S

0.5 -+- 4.5

0.0- I

0.0 0.4

Figure 3.2

0.8 1.2 1.6

HW D

2.Q 2.4 2.8 3.2

Entrance Headloss Coefficient for Submerged Conditions, Pipe Grates (Eq. 3.5 )

3.6

Ce

'-.J '-.J

2.21 i r

1.8

1.6 Ce -0.023 + 0.595

D - 0.086

1.4

1.2

1.0

0.8

0.4

0.2

0.0- • 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8

D

Q BDT. 5

.5

1.5

2.5

3.5

4.5

3.2

Figure 3.3 Entrance Headloss Coefficient for Submerged Conditions, Bar Grates (Eq. 3.6)

•

,

3.6

-..J 00

Ce

I 1.1r---,---,-----r---.---,---.,----r------r--......

1.

0.4

0.3

0.2

0.1

0.0

Q

BD 1. S

0.0 0.5

Figure 3.4

Ce 0.421 + 0.102 l(-Q-] -0.348(IlW-TH] BD 1. S D

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

H~I - TW ---

D

Entrance Headloss Coefficient for Submerged Conditions, No Grates (Eq. ).7)

Ce

.......

'"

I 1.1r--.---,., ---,----r---..,---,.----r------.--........

1.

0.4

0.3

0.2

0.1

0.0 0.0

_Q BD 1. 5

0.5

Figure 3.5

1.0

( Q ) () Ce 0.470 + 0.08 l---J - 0.254lHW-TWJ

BD 1. 5 D

1.5 2.0

HW - TW D

2.5 3.0 3.5 4.0

Entrance Headloss Coefficient for Submerged Conditions, Pipe Grates (Eq. 3. 8 )

4.5

Ce

00 0

1.1, ~ I

1.

u.o

0.5

0.4

0.3

0.2

0.1

0.0 0.0

Q

BDl. 5

0.5 1.0

Ce 0.616 + 0.063 (_Q_] - 0.433 [HW-TW] BD 1 • 5 D

1.5 2.0 2.5 3.0 3.5 4.0

HW - TW --D

Figure 3.6 Entrance Headloss Coefficient for Submerged Conditions, Bar Grates (Eq. 3.9)

4.5

" .

in these regimes. A summary of the regression equations and results are

presented in Table 3.11. The best fit regressions are as follows (Eq. 8, Table

C.l ):

No Grates

Ce

= -0.040 + 1.000 (HOW) - 0.276 (;;0) (3.10)

Pipe Safety Grates

C (HW) (~) e = - 0.122 + 1.046 0 - 0.262 B01.5 (3.1l)

Bar Safety Grates

Ce

= -0.213 + 1.448 (HoW) - 0.366 (;;0) (3.12)

The coefficients of determination for Eqs. 3.10, 3.11, and 3.12 are 0.81, 0.79, and


3.10, 3.11, 3.12.

3.9 Regression Equations for Submerged and Unsubmerged Combined

For the combined submerged and unsubmerged inlet conditions,

regresssion equations were developed using the data for all slopes and discharges

for the outlet control regimes. A summary of the regression equations and

results are presented in Table 3.12. The best fit regressions are as follows (Eq.

8, Table C.l):

No Grates

HW ~ Ce = - 0.187 + 0.614 (0) - 0.060 (B01.5)

Pipe Safety Grates

HW Ce = -0.172 +0.479(0) +

81

0.001 (~1 5) BO •

(3.13)

(3.14)

Table 3.11 Summary of Regression Results for Unsubmerged Conditions

Type Of B B1 B2 B3 B4 Equation Number Grates 0 R

No 2 Grates -0.053 4.070 -2.039 -0.152 0.71 8 -0.040 1.00 -0.276 0.81 9 -0.074 1.096 -0.294 -0.030 0.82

11 0.004 0.921 -0.258 -3.618 0.82 13 0.800 0.535 -0.585 0.062 -3.974 0.88 16 0.400 -0.046 -13.00 0.53

0.355 -0.045 0.29

Bar 00

2 Grates 0.035 3.881 -2.288 0.090 0.85 N

8 -0.213 1.448 -0.366 0.82 9 -0.232 1.538 -0.388 -0.033 0.83

11 -0.127 1.285 -0.318 -12.818 0.85 13 0.980 0.639 -0.797 0.110 -10.352 0.87 16 0.470 -0.033 -27.00 0.55 20 .446 .062 O.

Pipe 2 Grates 0.022 3.933 -2.111 -0.092 0.65 8 -0.122 1.046 -0.262 0.79 9 -0.153 1.125 -0.274 -0.028

11 -0.159 1.12 -0.282 4.554 0.80 13 0.464 0.605 -0.377 0.018 3.95 0.89 16 0.320 -0.017 -9.19 0.28 20 0.300 -0.023 0.13

(Xl UJ

1.1, t±

o.

Q BD l • 5

0.81

Ce -0.04 + 1. 0 (HW] - o. 276 (~] lD BD l • 5

1.0

~l 1\./1

I

1.5

2.0

///~2.5 / / / / /

3.0

_Q

BD 1 • 5

I

0.5

3.5

0.0. y < < ,< < < , < ,

0.0 0.2

Figure 3.7

0.4 0.6 0.8

HW D

1.0 1.2 1.4 1.6

Entrance Head10ss Coefficient for Unsubmerged Conditions, No Grates (Eq. 3.10)

1.8

00 +"

Ce

1.1r .. ----~--------r-------~------~------~--------r-------~-------r------~ i i i I

0.5

0.8 Ce = -0.122 + 1.046 [HDW] - 0.262

o.

0.5

4.0

0.2 0.6 0.8 1.2 0.01 V r < K ..L < 4 <

0.0 ' 1.8 1.0 0.4 1.4 1.6 HW D

Figure 3.8 Entrance Headloss Coefficient for Unsubmerged Conditions, Pipe Grates (Eq. 3.11)

00 VI

Ce

1.1, • j ) I

-0.213 + 1.448 D

- 0.366 r~)J tBD 1 • S

0.5 1.5

2.0

2.5

3.0

3.5

4.0

0.0' (r ( ( { A ( ( ( 0.0 '

Figure 3.9

0.2 0.4 0.6 0.8

HW D

1.0 1.2 1.4 1,6

Entrance Head10ss Coefficient for Unsubmerged Conditions, Bar Grates (Eq. 3.12)

1.8

Table 3.12 Summary of Regression Results for Submerged and Unsubmerged Conditions Combined

Type Of B Bl B2 B3 B4 Equation Number Grates 0 R

1 No 0.452 2.279 -2.734 0.55 2 Grates 0.485 1.365 -2.291 0.524 0.55 6 0.417 0.387 0.16 8 -0.187 0.614 -0.060 0.76 9 -0.174 0.362 0.005 0.146 0.80

11 -0.188 0.614 -0.060 0.159 0.76 13 0.131 0.206 -0.005 -0.006 1.340 0.75 16 0.211 0.073 9.200 0.26

Bar Grates

co 8 -0.025 0.643 -0.111 0.78 0'\

9 -0.004 0.301 -0.029 0.211 0.82 11 -0.024 0.644 -0.110 -0.538 0.78 13 0.370 0.216 -0.123 0.008 2.369 0.77

0.290 0.070 7.580 0.28

Pipe Grates

8 -0.172 0.479 0.001 0.73 9 -0.004 0.311 0.036 0.110 0.74

11 -0.143 0.477 0.000 -6.193 0.74 13 0.274 0.149 -0.064 0.013 -5.715 0.70 16 0.230 0.100 -7.900 0.36

Bar Safety Grates

Ce

= - 0.025 + 0.643 ( HDW) 0.111 (~1 5) BD •

(3.15)

The coefficients of determination for Eqs. 3.13, 3.14, and 3.15 are 0.76, 0.73, and


3.13,3.14, and 3.15.

Figures 3.10 - 3.13 present a comparison of equations of the form

Ce

= f{ HDW, ~) considering submerged conditions, unsubmerged condi

tions, and combined submerged and unsubmerged conditions. Figure 3.13 shows

graphs of Eq. (3.4) for submerged conditions, Eq. (3.10) for unsubmerged

conditions, and Eq. (3.13) for submerged and unsubmerged combined. Each of

these curves in Figure 3.13 are for ~1 5 = 1.0 and no grates. Similar graphs BD •

of Eqs. (3.4, 3.10, and 3.13) for ~1 5 = 3.0 and no grates are shown in Fig. BD •

3.14.

Figure 3.15 shows graphs of Eq. (3.6) for submerged conditions (bar

grates), Eq. (3.15) for unsubmerged conditions (bar grates), and Eq. (3.15) for

submerged and unsubmerged combined (bar grates). These graphs are for

----.SL = BD 1•5

3.16.

1.0. The same set of graphs for ~ = 3.0 are presented in Fig. BD1.5

87

CJ) CJ)

Ce

1.1, i i ))})A}}}} I

0.6

0.3

Ce -0.187 + 0.614 [~) - 0.060

~ BO l • S 0.5

1.0 1.5 2.0 2.5

3.0 3.5 4.0 4.5 5.0

0.01 ItttttttAt

0,0 ' 0.4 1.2 3.2 0.8 2.0 1.6 2.4 2.8 3.6

Figure 3.10

H~I

D

Entrance Head10ss Coefficient for Submerged and Unsubmerged Conditions Combined, No Grates (Eq. 3.1~

CXl \.0

Ce -0.172 + 0.479 D + 0.001

Ce 5 O.

0.01 4 0.0 0.4 0.8 1.2 1.6

HW D

2.0

-L BD 1• 5

2.4

0.5 -+ 4.5

2.8 3.2

Figure 3.11 Entrance Headloss Coefficient for Submerged and Unsubmerged Conditions Combined, Pipe Grates (Eq. 3.14)

I

3.6

\0 o

Ce

1.1, 1 ; > i I ; ; ; , ; > I

1.

0.9

0.8

0.1

0.2

0.1

_Q BD l .5

0.5 1.0 1.5 2.0 2.5

3.5 4.0 4.5 5.0

Ce -0.025 + 0.643 [HW] - 0.111 r~] D lBD1.5

0.0' L ( { r l ( { (" l

0.0 0.4

Figure 3.12

0.8 1.2 1.6

mJ D

2.0 2.4 2.8 3.2

Entrance Head10ss Coefficient for Submerged and Unsubmerged Conditions Combined, Bar Grates CEq. 3.15)

I

3.6

\0 I-'

2.2a , 1 •

2.0

1.8' UNSUBMERGED

1.0

Eq. (3.

0.0' <I <

0.0 0.4 0.8 1.2

SUBMERGED /'

Eq. (3.13) //

/'/ //

~/ .

~§/

Eq. (3.4)

1.6

Q

HW D

2.0

1.0

2.4 2.8 3.2

, 3.6

Figure 3.13 Entrance Headloss Coefficient, BDl.S

No Grates (Eqs. 3.4, 3.10, 3.13)

1.0 , for the Outlet Control Conditions,

\,0 N

Ce

2.2. • iii i •

2.0

1.81

UN SUBMERGED SUBMERGED

//

// EQ.(/,/

0.8 //

//

Eq. (3.4)

// .--!L llD 1 . 5

3.0

0.2 Eq.

0.4 0.8 0.0' I <: / O~ I

, 3.2 3.6 1.2 1.6 2.0 2.4 2.'

D

Q Figure 3.14 Entrance Head10ss Coefficient, BD1.5 = 3.0, for the Outlet Control Conditions,

No Grates (Eqs. 3.4, 3.10, 3.13)

\0 w

2.2 r iii i i :::I

2.0

1.8' UNSUBMERGED SUBMERGED

Ce

0.6

0.4 // 0.2

0.0 0.0 0.4 0.8 1.2 1.6

Q

Figure 3.15 Entrance Head10ss Coefficient, BD 1 •5

Bar Grates (Eqs. 3.6, 3.12, 3,15)

Eq.

Eq. 0.6)

1.0

2.0 2.4 2.8 3.2

D


3.6

Ce

1.0 +:--

2.2

2.0

1.8'r UNSUBMERGED

1.6

// /'

SUBMERGED

1.4

1.2

EQ.(3.1SY/

//' 1.0

.... / '/ Eq. (3.6)

//

Eq.

0.2

0.4 0.8 0.0' L <

O 0

Lp , iiI" ' . ... 1.2 1.6

HW D

Q Figure 3.16 Entrance Head10ss Coefficient, BD1.5

Bar Grates (Eqs. 3.6, 3.12, 3.15)

~ 3.0 BD1. 5

,

2.0 2.4 2.8 3.2 3.6


CHAPTER 4 CLOGGING TESTS - BOX CUL VER T

To demonstrate the effect of clogging, the open surface area of the

safety grates was covered with boards. The simulated clogging ranged from 15

to 90 percent of the open surface area of the grates (Figs. 4.1-4.3). The bar and

pipe safety grates were covered with boards (simulating clogging) in intervals of

15 percent of the original open surface area. The clogging was placed in three

different patterns; from top to bottom, from bottom to top, and randomly

posi tioned.

4.1 Test Procedure for Clogging

The clogging tests were used to determine the relative effects of

various percentages of clogging. Empirical tests were difficult due to the

unpredictability of field conditions. The measurements were made under free

outfall conditions. The steps in the clogging tests were the following:

1. A constant discharge was established where the water surface was at or above the top of the culvert.

2. A 15 percent clogging was placed at the top of the grate and all measurements were taken after the water flow stabilized. The sequence of measurements were the same as the free outfall tests.

3. The rest of the clogging was placed from the top downward until 90 percent of the grate was clogged. All measurements were taken at each different percentage of clogging.

4. The entire procedure was repeated with the clogging placed from bottom to the top of the safety grates.

4.2 Relationship of Headwater - Percent Clogging

Flgures 0.1 through 0.11 are graphs illustrating the headwater/depth

( H~ ) versus percentage clogging for the plpe safety grates on the box culvert.

9S

1.0

'"

15i, C logg i ng

Figure 4.1

•

30% Clogging

Clogging From Bottom To Top

•

• • •

• -• , -0

• • • • • • • I • • • , I • • • • • • • -0

-• • • • • , • • • • • • • •

0

• • • •

•

"

•

•

..

•

;: !

! ! • -

• , , I • • • ! , -! -• • • • •

•

•

For slopes of 0.0008 and 0.0063, the results of placing the clogging from top to

bottom and from bottom to top on the pipe grates are shown in Figs. D.l through

D.9 for several discharges. Figures D.9 through D.ll show the effect of various

culvert slopes for the same or similar discharges. Basically, the steeper slopes

do have smaller ( HDW) for the same discharges. Obviously, the general trend was

an increase in headwater depth with an increase in percentage of clogging.

Below 45 percent clogging, the headwater is affected very little by the clogging,

while above 45 percent, the headwater is not only affected by the clogging, hut

also by the placement of clogging. The headwater depth increases much more

rapidly when the clogging is placed from the top downward than placing clogging

from the bottom upward.

The clogging tests for the bar safety grates were only conducted

using a .0063 slope. Test data from top downward and from bottom upward

clogging are presented in (Figures D.12 through [,.16) with constant discharges.

As for the clogging tests on pipe grates, the headwater increased very little for

clogging less than 45 percent but increased rapidly for clogging greater than 45

percent. At the higher percentage of clogging, the headwater was higher for

clogging starting at the top than for clogging starting at the bottom. Figures

D.17 through D. 19 present clogging data for both the pipe and bar safety grates

under similar conditions (slope and discharge).

4.3 Relationship of Entrance Headloss Coefficient - Percent Clogging

The effects of the percentage of clogging and the placement of

clogging for the pipe safety grates are illustrated in Figures D.20 through D.35.

Figures D.20 through D.23 are the relationships of C versus percent e

clogging for a culvert slope of 0.0008 and for the discharges of 9.02, 9.62, 10.7,

and 11.2 cfs, respectively. Figures D.21 and D.23 illustrate the effect of the

99

position of clogging from top to bottom as opposed to clogging from bottom to

top. The effect of clogging from top to bottom has a much more pronounced

effect on increasing the Ce for larger percentages of clogging. Figure D.24

shows the effect of increasing C for a culvert slope of 0.0063 and dishcarges of e

8.04,9.10,10.04 and 11.07 cfs.

Figures D.25 through D.28 are for the purpose of illustrating the

effect of various culvert slopes for various percentages of clogging using pipe

grates. Figure D.25 shows Ce versus percent clogging for culvert slopes of

0.0008 and 0.0128 and each with a discharge of 9.02 cfs. This figure clearly

illustrates the drastic effect of increasing the Ce

for larger percentages of

clogging for the mild slope. This is also illustrated in Figure D.26 for the slopes

of 0.0063 and 0.0128. Figures 0.27 shows the relationship for the three slopes,

0.0008, 0.0063, and 0.0128.

The effect of the placement of the clogging (bottom 1/3, middle 1/3,

or top 1/3 of grate) on Ce for various discharges and percentages of clogging are

illustrated in Figures D.29 through D.31. Discharges of 7.94, 9.03, 10.00, and

10.82 cfs were considered for the various percentages and placements of

clogging. Similar conclusions as before to the placement of clogging were found.

Clogging closer to the tope of the grate causes larger values of Ceo

A comparison of the effect of clogging for the bar grates and the

pipe grates was also performed. Figure D.32 shows the relationship of C versus e

percent clogging for a culvert slope of 0.0063 and discharges of 9.09, 10.11 and

11.05 cfs for the bar safety grate. The larger dishcarges result in large C e

values for the same percent clogging as shown before for the pipe grates.

Figures D.33 through D.35 show a comparison of the effect of the pipe grates as

100

opposed to the bar grates for various percentages of clogging, for a culvert slope

of 0.0063 and discharges of approximately 9, 10, and 11 cfs.

For the discharge of 9 and 10 cfs (Figures D.33 and D.34) it is

difficult to say which Type grate had the greatest effect, except for the 90

percent clogging. However, for the discharge of 11 cfs (Figure D.35), the effect

was definitely greater for the bar safety grates.

101

CHAPTER 5 PIPE CULVERT RESULTS

The experimental tests of the safety grates for the pipe culvert

model are presented and analyzed in this chapter. Figures are presented to

compare the hydraulic effect with and without the pipe safety grates under

various combinations of slopes, discharges, headwater depths, and tailwater

depths. For comparison, the experimental tests without safety grates are also

included on selected figures. Discussions of the tests are presented describing

changes in the hydraulics due to the safety grates. Regression equations are

presented for predicting entrance head loss coefficients for different conditions

of outlet control. Also, regression equations are presented for determining

headwater-discharge relationships for inlet control.

Geometric similarity (of the corrugations) is not completely satisfied

in this experiment. The safety grate similarity is easily satisfied by the

construction of a 1:4 scale model grate. However, geometric similarity of

corrugations between the 15-inch diameter model pipe culvert and a prototype

culvert is not possible due to the constant corrugation sizes in helical corrugated

metal pipe for all pipe diameters. In other words, the relative size of the

corrugations to the pipe diameter decreases with increasing diameter. Further

more, the angle of corrugations for helical pipe as fabricated, is not constant

throughout the various pipe diameters.

Kinematic similarity is partially upheld for reasons similar to those

for geometric similarity. The velocity ratio is satisfied for increasing diameter.

However, because of constant corrugation size, complete kinematic similarity

cannot be satisfied. Satisfaction of dynamic similarity is not complete for

103

reasons also due to the constant pipe corrugations. The inability to precisely

model the corresponding lengths and velocities of model and prototype may limit

the application of regression equations for C • Data for the regression analysis e

is listed in Appendix G.

5.1 Entrance Headloss Coefficient With and Without Safety Grates

A direct comparison of the entrance headloss coefficient with grates

installed and the entrance headloss coefficient without grates for the mild

slopes, 0.0007 and 0.008, are presented in Figures E.l and E.2. For the milder

slope, 0.0007, the entrance headloss coefficients for grates installed are greater

than those without the grates. This clearly indicates that the grates do have an

effect; however, the effect does not seem to be major. For the steeper slope,

.008, the entrance headloss coefficients are significantly greater for the lower

discharges and seem to have little effect for the higher discharges. In fact, the

effect of the grates on the entrance headloss coefficient at the high discharges

was insignificant.

5.2 Headwater-Discharge Relationships

The headwater-discharge relationships for inlet control are shown in

Figures E.3, E.4, and E.5 for the slopes 0.0007, 0.008, and 0.05, respectively.

Th 1 tt d HW 0 with and without the safety grates e curves are poe as D vs ~

installed. The safety grates do showDa~ increase in Hri which is relatively

constant throughout the range of discharges.

Regression equations for inlet control were developed using the

general form

HoW = ao + at ( D~.5) + a2 ( D~.5 ) + ••• + an ( D~.5 )n (5.1)

104

where HOW is the dependent variable and o is the independent variable. 0 2. 5

The results of the regression analysis are summarized in Table 5.1 for no grates

and the grates installed. As an example of the equations developed, the simplest

form for the no grates and grates installed are, respectively,

HW 0 o = 0.166 + 0.385 ( 0 2.5 ) (5.2)

and

HW 0 o = 0.158 + 0.389 ( 0 2•5 ) (5.3)

5.3 Entrance Headloss Coefficient - Headwater Relationship

Entrance head loss coefficient - headwater relationships are plotted in

Fig~. E.6 through E.13 for various flow regimes of the two slopes, 0.008 and

0.0007. Figure EJ, illustrates the C e vs H6' for flow regimes 1, 2, 4A anc' 4B

with and without the grates for the slone of 0.008. Figures E.7, E.8, E.9, and

HW . E.ll are separate graphs of Ce vs D for flow regImes, 1, 2, 4A, 4B

respectively. Figures E.ll, E.l2, and E.l3 are for the slope, of 0.0007,

considering flow regimes 4A and 4B combined, 4A and 4B respectively. Probably

the most significant conclusion from these graphs is that C is significantly e

affected by H;' . The entrance headloss coefficient for safety grates installed

are greater than for no grates for unsubmerged inlets. The effect of safety

grates on the entrance headloss coefficient is relatively constant for submerged

inlets. The entrance headloss coefficient with and without grates installed,

increases substantially for an unsubmerged inlet.

5.4 Entrance Headloss Coefficient - Discharge Relationship

Entrance headloss coefficient-discharge relationships (C vs °2" 5 ) e O.

are plotted in Figures E.l4 through E.19 fer various flow regimes for the two

slopes, 0.008 and 0.0007. Figure E.l4 illustrates the Ce vs 0~.5 relationship

105

Table 5.1 Headwater-Discharge Relationships for Inlet Control

(a) No Grates, 31 Data Points

Equation a a 1 a 2 0 a3 a 4 a 5 R

1 0.166 0.385 0.9868

2 0.516 0.144 0.036 0.9923

3 -0.129 0.845 -0.190 0.022 0.9943

4 2.267 -2.606 1.524 -0.331 0.026 0.9977

5 0.236 1.088 -1.00 0.482 -0.099 0.007 0.9980

(b) Grates Installed, 30 Data Points

Equation ao a 1 a2 a3 a 4 a 5 R

1 0.158 0.389 0.9839

2 0.645 0.053 0.049 0.9941

3 -0.082 0.846 -0.206 0.025 0.996

4 1.656 -1.656 +1.035 -0.230 0.019 9.9983

5 -0.774 2.775 -1.999 0.749 -0.132 0.009 0.9990

106

for flow re~imes l, 2, 4A, and 4B with and without grates for the slope of 0.008.

Figures E.l5, E.l6, E.l7 and E.l8 are separate graphs of C vs ~2 5 for flow e D'

regimes l, 2, 4A and 4B. Figure E.l9 shows the relationship for flow regimes 4A

and 4B for a slope of 0.0007. The most significant conclusion is that the

entrance headloss coefficient increases substantiaHy for increased discharges for

submerged entrances.

5.5 Headwater-Tailwater Relationships

For the tailwater tests, the tailwater ranged from free outfaH

conditions to fuH flow. Figures E.20 through E. 23 show the relationship of HW D

vs ~W with and without grates instaHed. Figure E.20 shows the relationships for

a discharge of 5.6 cfs and a slope of 0.0007. Figu res E.21, E.22, and E.23 are for

the slope, of 0.008, and discharges 3.6, 4.5, and 5.5 cfs. The headwater depth is

unaffected by rising tail water depths less than critical depth. The flatter the

culvert slope, the greater the effect of tailwater depth on the headwater depth.

5.6 Regression Equations for Submerged Inlet Conditions

Regression equations were developed for the entrance headloss

coefficient for submerged inlet conditions, HDW ~1.2. The various regression

equations considered are listed in Table 5.2. The resulting coefficients, B 0' ... ,

Bn for each of the regression equations are listed in Table 5.3 for no grates and

in Table 5.4 for the grates instaHed.

From the viewpoint of design considerations regression equations for

C should be at the simplest form with the least number of independent e

variables. Equation 13 in Table 5.2 is one of the simpler forms considered. The

regression equation for no grates is

C = - 0.119 + 0.364 ( °25

) - 0.133 (HW-TW) e D' D

(5.4)

107

Table 5.2 Regression Equations for Pipe Culvert Equation

1. C ~ ~ 2 ~3 ~ = Bo+Bl (02.5)+B2 ( 0 2.5) +B3( 0 2•5 ) +B4( 0 2•5 ) e

2. Ce = Bo + Bl (~) + B/So)

3. Ce BO+Bl{~)

4. Ce = ~2 Bo+Bl (02•5 )

5. Ce = HW ~ Bo + Bl (O) + B2 ( 0 2•5 )

6. Ce = ~2 HW Bo + Bl ( 0 2•5 ) (0)

7. Ce = (~f2{HW) {~f2 Bo + Bl 0 2•5 0 + B2 0 2•5

8. Ce = (~f2 (HW) {~f2 {~f2 ( ) Bo + B1 0 2•5 D + B2 0 2•5 + B3 0 2•5 So

9. Ce = Bo + B1 (~f2 0 2•5

10. Ce = HW ~ Bo + B1 (O) + B2 ( 0 2•5 ) + B3 (So)

11. Ce = HW2 ~ ~ Bo + B1 (0) + B2 ( 0 2•5 ) + B3 ( 0 2•5 ) + B4 (So)

12. Ce B + B HW HW 2 ~ ~ 2 a 1 (O) B2 (O) + B3 ( 0 2•5 ) + B4 ( 0 2•5 ) + B5 (So)

13. Ce = ~ HW-TW B a + B 1 ( 0 2•5 ) + B2 (---0-- )

108

•

Table 5.3 Regression Results for Submerged Conditions, No Grates, 90 Data Points

Equation B B1 B2 B3 B4 BS R 0

-----.----------<----------~-----.-------~

1 9.1511 -11.4430 5.5038 1.1215 0.0835 0.823 2 -0.0443 0.2623 17.1550 0.877 3 0.1448 0.230 0.811 4 0.5071 0.0352 0.798 5 0.0853 0.0937 0.1929 0.828 6 1.0738 -1. 0640 0.504 7 1.1041 1.2168 -4.2980 0.813 8 1.1996 1.2439 -6.3351 205.8080 0.908 9 1.1585 -2.5967 0.758

10 -0.1160 0.1040 0.2221 17.6738 0.897 11 -0.7412 0.0321 0.6744 -0.0715 20.1376 0.912 12 -1.3816 1.0003 -0.2317 0.4842 -0.0398 21.1668 0.937 13 -0.1190 0.3640 -0.1330 0.860

--------,--------------- .. --------~

Table 5.4 Regression Results for Submerged Conditions, Gra tes Installed, 87 Data Points

Equation B B1 B2 B3 B4 B5 R 0

-------- -----------------_._---------_._----------

1 13.4540 -16.4665 7.6996 -1. 5431 0.1134 0.896 2 0.1165 0.2314 11.2522 0.913 3 0.2414 0.2102 0.877 4 0.5743 0.0319 0.864 5 0.2156 0.0501 0.1881 0.883 6 1.1295 -1.1600 0.582 7 1.1568 0.6726 -3.4833 0.855 8 1. 2298 0.6702 -4.9686 150.2440 0.921 9 1.1951 -2.6103 0.834

10 0.0869 0.0541 0.2079 11.4102 0.920 11 -0.4294 0.0164 0.5609 -0.0549 13.4505 0.931 12 -0.7092 -.5799 -0.1356 0.3933 -0.0279 13.7285 0.944 13 0.0190 0.3230 -0.1110 0.920

109

and for grates installed is

C e :: ~ HW-TW 0.019 + 0.323 ( D2.5) - 0.111 ( D ) (5.5)

The coefficients of determination are 0.86 for Eq. (5.4) and 0.92 for Eq. (5.5).

Equation (5.4) is plotted in Fig. 5.1 and Eq. (5.5) is plotted in Fig. 5.2. A

comparison of the two equations with and without grates is given in Figure 5.3.

The values of C with grates are clearly greater than those without grates. e

Another simple equation is Eq. 2 in Table 5.2. The regression

equation for no grates is

C e o :: - 0.044 + 0.262 (-2"-5-) + 17.155 (5 )

D' 0


(' Ce :: 0.117 + 0.231 (D2.5 ) + 11.252 (So)

(5.6)

(5.7)

The coefficients of determination for these equations are 0.877 for Eq. (5.6) and

0.913 for Eq. (5.7). These two equations (5.6) and (5.7) are plotted in Fig. 5.4 for three

example slopes, So :: 0.0005, 0.005, and 0.0 I. These curves indicate that the

differences in C for no grates and grates installed decrease for the larger slopes e

and for larger values of ( D~.5 ). An even simpler form for Ce is Eq. 3 in Table 5.2. The regression


C :: 0.145 + 0.230 (~2 5) e D'

(5.8)


C :: 0.241 + 0.210 (~2 5-) e D'

(5.9)


0.88 for Eq. (5.9). These equations are plotted in Fig. 5.5.

110

. "

t-' t-' t-'

Ce

Ce -0.119 + 0.364 - 0.133

1.0 1.5 2.0 2.5 3.0 3.5 ".0 4.5 HW - TW

D

Figure 5.1 Entrance Headloss Coefficient for Submerged Conditions, No Grates (Eq. 5.4)

t-' t-' N

Ce

Ce 0.019 + 0.323 [~J - 0.111 l'HW-TW] D2 • 5 D

0.1

0.01 ::=-:-:,.,:-=-t:>. ~ ,::=-:-:,., :::c:.... I 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

HvJ - TW D

Figure 5.2 Entrance Headloss Coefficient for Submerged Conditions, Grates CEq. 5.5)

t-' t-' W

C e

1.11--...... ----,. .......... ., ............ ,.----~::::::-:::::::----T" .. --------.,-:::----.... t:--.... ----., .... ------.. ~ '< ¥C ;:::: <:::; I

1. (GRATES

--~.5

-----...... (NO GRATES 4.5

---......--.. -.......

-......----......-....... -"""-"""-........-.......

-......---...... ---------...... ----........ ___ 2.

-.......-....... 2. __

-"""-........-........ -........----........

0.8

0,7

0.5

-........-.......----------

-...... -- --....g.",~ = 1. D~ ___ __

~ ;>, ~::::::::~~~~~~::==::~~~~~~;::;;=~~:::-.......~~~~------~s_------~~----~ :> 0.0' 0.0

0.1

0.5 1.0 1.5 2.0

Hltl -D

2.5 3.0 3.5 4.0 4.5

Figure 5.3 Entrance Headloss Coefficient for Subme Conditions, Grates and No Grates (Eq s. 5.5, 5.4 )

Ce

...... ...... ..j::'-

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5 (NO GRATES ) -0.044 + 0.262 [D2Q.S] + 17.16

0.4 (GRATES-------) Ce : 0.117 + 0.23 + 11.25 (So)

0.3 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Q

~

Figure 5.4 Entrance Headloss Coefficient for Submerged Conditions, Grates and No Grates (Eq s. 5.7, 5.6)

,..... ,..... I..n

Ce

1.1.r----------r---------1i---------,----------r----------r----------r---------~--------~~--------4 j a;: I

1. (NO GRATES --)

0.9: ( GRATES -------)

0.8

0.7

0.4

0.3

0.2

0.1

0.0 0.0 0.5 1.0

Ce = 0.145 + 0.23 [~J D2.5

Ce = 0.24 + O. 21 [~J D2 .5

1.5 2.0 Q

D 2.5

2.5 3.0 3.5 4.0

Figure 5.5 Entrance Headloss Coefficient for Submerged Conditions, Grates and No Grates CEq s. 5.9, 5.8 )

4.5

5.7 Regression Equations for Submerged and Unsubmerged Inlets

Combined

Regression equations were developed for the entrance headloss

coefficients for submerged and unsubmerged inlet conditions. The various

regression equations considered are listed in Table 5.2. The resulting coeffi-

cients, B , ... , B for each of the regression equations are listed in Table 5.5 for o n

no grates and in Table 5.6 for the grates installed. The simple forms of the

equations for C used for the submerged conditions are also considered. e

The first set of equations are 13 in Table 5.2. The regression


o HW-TW Ce = - 0.115 + 0.350 ( D2•5 ) - 0.109 ( D ) (5.10)


Ce = 0.187 + 0.252 (~) - 0.062 (HWDTW) (5.11)

The coefficients of determination for these equations are 0.90 for Eq. (5.1 0) and

are 0.92 for Eq. (5.11). Equation (5.10) is plotted in Figure 5.6 and Eq. (5.11) is

plotted in Fig. 5.7. A comparison of the two equations for no grates and grates

installed is given in Fig. 5.8.

Utilizing Eq. 2 in Table 5.2, the regression equation for no grates is

C = - 0.176 + 0.302 (~ ) + 15.705 (S ) (5.12) e D. 0


C = 0.133 + 0.227 (+5 ) + 10.754 (S ). (5.13) e D • 0


0.93 for Eq. (5.13). These two equations are plotted in Fig. 5.9 for four example slopes

0.0005, 0.005, 0.010 and 0.015. These curves clearly indicate that the differenc-

es in C for no grates and grates installed decrease for the larger slopes and for e

larger values of ( D~.5 ).

116

Table 5.5 Regression Results for Submerged and Unsubmerged Conditions Combined, No Grates, 106 Data Points

Equation B1 B2 B3 B4 B5 B6 R

---------------------_._-----.--.. ---.--~--~ ---------.----~

1 0.1940 0.0414 0.0417 0.0191 -0.0046 0.886 2 -0.1764 0.3024 15.7059 0.901 3 -0.0003 0.2721 0.874 4 0.3925 0.0446 0.848 5 -0.0329 0.1374 0.2016 0.894 6 1.1026 -1.4156 0.563 7 1.0012 0.1119 -1.6237 0.730 8 1.0452 0.0637 -2.5535 109.9870 0.747 9 1.0151 -1.5487 0.730

10 -0.2230 0.1489 0.2279 16.7126 0.924 11 -0.5012 0.0368 0.5103 -0.0459 17.8104 0.926 12 -0.6018 0.7528 -0.1697 0.1509 0.0109 17.5524 0.Q39 13 -0.1150 0.3500 -0.1090 O.gOO

Table 5.6 Regression Results for Submerged and Unsubmerged Conditions Combined, Grates Ins ta :.led • 101 Data Points

Equation B B1 B2 B3 84 B5 R 0

~-----.----------.. --.-------------.------~-~---~--------

I 1.4217 -1.3742 0.7437 -0.1453 0.0100 0.914 2 0.1329 0.2266 10.7540 0.926 3 0.2530 0.2062 0.g04 4 0.5471 0.0341 0.895 5 0.2431 0.0491 0.1800 0.908 6 1.1242 -1.2200 0.631 7 1.0594 -0.3908 -0.8262 0.703 8 1.0926 -0.4388 -1.4950 80.3584 0.720 9 1.0092 -1.0820 0.693

10 0.1197 0.0540 0.1982 10.9763 0.932 11 0.1074 0.0129 0.2386 -0.0060 11.0500 0.930 12 0.0765 0.3324 -0.0765 0.0685 0.2070 10.8565 0.935 13 0.1870 0.2520 -0.0620 0.920

117

t-' t-' C):)

Ce

Ce = -0.115 + 0.35 0.109 fHW-TWl l D )

1.1 I ~ 'fZ: f <::::: ~ acc:::t I

1.

0.0 0.5

Figure 5.6

2.0 2.5 3.0 3.5 4.0

D

Entrance Head10ss Coefficient for Submerged and Unsubmerged Conditions Combined, No Grates CEq. 5.10)

4.5

..... ..... '"

4.5

,., 4."

Q Hw-'fw

C "0.181 + O.I"~) • O.06I( =P ) e 1)2.

5

'" 4. 0 1)2.

3. 75

Ce o.S'

D""

0.2

0.1 0.0 20 2' 3.0 3.' 0.0 0'

00 0.' ,.0 ,.S . . . ~~. 1~ ----- ------D

Figure 5.7 d1 C ff

' 'ent fo~ Subwerged and "n'Ubroer,ed ConditiOn' combined,

Entrance Rea oSs oe LCL" ~ Grates (Eq· 5.

11)

t--' N o

1. (NO GRATES _

S __ ) (GRATE ___ _ =----"---==----A. = 2.5

----~ ~.5

0.8 =-----------..0._____________ ~

3. ~.

--_Q = '-'---------------=---~ -----

]. ~ 0.41=--_________ --= ---==---___ _

______ 1.

0.0 0.0 0.5 1.0 1.5 2.0 2.5

Hvi - TW

Figure 5.8

D

Entrance Headloss Coefficient for Submerged Grates and No Grates (Eqs. 5.11, 5.10)

3.0 3.5 4.0

and Unsubmerged Conditions Combined,

4.5

t-' N t-'

Ce

1.1r--~----r-------'--------r-------'--------~------~~~~~i./.~~~~'------4 > > > >.» »> I

1.

0.9

0.8

0.7

0.6

0.5

0.4

0.0' < < <

0.0 0.5 1.0

0.0005

(GRATES -------) Ce 0.133 + 0.227 (D2~S] + 10.75 (So)

(NO GRATES

1.5 2.0

Ce -0.176 + 0.302 [D 2Q. S] + 15.7 (So)

Q .~

2.5 3.0 3.5 4.0

Figure 5.9 Entrance Headloss Coefficient for Submerged and Unsubmerged Conditions Combined, Grates and No Grates (Eqs. 5.13, 5.12)

, 4.5

The simplest form of the equation for C is 3 in Table 5.2 The e

regression equation for no grates is

C = -0.0003 + 0.272 ( ~ 5 ) e O.

(5.14)


Ce = 0.253 + 0.206 ( 0~.5 ) (5.15)


0.904 for Eq. (5.15). These equations are plotted in Fig. 5.10.

Figure 5.11 is a comparison for no grates of Eqs. 5.12 (for So =

0.0007 and 0.008), Eq. 5.14 and Eq. 5.16 (from Eq. 4 in Table 5.2),

Q 2 C e = 0.392 + 0.045 ( 0 2.5 )

The coefficient of determination for Eq. 5.16 is 0.85.

122

(5.16)

~ N W

Ce

1.1, 1 )jP I

~--'---.-- )

(NO GRATES ---

0.5

//

//

0.2

0.1

Ce 0.253 + 0.206

-0.000 + 0.272

//

// //

// //

~~ /~ /

0.0'« , 0.0 0.5 1.0 1.5 2.0

Q

D .

2.5 3.0 3.5 4.0

Figure 5.10 Entrance Head10ss Coefficient for Submerged and Unsubmerged Conditions Combined, Grates and No Grates (Eqs. 5.15, 5.14)

4.5

t-' N .l>

Ce

1.1

1.

0.9

I 0.8

0.7

I

0.6 2 Ce 0.393 + 0.045 (-)

#'//~ /..::~/

/.~/ / , ~

0.5 1.0 1.5

~/ ,

~/~ / '/

///// ~,~//

-;Z/;/ /'

/~.~ ~ Ce = 0.0 + 0.27[~J #' / D

2

•

5

S1 0.008

~ S2 0.0007

. -)

( ___ ) ~0.176 + 0.302 [IfsJ + 15.7 (S2)

(---) Ce -0.176 + 0.302 [rfsJ + 15.7 (S1)

2.0 2.5 3.0 3.5 4.0 Q

D 2.5

Figure 5.11 Entrance Head10ss Coefficient for Submerged and Unsubmerged Conditions Combined, No Grates (Eqs. 5.12, 5.14, 5.16)

4.5

CHAPTER 6 CONCLUSIONS

6.1 Conclusions for Box Culvert Model

6.1.1 Pipe Safety Grates

Based on the experimental study for the box culvert using pipe safety

grates, the following conclusions are made:

1. For steep and mild slope regimes with full barrel flow, the pipe

safety grates increased the entrance headloss only slightly. The

comparison of Ce values with and without the safety grates

(Figs. B.1 - B.5) indicate only a small increase in the entrance

headloss coefficient for outlet control with slopes .0008 and

.0063 and for inlet control with slopes .0108 and .0128. For

slope .0013 (outlet control) the entrance headloss coefficient

was not affected by the safety grates.

2. For full flow conditions and for submerged entrance conditions

(Type ~A and ~B flow regimes), the pipe safety grates have

little effect on the entrance headloss coefficient. Referring to

the comparison plots of the Ce values with and without safety

grates installed (Figures B.1 - B.5), the data points for Type ~A

and ~B flow regimes appear scattered and the regression lines

generally have the lowest correlation coefficients (Table 3.1).

3. The headwater depth was not measurably affected by the

installation of the pipe safety grates. Referring to the head

water versus discharge plots (Figures B.9 -B.13), the data points

125

with the safety grates plotted almost identical with the data

points without safety grates. Referring to the headwater

versus tail water plots (Figures B.33 - B.47), the data points with

and without the pipe safety grates are approximately the same.

4. Conventional hydraulic design of culverts uses a constant

entrance headloss coefficient for a11 Types of flow conditions.

However, based upon this experimental study, the entrance

headloss coefficient can vary with headwater, discharge, tail-

water, and consequently with flow regime. From the entrance

headloss coefficient versus headwater plots (Figures B.17 -

B.21), the entrance headlosses increased with an increase in

headwater depth. The increase in headwater was due to

increases in tail water and/or discharge. The maximum en

trance headloss coefficients were obtained for (~W) greater

than approximately 1.5. The lower C values were genera11y e

for outlet control with an unsubmerged entrance. The higher

entrance head loss coefficients were for fu11 culvert flow condi-

tions.

5. The entrance head loss coefficient can be determined by re-

gression equations based on combinations of headwater, tail-

water, slope, and dishcarge. The regression equations with the

best fit were for outlet control with unsubmerged entrance

conditions (Type 1 and 2 flow regimes) and for submerged

entrance with outlet control conditions (Type 4B flow regimes).

6. When the pipe safety grates experience dogging greater than

45 percent, the headwater and the entrance headloss coeffici-

126

ents increased dramatically (Figures B.l - B.ll and B.20 - B.31,

respectively), and the efficiency of the culvert was substanti-

ally decreased. The increase in headwater and entrance head-

loss coefficient was higher for the larger discharges. While

there is an obvious propensity for clogging with safety grates,

this study did not incude an evaluation of that propensity.

6.1.2 Bar Safety Grates

Based on the experimental testing program for the bar safety grates,

the following conclusions are made:

1. The entrance headloss coefficients for the bar safety grates

were higher than without the safety grates. The comparison of

entrance headloss coefficients with and without bar safety

grates (Figs. B.7 - B.9) indicate an increase in C for aU flow e

regimes tested on slopes 0.0008 and 0.0108 and an increase in

Ce for Type 2 and 4B flow regimes for the slope 0.0063. The

data points for Type 1 and 4A flow regimes were rather

scattered for slope 0.0063.

2. Along with the increase in the entrance headloss coefficients,

there was a corresponding increase in the headwater due to the

bar safety grates. Referring to the headwater versus discharge

plots (Figs. B.14 - B.16), the bar safety grates caused higher

headwaters than with no safety grates under similar condtions.

The increase in headwater was also evident in the headwater

versus tail water plots (Figs. B.34 - B.47). The headwater depths

with the bar safety grates were higher- than the headwater

depths without the safety grates for the same discharge and

127

tailwater. The increase in headwater due to the bar safety

grates was less obvious for higher tailwater depths. The higher

tail water depths were less stable in this experiment, and thus

less accurate.

3. The entrance head loss coefficient with the bar safety grates

were also varied with headwater, discharge, tailwater, and flow

regime. The entrance headloss coefficient increased with an

increase in headwater as evident by the entrance headloss

coefficient versus headwater plots (Figs. B.22 - B.24). The

maximum Ce values were again obtained for HDW greater than

1.5. Outlet control with unsubmerged entrance (Type 1 flow

regime) and full flow condit.ions (Type 4A flow regime) had the

lowest and highest entrance headloss coefficients, respectively.

4. The developed regression equations for the bar safety grates

can he used to determine the entrance headloss coefficients for

Type I, 2, 4B, and to a lesser extent, 4-A flow regImes (Table

3.5). For the bar safety grates, the empirical curves (Table 3.6)

were also determIned for inlet control flow conditions <Type 3A

flow regime).

5. The bar safety grates experienced the same response as the

pipe safety grates did to clogging. The entrance headloss

coefficient and headwater increased rapidly above 45 percent

clogging and the increase was greater for the higher discharges

(Figs. B.15 - B.12 and B.22 - B.35, respectively).

128

6.1.3 Summary of Regression Equations for Oesign

1. Regression equations have been developed for determining the

headwater-discharge relationships for inlet control. Five equa-

tions (I st order to 5th order polynomials) were developed for

each situation, with or without pipe safety grates and with bar

safety grates. The effect of pipe grates were insignificant so

the same equations can be used with or without these grates.

The regression coefficients are summarized in Table 3.3. The

fifth order equation for no grates is

HW ( Q) (~)2 ( Q )3 -0 = 1.888 - 3.745 -1 -5 + 3.631 1 5 - 1.539 -1-5 BO . BD . BO .

o 4 0 5 + 0.307 (~l 5) - 0.231 (~l 5)

BO . BD .

and for the bar grates installed is

HW 0 ( Q )2 Q 3 -0 = 1.3236 - 2.661 (--~l 5) + 2.907 '-1-5 - 1.333 (---1 5) BO . BO . BO .

Q 4 ( Q )5 + 0.2843 (-1-5) - 0.0226 --1-5 BO . BO •

2. Recommended regression equations for design considering sub-

merged inlet, outlet control conditions are:

No Grates

o HW-TW C = 0.421 + 0.102 (-"1--5) - 0.348 (-0--)

e BO • (6.1 )

Pipe Safety Grates

C = 0.474 + 0.080 (~l 5) - 0.254 (HW 0- TW) e BD •

(6.2)

Bar Safety Grates

129

Q HW - TW C = 0.616 + 0.063 (--1--5) - 0.433 ~ 0 )

e BO • (6.3)

3. Recommended regression equations for design considering

unsubmerged inlet, outlet control conditions are:

No Grates

HW ~ C = - 0.040 + 1.000 (-0 ) - 0.276 ( 1 5) e BO •

(6.4)

Pipe Safety Grates

HW Q Ce - 0.122 + 1.046 (D) - 0.262 (B01.5) (6.5)

Bar Safety Grates

C = -0.213 + 1.448 ( HOW) - 0.366 (~1 -'5) e BO '.

(6.6)

4. Recommended regression equations for design developed con-

sidering both submerged and unsubmerged inlet, outlet control

conditions are:

No Grates

C = - 0.187 + 0.614 ( HOW) - 0.060 (~t 5····) e BD •

(6.7)

Pipe Safety Grates

Ce - 0.172 + 0.479 (HOW) + 0.001 (~) (6.8)

, Bar Safety Grates

HW Q Ce = 0.025 + 0.64:3 ( - 0.111 (---)

B01.5 (6.9)

130

..

5. The inclusion of the ( H;) term in Eqs. 6.1-6.9 wiU add yet

another level of trial and error manipulations to the standard

procedure of culvert design. A possible procedure would use a

first estimate of C to ontain, as per standard procedures, e HW 0 values for ( ) and ( --1-5 ). Next a new value for C could

BD • e be obtained using the appropriate equation (6.1-6.9), etc, until a

solution is converged upon.

6.2 Conclusions for Pipe Culvert Model

The following conclusions were made based upon the experimental

study using the 15-inch diameter helical corrugated metal pipe culvert:

1. A t low discharges, the entrance coefficients are substantially

higher for the grate treatment than for the no grate conditions.

The effect of the grates on the entrance coefficient is more

significant at higher discharges. (Figs. E.l - E.2, E.14 - E.19).

2. Headwater depth increases linearly with increasing discharge up

to headwater depths equal to approximately 1.2 times the

culvert diameter. The effect of the safety grates on headwater

depth is virtually constant throughout the discharge range.

(Figs. E.3 - E.5).

3. The entrance coefficient for the safety grate condition is

higher than that for the no grate condition for unsubmerged

inlets. The effect of safety grates on the entrance coefficient

is relatively constant for a submerged inlet (Fig. E.l2). The

coefficient for both conditions increses substantially for an

unsubmerged inlet (Fig. E.11).

131

4. The entrance coefficient increases substantially for increasing

discharge for a submerged entrance (Fig. E.14).

5. Headwater depth is unaffected by rising tail water depth for less

than critical depths (Figs. E.20 - E.23).

6. The flatter the slope, the greater the effect of tailwater depth

on headwater depth (Figs. E.22 - E.23).

7. For available headwall elevations greater than 1.2 times the

culvert diameter, the effects of safety grate treatment on

design criteria is insignificant. For available headwall eleva-

tions less than 1.2 times the culvert diameter, the effect of

safety grate treatment on design cri!eria}~substantial.

8. Regression equations have been developed for determining the

headwater-discharge relationships for inlet control for no

grates and for grates installed. Five equations (1 st order to 5th

order polynomials) were developed for each situation, with and

without grates. The regression coefficients are summarized in

Table 5.1. The fifth order equation for no grates is

HW Q Q 2 0 3 (-0 ) = 0.236 + 1.088 (-1-5) + (-1-5)0 + 0.482 (-1-5)

BO • BD • BO •

o 4 (Q 5 + 0.099 (~l 5) + 0.007 ~l 5)

BO • BO •


HW 0 ( 0)2 ( Q 3 (-0 ) = - 0.774 + 2.775 (~l 5) - 1.999 ~l 5 + 0.749 ~1-5) BO • BO • BO •

Q 4 ( Q )5 - 0.732(-1-5) + 0.009 -1'-5 BO • BD •

9. Regression equations for outlet control conditions were de-

vel oped for determining Ce for use in design procedures. The

132

suggested equations for submerged conditions are summarized

as follows:

No Grates - Submerged Inlet

C = - 0.044 + 0.262 (~5 + 17.155 (S ) e D2.5' 0

(6.10)

or

o c = 0.145 + 0.230 ( 2 5) eO·

(6.11 )

Grates InstaUed - Submerged Inlet

C = 0.117 + 0.231 (~2 5' + 11.252 (S ) eO. 0

(6.12)

or

° C = 0.241 + 0.210 (~2 5' e o. (6.13 )

The suggested equations for submerged and unsubmerged conditions

combined are summarized as follows:

No Grates - Submerged and Unsubmerged Inlets

C = - 0.176 + 0.302 ( ~ 5) + 15.705 (S ) e O. 0

or

c = - 0.0000 + 0.272 ( ~ 5) eO·

Grates Installed - Submerged and Unsubmerged Inlets

o C = 0.t33 + 0.227 (~2 5 + 10.754 (S ) e D • 0

or

C = 0.253 + 0.206 ( °2 5) e O.

133

(6.14 )

(6.15)

(6.16)

( 6.17)

10. As discussed in Chapter 5, the extrapolation of the test results

for the pipe culvert model should be done with caution keeping

in mind that the corrugation sizes were not properly modeled.

6.3 Final Discussion

In the process of investigating the hydraulic performance of culverts

with safety grates, experimental data was also col1ected and analysed for the

same culverts with no safety grates in place. Typical design procedure

incorporates conservative estimates for Ce which vary with entrance geometry

and culvert type, but are considered independent of slope, HW, TW and Q.

The equations presented here suggest that Ce can vary with slope, HW, TW

and/or Q. Comparison for a given flow situation, of the C values calculated e

from the noted equations, whether with or without safety grates, with the value

provided by typical practice can provide insight leading to more effective design

of highway culverts.

134

REFERENCES

1. American Iron and Steel Institute, Handbook of Steel Drainage and Highway Construction, 2nd Edition, 1971.

2. Blaisdell, F. W., "Flow in Culvert and Related Design Philosophies", Journal of the Hydraulics Division, ASCE, Vol. 92, March, 1966, pp. 19-31.

3. Bossey, H. G., "Hydraulics of Conventional Highway Culverts", U.S. Department of Commerce, Bureau of Public Roads, Unpublished paper, August, 1961.

4. Chow, V. T., Open Channel Hydraulics, Mc-Graw-Hill Book Co., 1959, pp. 475-480.

5. French, J. L., Discussion of IITests on Circular-Pipe-Culvert Inlets", Highway Research Board, Bulletin 126, January, 1955, pp. 20-22.

6. French, J. L., "Effect of Approach Channel Characteristics on Model Pipe Culvert Operation", National Bureau of Standards Report No. 5306, June 3, 1957.

7. French, J. L., IITapered Box Culvert Inlets - Sixth Progress Report on Hydraulics of Culverts", National Bureau of Standards Report 9355, June, 1966.

8. Mavis, F. T., "The Hydraulics of Culverts", Bulletin 56, Engineering Experiment Station, Pennsylvania State College, 1942, pp. 1-29.

9. Schiller, R. E., "Tests on Circular-Pipe-Culvert Inlets", Highway Research Board, Bulletin 126, January 1955, pp. 11-19.

10. Shoemaker, R. H. and Clayton, L. A., "Model Studies of Tapered Inlets for Box Culvert", Highway Research Board, Research Report 15-B, January, 1953.

11. State Department of Highways and Public Transportation in Texas, THYSYS, Bridge Division.

12~ State Department of Highways and Public Transportation in Texas, _~~!:au}i~ __ lia_~Ll.-:0, Bridge Division, September, 1970, pp. IV 1-6tL

135

13. Statistical Engineering Laboratory at The National Bureau of Standards. OMNITAB, 1966.

14. University of Texas Computation Center, RLFOR, Austin, Texas.

15. U.S. Department of Transportation, "Hydraulic Charts for the Selection of Highway Culverts", Hydraulic Engineering Circular No.5, December, 1965. pp. 1-54.

16. U.S. Department of Transportation, "Capacity Chart for the Hydraulic Design of Highway Culverts", Hydraulic Engineering Circular No. 10. March. 1965. pp. 1-90.

17. U.s. Department of Transportation, "Hydraulic Design of Improved Inlets for Culverts", Hydraulic Engineering Circular No. 13. August, 1972. pp. 1-172.

D6

APPENDIX A

User's Manual And Fortran Listing

For Computer Program

"CULVERT"

Appendix A.l

User's Manual for Computer

Program "CULVERT"

The computer program, CULVERT, was designed to convert test

data into headwater, tailwater, discharge, energy gradeline, and

hydraulic grade line measurements. CULVERT was able to analyze test

data from both box and cirular culverts. The output from the pro-

gram consisted of two entrance headloss coefficients, the critical

depth, the critical slope, and HW/D, TW/D, and Q/BD1

.5

values. The

entrance headloss coefficient was determined by both the energy and

the hydraulic gradelines. The CULVERT output format was modified

for use in several plotting routines and for the OMNITAB II and

RLFOR statistical programs.

The arrangements and descriptions of the input cards are

given as follows.

Input Data

The first data card will identify the culvert type being

tested. a one or a two will mean a circular culvert, while a

three or a four will identify a box culvert. The format is

FORTRAN Name

SHAPE

Format

IS

Card Column

1- 5

Description

Type of culvert being tested

The second data card will read in the slope, the physical

dimensions, and the Manning's n for the culvert. The format is

as follows:

139

FORTRAN Name

SLOPE

LENGTH

MANN

WIDE

HIGH

Card Format Column

FlO.5 1-10

FlO.5 11-20

FlO.5 21-30

FlO.5 31-40

FlO.5 41-50

Description

The measured slope of the culvert

The measured length of the culvert in feet

The assumed Manning's n for the culvert

The width of the culvert in feet. Diameter (DIAM) if the culvert is circular~

The height of the culvert in feet. Leave blank for circular culvert.

The third data set contains conversion factors which will

change the raw measured data into actual measurements of headwater,

tailwater, discharge, and hydraulic depth in the culvert. The

determination of each conversion factor is given in Section 2.6,

Testing of Data Reduction. The format is

FORTRAN Card Name Format

HWLELE FlO.5

HWRELE FlO.5

TWLELE FlO.5

WEIREL FlO.5

GAGEL FlO.5

Coltnnn

1-10

11-20

21-30

31-40

41-50

Description

Conversion factor for the left upstream gauge measurement

Conversion factor for the right upstream gauge measurement

Conversion factor for the discharge channel piezometer

Conversion factor for the weir point gauge reading

Conversion factor for gauges 1 through 12

(continued)

140

FORTRAN Name

GAGOUT

Format

F10.5

Card Colwnn

51-60

Description

Conversion factor for gauge 12

The fourth and fifty data cards will read in the

distances that the twelve piezometers are from the culvert entrance.

The format is

FORTRAN Name

DY (I)

Format

F10.5

Card Column

1-80

Description

Location of each piezometer along the culvert in feet. I = 1 through 12.

The sixth data card reads in the discharge, date, and

other information for each different safety grate test. This

card, along with the following cards, will be repeated for each

test conducted. The format is as follows:

FORTRAN Card Name Format Column

HWE1R F10.5 1-10

8 A10 21-80

Description

Measurement of the weir point gauge in feet. A 9999.0 will terminate the program.

The date, the tailwater conditions, the grate type, and other pertinent information of the test.

The next two data cards will give the actual measurement

for each safety grate test. These data cards are repeated each

time the safety grates are removed or installed. A one in column

5 of the first card will mean the test was run without any safety

grates in place. A test with just an upstream safety grate will

have a two. with both safety grates, a three will be in column 5.

The format of the first card is as follows:

141

FORTRAN Name

I CO NO

DX (I)

Format

IS

F10.0

Card Column

1- 5

11-80

Description

Location of the safety grates 1 = No safety grates, 2 = Upstream safety grate, 3 = Both safety grates

Piezometric readings inside the culvert.

The format of the second card is as follows:

FORTRAN Name

DX(I)

HWL

HWR

TWL

Format

F10.0

F10.0

F10.0

F10.0

Card Column

1-50

51-60

61-70

71-80

142

Description

Remaining piezometric readings

Upstream left point gauge measurement

Upstream right point gauge measurement

Discharge channel piezometer reading.

· .

APPENDIX A.2

Listing of Computer PrografTI

"CULVERT"

PROGRAM CIJLVtRT(INPUT,OUr P UT,TAPE1,TAPE2,TAPEJ,TAPEII,lA PEr, , TAP E !, ,

ITAPE1,TAP~8,TAPE9'

IlfAL MHJN,t FNGTtI I,',TEGER SHAPf I) r ME~IS ION A (~" 13 (b l, DY (12) , f)X (12', EGL (12) IIATA A(ll/l~HW-O GRATES/,A(2'/ldHW-US GRATE/,A(ll/IMHBO

THGRATt:SI IlATA C/t~'H,.t~O--DATA*I,NT/lI

C C,.A*******,.,.*************,.****A***,.**,.**"*********""*,,,.***,.*,. C** INPUT CULvEnT PROPERTlfS (*- SLOPE,LfNGTtl,MANNING~S N,AND CULVFRT DIMENSIONS (u SHAPE:: t FOR CIRCULAR CULVERT (** Q FOR HOX CULvERT (U [)TH1:: CIRCULAR CULVERT DIAl-IETER Cu ioIIDE:: ROX CULVERT I</IDTII (** HIGH::. R()X CULVEfn HEIGIIT

C*A****"**""****~******AA •• ***"**.******"************. **.**** C

I! F ~ I tl D I~ T PfAD l'j,',SH/lPF.: l;('l ro (,,\,.,,;n,SHAPE III' AD 1 I,SLOPF,LtNGTH,MANN,DJAM p!./ r ~ J l' ."S " I , [) I />. ~I , !. f N G T H , 5 LOP E

'F/ F()iHIAT(IIH,ljx*CJRCULA~ CtJ'VF~T M(lI)[L*I';X*DIAMETER (IN F 1:) =*Fl ',3

I

GO Tn 3 ;> kfAO I' I,SLIlPf,LENGTII,MANN,WIDF,HIGH

P P I '11 )';>, H r Gil, \oJ In E , LEN G r H , S LOP f ~ ~, ;;> r 0 R MAT ( I H t , 4 X * H 0 X C U L V f R T MOD E l '" I 5 X * DIM ENS ION (I N FT:'

:HI,:.>,2x, 1 * FJY * F 1 >< 3 , <) x * LEN (; T" :II F 1 " • ~ , 5 x * S lOP F = * F 1 ~: il

!I/) C r**",*******************,.***,.*,.**~**,.**,.*************** ******* C** 1~t-'lJT CONV~IiSION FACT(JI~S C A _ II \II L t. L E = UT T U fl S r R f A M GAG E (*. HWRELfaRIGHT UPSTREAM GAGE e** TWLELE=1ATLWATER GAGE C*A W~rREl=~fIR CnNvERSION r ~ * I; ~ (; f L': r, 1\ r. f SIT H R II I 1

C~* Ij/l(;OUT = GA(;f I?

C*a***_*",.*************.***,.******A***,.***"****************** [

~ i< FAD I " Ihll f L F , 14 \oJ i~ fI. f , T W L E l. E , WE r R E L , GAG E L , r, AGO 11 T c C*******,.**,.***********,.****************,.******************,.* C ** H! P I J T PIE Z 'l M f H R S I 0 CArr 0 N S r N C I J L V E R T C*****,.,.*A**********,.*******************,.*,.***************,.** r:

r:

I, F' A D I.: I , (D V ( I ' , t = I ,I? , I",' FORMAT(tSl 1"1 For~MAT(Hfl,':5'

C****,.****,.,..******~*******"'******,.**,.**·**,.******,.*** ******* Cu IIE.AO 1 N IJISCHAI(LE. DATA Cu Ihl(IR I: WE l~ flEADING Cu (Jpp a DISCIIAGE (CrSl C****~**"***********"*~·****A*~****""A**""************ ****.**

145

r:

c

II ,I E A 0 II: 3, H W f. r R , B I ~ ~ FOR MAT( F 1'~ ~ '5 tl " X, 6 A I " 1

IF(HWEIR :(0: ~~qq) GU TO qp~ HriE IR::H"E t "+wf. r ;ltL QPP=3:33~q~*HWEIA~Al:5

r:****~*.~***~*****~****~*~~***~~~*.*~~******~**************** CU C('l:~PUTE CRITICAL OEPTH,CRIT1CAI SLOPE, AND NORMAL DEPTH CH CRITD:: CRt rICAI f)(PT~i r:** CRSlPE ~ CHITICAL SLOPE C** Uf)EP: NORHll OEPTH C**************~****~*~*~************************************ r:

c

CALl. CRTT(C(SHAPE,OIAM,HIGI1,wIDf,MANN,QPP~CRSlPE,CR1Tl)l CALL HOxun (SHAPE,DIAM,H[GH,WIDE~MANN,QPP;SLOPE,UDEP) PRINT ?~l,QPp,B,MANN,cnJTD,UDEP,CRSLPf,SlOPE

l( FQRMAT(115X,*OlSCIIARGE. *,FI~:5,* CFS*,5x,bAla,1 I ~X*MA~NING =*F7.~,5x*CRITICAL DEPTH =*F7:Q, I SX*NONMAI ntPTH z*F7:~,5X*CRITICAL SlOP[=*F7~~

! I ? 3

t; X * S LOP f = * F 7: II I I 1 " X , * COl: D IT I 0" 5 * , 5 X , * H [ A 0 ~ W ATE R * , 5 X , * F:: G • L. f) F * 5X,* H-OVER-D*,5X,*NON-DIMENO*,5X,*HYO:C:L:CE* 5X,* E.G.I: C[*,5X,* lW~OVER.D*/)

C********************~A.*.~***A*******~~***~***~************* Cu HfAO TN flEADWATER,TATLWArER;AND DFPTI\ OATA T~ CULVERT C** UX(I' = PlfZQMETfR READINGS C** HWL = LH"f UPSTkF:AM POINT GAGE Cu 'Hil< = rncHl UPSTUf:M1 popn GAGF. Cu Hil :: DISCH~p(;r CHA"INEt GAGE C*****-*~***********.****************A*********************** C

c

'5 HFAO 1.);:>, TCOND, (OX(P,I-1 ,t?J,HI;I.,HWR,TWL 1~2 FO~MAT(15,SX,7fI0:~/"Fld:~)

IFU1Wl :fR ..... ,l r.o TO q HOwL .ErJ:. ,'.,,) GO TO Ii'

c****~**************~***~*********************.*****.******** C** lOIlV[Rl TfST nATA INTO ACTUAL MEASUREMf..NTS C** HW :: AVERAGE HEADWATER DEPTH e** TW :: TAtlWITER DEPTH C

C*****·.**.*********.********.*.*****·***·********·*.* ••• * •• * e

C

TW:(TWL/l':J+TWLELE G(l T? I I

! (, 1 W=;'. Ii !I CO'HINUE

i'l w:: ( H W L + It W L F l f + H W P t Ii W P f L E ) I it :

C,**********************A********* •• *******************.***** c.. START OF LINEAR ~EGRF:sStON BY DE1F:RM[NG THE C** E'JERGY ANO HYDRAlIl IC GRADE. LINES

r.*****~********.***A*******A*****A*A************************* c

XG5:,< ,I x 5 =~: YS= ;: DN=S: D () Z 5 ,) Z 0, 1 "

146

C

OfPTH=DX(Jl t GAGEL i)F"P=OEPTtf t SLOPEAOY(J' G (' TO C 3;j , ") >' , 3 f , ~ I 1 , S II II P E

'J CALL CI~CLE(UfP,APEA,FSLOPE,DIAM,QPP,MA~N) GO TO .);>

'I CALL BOX(DEP,ARfA,fSLOPE,W1DE,IHGH,MANN,QPPl ,? VEL=QPP/AR!':h

t;.CL(Jh:[)EPTH t VlLU;>/hQ:ll X s = X S t [) f. f' T H XC;S = xes t ECLCJl

75 YS :I YS t OY(Jl X~ :I XS/DN n'=YS/DN XGLM=XGS/ON tGP:,':; XP= < YP:'" : I) (J ;> ~ K = b, I " XP=XPt(DXCKltGAGtL-XH1.(OY(Kl-YMl EGP=fGPtCEGLCK1_XGt.Ml",CDY(Kl-YMl

?h YP:Yp+(OYCK1-YMl •• 7

C···.··.· ......... ~ ........ A ••• "' ••••• AA •••• "'."' ••• "' •••• ••••• "'''' Cu Cf.LClJLATlON OF OEPTH AT ENTRANCE HY EXTRAPOLATfON OF CH IHE fUE~GY AI,!) HYDfiHILlC GRADfl.1NfS Cu Uf. = tfYOHlIl IC DFPTH c.. pr;AMMA = FNEQGY DEPTH C"' ••••••••••• *.* •• * ••••••••••••••••••••• *"' ••• "' •• **"'."'. "' •••••• r.

C

flr=XM_(XP/YPl.YM P~AMMA=XGLM_(EGP/YPl.YM r pi UD= ,;. ,1

C •• * •••• * •••••••••• * •• *.*.* •••• * •••• ** •••••••••• ~ •• * •• * •• * •• * r:u CALC\ILAT1(1'J OF H-OVER':'n,TW-OVER';'D,ANO AI~EA I')F FLOI'I c.. ~ = QPp/(o.n.*1.5 l

Cu :iW(jf) = HFAO\o,ATER/ttIGH r.. 1"00" TAIL"'flTEfi/tfJGH

c

C

Go TO(6,i>,7,n,StfAPE h CALL CJRCLtCOE,AHEA,FSLOPE,OIA~,QPP;MAN~l

HIoI'UD=HW/f) 14"1 ~=I.JPP/{)TA'1·.?:5

I~ (TW:E(~~<'" GO To F\

[WUD=Tw/IJfAM Go Tn 1\

7 C4LL IiOX(Ot,H'EA,FSLOPF,WJOE,1t1Gt1,MANN,()PPl I-\.,OIJ=HW/H r ral F=QPP/(~IDE.HIGH •• 1:51 IF (rw:J:Q:'>4 l G(1 Tn II

TI'IOIJ=TW/HJGH

C •••• *·.· ••• ~ •• *.*~ •••••••••• * •• * •••• A.** •• *.****** •• * •••• *** c.. DrTERMINATION OF AVERAGE VELOCITY C* ••• ~ •• ~ ••••••• ~ ••••••••••••• k •• * ••• * ••• ** ••••••• *.* • •• * •••• e

/1 VFL=QPP/AREA C C.* ••• •••• •• -**·*~·········*···.~ •••• *··~** •• *· ••• *~** •• * •••• Cui) f1 E R M I ~I A TI 0 N 0 F C F [l Y usE 0 F IJ 0 T II F N f R G Y AND Cu IIyIJf.</IlJLIC G"ADE LINES

147

r:

C

C F. ::: ( tl W. P G A'" /of All r V f L * * ;> :- 16 n : Il l H~CE:::(HW.OEl/(VEL**?/6n~ql-1 P R 1 rn ?,. ? , h. ( leo N D' , ~i w , P GAM Mil, II W 0 l) , r , H GeE, C E, T Ii 0 0

C.* •• *.*.*.* ••• *.**.*.**.* •••• ******.* •• ***** •••• *.*.******** C.. S[PARATION OF DATA INTO DI~FERENT FLOW REGIMES Ct. USING TEXAS HWY: DEPT: CR~TERIA ( •••• **~.*.*******.*.** •••• ****.**** ••••• ***.****.**.******** r:

C

SC=CRSLPE 5L=SL<)PE *LE NGTH OC=CRI fO IC"'lcQnD If (SLOPE:GE:SCl GO TO til IF (rw:Gr:ocl GO TO q2 IF (HW~(;t;(!:;>.HIGHH GO TO IlQ IF ow, Ell.,'., , GO TO n6

c ••• *** •• * •••••••••••••••••••••••• ***.* •••• **** ••• * ••• * •••••• Co. ~LOw lyPE I C.. SLOPE L:T: CRSLPE C.. H~ L:r: l:?HIGH C.. TW l:T: (~ITD C •••••• ~· •• * •• *** ••••• ********* ••• **.** ••• * •••• ** •• ***** ••• *. r.

C

"'RlTfe?,?"'?l (l(lCQNf)l,flW,PGM1MA,fiWOJ),F,HGCE,CE,HIOI) lo (1 T" '/

1.1/) IF (ICO~I{):f'(~~;)\ GO TO Q

IF (ICOND:EQ.J' Ie:? wRITF.(IC,?·I?l AIICONOl,HW,PGAMMA,HWQO,f,HGCf,CE,T,40fl GO To q

C*·.***~****.**.***********~****.***** •• *·* •• ***.*.* ••• **.* •• co. FLOW TYPE ~H

CU 'IW G:T;I.2.HTGH c.. r.., L.T. H[GH

c ••••• *.** ••• * •••••• *·* •• *****.** ••• ~ ••••• A ••••••• **.*** ••••• C

C

Q9 l~ (T~:NE;~:r'GO 10 q7 II' (ICON().EO.~l GO TO Q

IF {JCO~W:f.Q~ 1\ Ie:7 IF (ICONIJ:EQ~3' 1(:8 GO TO ll3

117 l(=~

1l"5 w R 1 H ( I C , ?,~ 1 , A ( 1 CON D , , ~I \II, P r. AM M A , It W 0 D , f , H GeE, C f , T \II 0 [) Gn TO ')

~I? IF (TW~Gf:Hlr;ln GO Tn qll I F ( H W '. G E : ( 1 : ;> it It 1 r. H l' GOT Q 4 7

( ••• *.it* •• *.*** ••••••••••• *.* ••••• ** ••• * •• * •• * •• **.* •••• ft •••• c.. FLOW TYP( 2 C** SLOPF. L: T: Cf-5LP[ Cu IiW L: r: 1.?*HIGH c.. rw C:T: CPlTO HUT cu L:T: IIIGH c ••• ** •• ** ••••• ***.*.* ••••••••••• ** •••• *** •••• *.****.**.**A**

WRITE(3"~2l a(TCnNDl,HW,PGAMM4,Hwnn,F,HGCf,CE,Twno lil') TO q

tll IF (n(GE:Sl:"ND:TW:LT:~(5lttlI£;Hll GO TO 45

148

6"'71

Naill HI

((:i/·D) •• H.:l •• V.c':C)/:C •• N~V~.~C •• don=S dM/V=il

:2 .(1+3G I M=dl'l 30 I 1>', .O:'!

II~) I "" U (11~) I H .:) 9· S U ) .:4 r • !.(]=n

IH'i V~ 1'1 J" ]

•••••••••••••• , ••••••••••• , ••••••• ¥ ••••••••••••••••••••••••• J •• J

3dU1S 1V"'HO'. = S ¥¥J ~]13~V~Yd 03113" : d~ .'J

V3HV ~Ol~ = , ¥'J 3dLl1S 1VHtlUI'I (J': if •• J

·H3.13~VHVd UH.1.:4M 'V]tjv !~UU :JHldHU] III JrU.1flU,j HJ (ddt)·NNVH·,I~IH·3QIM·S·V·SO)XO\j 3NllllU/j)jIIS

•••••••••••••••••••••••••••••••••••• + ••••••••••••••••••••••• J

J () ~; :~

du.1S C; 0.1 t,):J

11 0.1 U~) (1 • tJ}" (] N () J I) .:l I l l X 5' S~' I :l) L • X <; • :. I t{ ; x,' , ) 1 'if H Ii 0_1

b U.1 O:J a II M.1 ' ::l J ' _1 J 9 H ' ~ , 0 0 M H ' V H .. V ~ d ' M ) I • l (I N () J 1 ) V l ~, c' 6 ) :3 .1 I ti ,.,

:~ ::' b

/, c:,,(

SII

J •••••••••••••• , ••••••• , •••••••••••••••••• , •••••••••••••••••• :J

.1H!)I:3H + H.1~HU1.]d01S • .1·1 ¥fJ .1111:1 fd 9 N ::I h .:3 n 0 1 S ;.1: 9 M 1 H J

3d IStU : 1:9 3dO-'S .. :) 8~ 3dA.1 M01.:l •• J ........... , .............. , ................................. ]

:J b U.1 0~J

U 0 M 1 • 3 J ' :3 J ~ H ' :.I • U 0 M H ' HI I; V ~ d ' M Ii • [(I N 0 J I ) If l C ... C • 9 ) .:1.1 I .~ .. " n ii J

••••••••••• , •••••••••••••••••••••••••••••••••••••••••••••••• J H~IH + H.19N31.3d01S • 1 "!) I-ll •• J

GNY 3d-1SdJ :.1:~ 3d01s •• J (JO • ':J

H~lI II • .1'~ M I ,..j ON" jd -lSrlJ :1:1 3d01s •• J

V II 3dA.1 MD 1.:1 •• J .................. , ......................................... ) 6 U.1 U~l

U II M .1 • 3 J I .:l J :II j I j , (10M H ' V ~ ~ v !) diM H ' \ UNO J r ) v \ c . ) C I ) r ) :3 1 1 H ~ c, s= J 1 \;fl

,15 0.1 O~I

S:Jl ,'&."f.l3"GNO::ll) jl

b=JI ,1;tJ3:0NOJl) ~1 b U.1 O!) \c"tJ3:UNOJl) .:lJ \111 0.1 O~ ';:'f::3N)\1) .:41

)

J •••••••••••••••• ··., ••• , ••••••••••••••••••••••••••••• f •••••• J

1I.1~)N3,.3d01S ".1"-1 MI ":J 3dlSHJ :.1t~ 3d01S •• J

is:: • 3 d A.1 M 0 "l.:l •• J •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• J

J ~n 01 O~ 'lH~lH+'S):3D"M.1) ~I

t: "I f) SUBROUTINE tlRCLE(05,A,S,OtA~,QPP,MANN\ f(,,4L MANN

I~~ ~ALx(?~05-DIAH\/DIAM IF(AHS(VALJ:LT~I.' GO TO 2~ THETA=:< GO TO ?l

?~ THETA=?:~ACOSrVAL\ ?l A=DlhM~~?:/~:.(b.?R32-THfTA+StN(THF.Th)\

A I< = t : Il 1$,.,. r ( ( ( t>. ;> 8 32- T HEf H SIN ( T HEl A ) ) I R ~ } .. C; J I ( ( (h.? 1\ 3 2 -TlinA)

I 1?:'**?*r05/DIAM)**R$**(1:/3:' S:(QPP~MAN~/(IK~D~A*(R:/3~)))A~2 DC=D5 sc=s t<:[ I URN f.. ~I f)

r.~.*~*A~A*.~.**"'*.**~~~*.~*.**.********.**.*******.*** ••••••• <\.**~******

~w [~R 0 U T T N f eli TTl C ( S H" P E , D tAM, II I G Ii, WID E , MAN N , Q P P , C R 5l P f • r: R j Tn \ C koUTTNE TO CouPUTE CprTICAL DEPTH AND CRITICAL SLOPE C***.***.**.***.*** ••• * ••••• **.*.*.**.~.~~~**.***~t***~.* •• ** .*****~~.**

C C

INfEGF:R SH4PE QfAL MA~IN

l;O TO (1l.l1.1211?), SHAPE Ilit't =QPP. * 7.1 'Sl', 2

D'5=OT "M/?:., _" I i)E'iOM:2: iF (DTAM/DENOH :IT: ~:~85) GO TO J CALL CIQCLE(05,',CRSlPE,DIAM,QPP,MANN' T W (J: A" 31 ( 2: * s miT ( 1)5 * 0 I A M-DC; ~ 05) 1 I) E '~OM = DE. "I OM 11 2~ If' (ONE - riolO' il,'.11

? 115:D'5-DT A'1/DENOM I;(] TO 1

q D5=U5tUIAM/DENOM GO TO 1

, CRITf)=D5 1;0 TO III

I? CRITD=(QPP**2:/(3?:?*WIDE**Z:ll**{1/3:' CALL HOX([PI10.A,(PSLPE.WIOE,HIGH,MANN,QPP)

III K!,lliRN

~ ND

C*.***~ •• **~.~*.******* ••• *~**~***A •• A**~'~*********~* *11****.

S U [j H au T I N[ A 0 X IJ 0 r S 1-1 J\ P E , 0 I AM, H T G H. \Ii 1 0 E , MAN N , Q P P , S LOP E , liD EPl C ROUTINE TO COMPUTF THf UNIFORM OR NORMAL DEPTH c*******~***.,.*.,..***.*** ••• *.**~*.* •• *·~··*·*.*·*.***** ******* *******.***

I~E ilL MANN 1 t, TE'GER S'1APE 1;0 TO (t,"d2,ll', SHAPE THlr.H:I>IA'1<938111 II J .'1 A X I: D I A M

1.10 TO 5 ) THJRHI:HTGH*:9~57

H r t~ A X " ~1 t G H

150

li(, TI) 5 Ii THIGH-HIGH

rlI'';AX:HIGH '5 1)<,5:THIGHI?

OfrjOM=I~ : I:. liO TO 0,7",1,1,», SIUPE 7 tALL CIHCLE (D5,A,S,DIAM,QPP,M.NNl

GO TO 1 t I'~ CALL HOX«()S,A,S,WIOf.,HIGH,MANN,QPP\ 11 IFIS ~GT: SLOPE' GO TO 13

1)'5 =OS-lllT G H/DUW~ 1;0 Hl 111

13 DS=D5+TIlIGH/DFNCd1 1'1 IHTHIGH/DEI'WM :u: «""Sl GO TO 12

1)"IH')M=nE ~I(lMjt? ~ (;n TO b

I; I'DEP=D5 r. IF((rHlr.ll-UD(Pl :u: '1~~~5) lIDEP=HIMAX

151

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

APPENDIX B

Graphical Results For Box Culverts

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j j

j j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

I j

j

I-' \J1 \J1

1.0

0.9

0.8

0.7 CI) Q) -~ 0.6 --

C)

.c:

.~ 0.5 3t

Q)

o 0.4

0.3

0.2

0.1

0 0

PIPE SAFETY GRATES

Slope = .0008

.- Type 1 Flow Regime

.- Type 2 Flow Regime 0- Type 4A Flow Regime *- Type 4B Flow Regime

•

•

o

*

0.1 0.2 0.3 0.4 0.5 0.6

o

?

o

o

0.7 0.8 0.9 Ce Without Grates

o

1.0

Figure B.l Comparison of Entrance Headloss Coefficients With and Without Safety Grates, Slope = .0008

...... U1 0\

1.0 PIPE SAFETY GRATES

0.9 l- Slope = • 0013

CI) Cb -

0.8

0.7

~ 0.6 o .c:: .~ 0.5 ~

Cb (,) 0.4

0.3

0.2

0.1

.- Type 1 Flow Regime

.- Type 2 Flow Regime 0- Type 4A Flow Regime *- Type 4B Flow Regime

o

•

o

.,{J

o o

*

o ~c~~ ____ ~ __ ~ __ ~ __ ~ ____ ~ __ ~ __ ~ __ ~ __ ~

o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Ce Without Grates

Figure B.2 Comparison of Entrance Headloss Coefficients with and Without Safety Grates, Slope = . 0013

~ VI .....

1.0

0.9

0.8

0.7 CI) Q) -~ 0.6

(!)

.c: ~ 0.5

Cb (,) 0.4

0.3

0.2

0.1

PIPE SAFETY GRATES

Slope = 00063

.- Type 1 Flow Regime .- Type 2 Flow Regime 0- Type 4A Flow Regime *- Type 4B Flow Regime

•

*

. .

cP

c

o

o o o

.J

o ~¥ ____ ~ ____ ~ ____ ~ __ ~ ____ ~ ____ ~ ____ ~ ____ ~ __ ~~ __ --L

o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Ce Without Grates

Figure B.3 Comparison of Entrance Headloss Coefficients With and Without Safety Grates, Slope = .0063

,~

I-' VI co

CI) Q) -

1.0

0.9

0.8

0.7

~ 0.6 o :§ 0.5 ~

Q)

o 0.4

0.3

0.2

0.1

PIPE SAFETY GRATES

Slope = .0108

• - Type 3A Flow Regime * - Type 3B Flow Regime 0- Type 4A Flow' Regime

* *

*

o

o

o

* *

o o

o 0

o 0 o

DLJ

o AK __ ~ ____ ~ __ ~ __ ~ ____ ~ __ ~ __ ~ ____ ~ __ ~ __ ~



..

t-' V1 \0

II) Q) -

1.0

PIPE SAFETY GRATES

0.9 ~ Slope = .0128

• - Type 3A Flow Regime 0.8 ~ * - Type 3B Flow Regime

0- Type 4A Flow Regime

0.7

~ 0.6 C)

:§ 0.5 3t

Q)

(,) 0.4

0.3

0.2

0.1

o o

o

o ~~----~--~~--~----~----~--~----~----~----~--~ o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Ce Without Grates


I-' a-0

1.0

0.9l BAR SAFETY GRATES

Slope = .0008

0.8 l-• - Type 1 Flow Regime • - Type 2 F low Reg ime 0- Type 4A Flow Regime

0.7 I

* - Type 4B Flow Regime

CI) ..r'i 0 Q) -~ 0.6 0 .r::::: ~ 0.5

• • Q)

U 0.4

I • ~

0.3

0.2 ~ • • • •

0.1 •

o y~----~----~--~----~----~--~----~----~--~~----o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Ce Without Grates


"

I-' (j\

I-'

1.0

0.9

0.8

0.7 II) (1) -~ 0.6 Cl

.c: ::;: 0.5 ~

(1)

o 0.4

0.3

0.2

0.1

BAR SAFETY GRATES

Slope = .0063

• - Type 1 Flow Regime • - Type 2 Flow B-egime o - Type 4A Flow Regime * - Type 4B Flow Regime

oi 0

o

.::J o o

o

o ~K __ ~ ____ ~ __ ~ __ ~ ____ ~ __ ~ __ ~ ____ ~ ______ ~



1.0

0.9l BAR SAFETY GRATES

Slope = 00108 0 0 0

0.8 l-• - Type 3A Flow Regime 0 ;r 0 *- Type 3B Flow. Regime 0 0- Type 4A Flow Regime 0 0

0

0.7 ' 0

CI) Q) * * -~ 0.6

(!)

~Q) 0.5 r * / :::J

* * ..... * (j\

N (,) 0.4 *

0.3

0.2 r t * :'

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Ce Without Grates Figure B. 8 Comparison of Entrance Headloss Coefficients with and Without Safety Grates,

Slope = .0108

I-' 0\ w

'.

0 If)

Nl gl Nl

I

~I

~ ~l ~a I :~

~I 1m . a

o

I oJ . ~----°1~ 00

SLOPE = 0.0008 FREE (jUTFRLL [!) W/(jUT GRRTE5 x FIPE GRRTES

~I!I

IZI Pi!

Il!I I!l

I!I IZI

IZI J:l!IIm

D!I J:l!I

1m J:l!I

---------.------------,---_._--_. ----,.---- --- --- ------,-- - --- -,--_._-_ .. ------.~--

1.50 2.00 2.50 3.00 3.50 4.0D 4.50 Q/ (B*O**l. 5)

Figure B.9 Headwater vs. Discharge with and without pipe Grates, Slope = .0008

I-'

'" .;:-.

0

d III

~

g c.J

d III

~1

St~PE ~ U.UOl3 FREE ~UTFgtl [!] W"/~UT GR.R-TES x PIPE GAATES

•• .W

" ~5~ .-II W

.. • II

II

d III

d

g dl~~-on------'l~-5-n-----~~r-nn------~~r~5-n------3~rn-n------3~~5-n------~T~-n-n-----L~I-5-n-

Q/ tB-.O .. -.l .. 51

"

Figure B.10 Headwater vs. Discharge with and without Pipe Grates, Slope = .0013

..... 0-\JI

o If) . N

o o N

o If)

..... Cl ....... 3:: ::Co

o ......

o If)

o

o o

"

. .

SL~PE = 0.0062 FREE ~UTFRLL [!) W/~UT GRRTES x PIPE GRRTES

~ ~ w

M 1m

1m 1m

1m

Il!IIIl!II

Il!II

Il!II /I I!t

III

~ I I 1. 00 1. 50

,-- I

2. 00 2. 50 3. 00 50 I I

4. 00 4. 50 Q/ (B*D3IolE 1. 5)

Figure B.ll Headwater vs. Discharge with and without Pipe Grates, Slope .0062

t-'

'" '"

0 ..........

3::

a lJ")

· N

o o

N

a lJ")

· .....

SLaPE = 0.0108 FREE aUTFALL I!l W/aUT GRATES x F I FE GRATES

W

~ I!l X

:::Co I!i 0

· .....

~J 0

o o

" ..

III "

II III

III III

" I!!I

c:i t I I I I I I I 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50

.'

Q/ (B*O~O'E 1. 5)

Figure B.12 Headwater vs. Discharge with and without Pipe Grates, Slope = .0108

t-' Q\ -....J

Cl ,

d In

~

g rJ

d U1

• .-I

3: ::r:g

• .-I

d In

d

g

•

Sl~PE = U.OL2B FREE ~UTFBll (!J W/~VT GRflTES x PIPE GRflTES

• .. II II 81'.1

I:!I II II

II

IiII!

C!I II

dl~~-U-U------l~~5-U------~~'-UU------~~'-5-U------3~~-UU------3~~-5U Q.t lB --0 Illt 1 .. 51

lit IiII!

~

r i

4. .. o.u 4... SU

B.13 Headwater vs. Discharge with and without Pipe Grates, Slope = .0128

I-' 0\ 00

Cl

" ~

d I.n

~

d d

'" o I.n , ......

:r:g • ......

o I.n

d

g .-t

0t. .. o.o.

Sl~PE ~ U~UUOB FREE ~UTF~lL I!l W"/~Ut GRF.tTES x BA-R GRF.t T ES

M 8 M

S!I II

I! r!J I M

•

I I" ,---

L.So. 2... no. 2... 50. 3 .. 0.0. 0./ lS--OflJtl ... 51

~ ~

M III

x II

50. 4.... 0.0. 4... so.

Figure B.14 Headwater vs. with and without Bar Grates, Slope = .0008

.... .. .

...... 0\ 1.0

o "-3:

o lI')

('\I

o o . ('\I

o til

-Io

o

-o til . o

o o

..

SL~PE = 0.0063 FREE ~UTFALL (!] H/~UT GRATES x BAR GRATES

III X

III x M

i!§X M

l!tC

ilk I!II

I!II

r!!II ~

I!II III

d1 I I I I I I I 1. 00 1. 50 2. 00 2. 50 3. 00 3. SO 4. 00 4. SO

QI (8:1(0:'01( 1. 5)

Figure B.1S Headwater vs. Discharge with and without Bar Grates, Slope .0063

,... ...... o

o

" 3::

CJ Ln

N

CJ CJ

N

CJ Ln

......

ICJ CJ

......

CJ III

CJ

a a

II

SL~PE = 0.0063 FAEE OUTFALL (!] W/L1UT GRATES x BAR GRATES

If(

M: I!J

I!!IJ

l!I I!

l!I B

.. x

III x I!I

~x M

o I I I I I I I I 1. 00 1. 50 2. 00 2. 50 3. 00 3. SO 4. 00 4. 50

Figure B.16

,"

Q/ (8*0.31(1. 5)

Headwater vs. Discharge with and without Bar Grates, Slope = .0063

. .

'.

1.25

1.00 ~

.75 ~

Ce ,...

. 50 ~ ~ ,...

.25

o o

PIPE SAFETY GRATES

Slope = .0008

* - Type 1 Flow Regime 0- Type 2 Flow Regime • - Type 4A Flow Regime • - Type 4B Flow Regime

0

* rl

~o..

*

.5

** * * * I

1.0

• .. • • • •• • • •

• .. •

• •

HW -o

•

• • • • • • • • • • • • • • • • •• •

• • • •

• •

•

•

I I

1.5 2.0

Figure B.l7 Entrance Headloss Coefficient vs. Headwater For Pipe Safety Grates, Slope = .0008

.'

• •

•

2.5

f-I ...... N

Ce

,"

1.25

1.00

. 75

. 50

.25

o o

PIPE SAFETY GRATES

Slope = .0013

* - Type 1 Flow Regime 0- Type 2 Flow Regime • - Type 4A Flow Regime • - Type 4B Flow Regime

0

r!J* * a

.5

0 ~

*

1.0

• ~

~. • Ii

• • •

HW -D

• •

•

• • • • •

• •

•

•

1.5 2.0

Figure B.18 Entrance Headloss Coefficient vs. Headwater For Pipe Safety Grates, Slope = .0013

2.5

'.

,..... -....J W

".

Ce

1.25

1.00

.75

. 50

. 25

o o

PIPE SAFETY GRATES

Slope = .0063

* - Type 1 Flow Regime o - Type 2 Flow Regime • - Type 4A Flow Regime • - Type 4B Flow Regime

*

o

** *

*f1 *

* ~

.5

•

a*

1.0

• • • • • • • • • • • • •

•• • • • • • • • • •

• •

.. ~ . • ••••

1.5 2.0 HW -D


2.5

I-' ....... .p..

Ce

1.25

1.00

. 75

.50

.25 t-

o I

0

PIPE SAFETY GRATES

Slope = .0108

* - Type 3A Flow Regime • - Type 3B Flow Regime • - Type 4A Flow Regime

•

• •

"

• • • • •

• •

* * *~*' *'** * • * * * * .5 1.0

HW -D

• • ..

••

•

* 11 •

1.5

••

• • • •

• •

• • • • •

•

I

2.0


2.5

".

t-' ....., U1

".

Ce

1.25

1.00

. 75

.50

. 25

o o

PIPE SAFETY GRATES

Slope = .0128

~- Type 3A Flow Regime • - Type 3B Flow Regime • - Type 4A Flow Regime

•

...... .5

• •

~ . .....

·~ic· ** ~~?r it

1.0

•

• • • • .. • •

• • •• •

• • •

•

., .* *1#

• •

HW o

1.5

• •• • -•

• •

• • • • • •

2.0


2.5

1.25

1.00 ~

.75 ~

Ce

t-' .50 ~ ....... 0'\

. 25 ..

0 0

..

BAR SAFETY GRATES

Slope = .0008

* - Type 1 Flow Regime • 0- Type 2 Flow Regime • • - Type 4A Flow Regime • - Type 4B Flow Regime • • • • • •

o 0 • • •

• • • • • • • •

• 0 • •

0 0 • ~

~ 0

~ o rJ • ~ * • •

,p* * •

** *

*

.5 1.0 1.5 2.0 HW -D

Figure B.22 Entrance Headloss Coefficient vs. Headwater For Bar Safety Grates, Slope = .0008

• •

2.5

'.

..... -....I -....I

"

Ce

1.25

1.00

.75

.50

. 25

o o

BAR SAFETY GRATES

Slope = .0063

* - Type 1 Flow Regime 0- Type 2 Flow Regime • - Type 4A Flow Regime • - Type 4B Flow Reg ime

• ..itt •

Ii.1 * * ** IliI

* *0 0

* ...l-

.5 1.0

• . " •

• • • I!!I

•

* £I • •

HW -D

•

• • • • • • • • • •

• • • • • •

• • • • •

•

, ~

f I

1.5 2.0

Figure B.23 Entrance Headloss Coefficient vs, Headwater For Bar Safety Grates, Slope = .0063

2.5

1-' -..J 0:>

Ce

1.25

1.00

.75

. 50

. 25

o o

BAR SAFETY GRATES

Slope = .0108

* - Type 3A Flow Regime • - Type 3B Flow Regime • • - Type 4A Flow Regime

• • •

• • • • , • e •••

• • • • • • • • • • •

• • • • • • •

• •

• . ..;* ~ *f

* ****{* * * • • •

.5 1.0 1.5 2.0 HW -D

Figure B.24 Entrance Headloss Coefficient vs. Headwater For Bar Safety Grates, Slope = .0108

2.5

"

If)

N

· -SLClPE = 0.0008 ALL PClINTS I!JREGIME 1 (!) ffE G I M E 4 A

gl x REGIME 2 • REGI ME 46 · -~ (!)

Z W e i ...... • Ulf) (!) (!) • ...... r-- (!)

I lL..c:i (!) • lL.. (!)

W (!) I (!)

0 (!) e i • U 9 ,... ....... 0 (!) \0 Wlf) (!) (!)

U • x (!) • ZO (!) (!)

a: (!)

a: • ~

Zlf) •• WN X

I!l

· ~I!l I!l • 0 I!l

XI< • I!l I!l I!l

I!J I!l l!l

0 0

· 01. 00 1. 50 2.00 2.50 3.00 3.50 4.00 4.50 Q/ (8_01011. 5)

Figure B.25 Entrance Headloss Coefficient vs. Headwater For pipe Safety Grates, .0008

t-' 00 0

I-Z W -

In ('\/

-0 0

-Win

-~ lJ...o IJ... W 0 W

0 WI.f) Wei z cr: a::: I-Zl.f) W('\/ .

0

o o

SL~PE = 0.0013 RLL P~INTS I!I REGIME 1 (!)REGIME 4R x REGIME 2 ... REGIME 46

(!) (!)

(!)

(!)

(!) ~

~ I!I

~ , - ~----.-

(!) (!)

(!) ... ...

(!) ... ... (!) ... ...

(!) it!>

...

... ... x

X I!I

1!1

, ei' I III I 1. 00 1. SO 2. 00 2. SO 3. 00 3.50 4. 00 4. 0

"

Q/ (8-0:'01(1.5)


IJ')

N

· .......

gl · .......

~ z W ....... UIJ') ....... " lL...ci lL... W 0

..... U 00 ° t-' WIJ')

U • ZO a: a:: ~

Zln~ WN · °

° ° ci1: 00

SL(jPE = 0.0063 ALL P(jINTS [!) REGIME 1 (!)REGIME 4A x REGIME 2 • REGI ME 4B

(!) (!)

e (!) (!) (!)

@j (!)

m (!) (!)

~ (!)

~ [!) [!) (!l!) • ... ...

(!) [!) ;. [!)x [!)

[!J [!)

[!) I I!J

M

I I I I I I

1. 50 2.00 2.50 3.00 3.50 4.00 Q/ (B-OIOIE 1. 5)

Figure B.27 Entrance Headloss Coefficient vs. Headwater For pipe Safety Grates, Slope = .0063

~ 9

(!)

l

------. 4.50

I-' 0:> N

If) ("\I

~l

CJ CJ

..... t--:z W .......... Ulf) .......... C"-

LLci LL W 0 U

CJ Wlf)

uci Z IT a: t--Zlf) W("\I .

CJ

CJ CJ

I

I!J

SL(jPE = 0.0108 I!J AEGIME 3R x AEGIME 4R

I!J I!J I!J I!l

I!J

x

x

~

x

I!J

ALL P(jINTS

I!J I!J

~ x x

x

I!JI!J

x

~

I!J

I!J I!J I!J

I!J

ci +- 1 1 1- ------. 1.00 1.50 2.00 2.50 3.00

I I

3. 50 4. 00

"

Q/ (B*O**l. 5)


x

* x

I!J

I!J

'.

1

4.50

'.

III ('II

.....

Figure B.29 Entrance Headloss Coefficient vs. Headwater For Pipe Safety Grates, Slope .0128

1-' 00 .po

In N

~l 0 0

.... I-Z W _ Ul.f) _('o

l.1.... o l.1.... W 0 U

0 Wl.f) uci z cr: cc !-Zl.f) WN .

0

a a

I I

SL~PE = 0.0008 ALL P~INT5 I!] REGIME 1 e> RE.QIME 4A x REGIME 2 • REljIME 4B

~

x x

~

X I!l

I!]

I!]

I!] I!]

(!)

(!)

(!) (!)

~

x x ~

I!]

I!]

I!]

(!)

~

~

(!)

X

t!il!] •

(!)

I (!)

I!]

• • • ...

o+--- I I , I I I I 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50

Q/(B-O--l.S) Figure B.30 Entrance Headloss Coefficient vs. Headwater

For Bar Grates, Slope = .0008

f-' CD IJ'I

I-Z W -

U') N

......

0 0

......

wan _C'--

LLci LL W 0 U

0 WU')

wci z a: a::: I-ZU') WN .

0

o o

SLCJPE = 0.0063 ALL PeJINTS l!J REGIME 1 (!) REG I ME 4A x REG I ME 2 .. REGI ME 4B

(!)

(!)

(!)

IB m lB 8 m

(!)

(!)

(!)

e (!) [!)

(!) I!J I!J .. .. ~ I!J I!J • • [!)

I!J ~ [!)

I!J

I I i I I I

1. 50 2.00 2.50 3.00 3.50 4.00 Q/(BIEOlElEl.SJ

Figure B.3l Entrance Headloss Coefficient vs. Headwater for Bar Safety Grates, Slope = .0063

CDS (!)I (!)

(!)

I(!)

t e I

4.50

t-' 00 C1\

I:z W

If')

0J

.....

C)

o .....

....... UIf) ....... C"-

!.Lci !.L W D U

o WIf)

uci :z a::

e: I :z If) I

SLDPE = 0.0108 ALL F~INTS t!l REGIME 3A x REGIME 4A

I!I I!I

3E

* x

x

x

x

I!I I!I

I!I

x

~ Xx

I!I I!I I!I I!I

I!I

x

x

~

I!I I!I

01. 00 1. 50 ,

2.00 -, ,-------. 2.50 3.00 3.50

Q/ (B:JED:f:JE1. 5)

ji x

I!I dP I!I

1 -----.

4. 00 4. 50

Figure B.32 Entrance Headloss Coefficient vs. Headwater For Bar Safety Grates, .0108

'.

.JiW. D

~ 00 .......

'.

2.5

PIPE SAFETY GRATES

Slope = .0008 • 2.1 ~ * -Discharge 6.14 cfs •

• - Discharge = 8.12 cfs • • 0- Discharge = 10.40 cfs • - Discharge = 11.80 cfs • 0

* • •

1.7 f • • 0

• • • 0 • •

• 0 0

... * • • * * 0 • * 1.31

0 0 0 0 • * • * • • • **

0.9,f * * *

0.6 0.8 1.2 0.5 I~I ~ __ -:,;-__ ~~ __ --;;:;;-___ ~:-__ -:-:-___ ,--__ J

0.4 1.8 1.0 1.4 1.6

~ D

Figure B.33 Headwater vs. Tailwater For Pipe Safety Grates, Slope = .0008

.l:!.Yt. D

I--' co 00

2.5 ~ ------------------------------1

2.1 I-

1.7 I-

1.3

0.9 I

0.5 0.4

• * 0

BAR SAFETY GRATES

Slope .0008

0- Discharge * - Discharge • - Discharge • - Discharge

• • • *

4.0 cfs 6.5 cfs 8.1 cfs 11.0 cfs

•

• * 0

* * 0

0 0

I

• •

• • •

• • • rt 0

• cit-

• • * • *

0 0

• * *0

0

0.6 0.8 1.0 1.2 1.4 1.6

.L»:: D

Figure B.34 Headwater vs. Tailwater For Bar Safety Grates, Slope = .0008

•

• * 0

1.8

'.

.J:Uf. D

t-' CQ \0

~------I 2.5 ,

Discharge = 8.1 cfs

2.1 I-

1.7 .-

1.3

0.9

0.5 0.4

Slope = .0008

_ - Pipe Safety Grates • - Bar Safety Grates

• . - .-.-

I

0.6 0.8

• -

1.0

~ D

.- ,

1.2

• -..

i

1.4

, .-

i

1.6

Figure B.35 Headwater vs. Tailwater for both Pipe Safety Grates and Bar Safety Grates, Discharge = 8.1 cfs, Slope = .0008

-• -

1.8

HW [)

I-' '-D a

2.5

2.1 ~

1.7 ~

1.3 I

0.9 ~

0.5 0.4

PIPE SAFETY GRATES

Slope = .0063

* - 6.14 cfs • - 8.12 cfs 0- 9,66 cfs .- 11.81 cfs

• • • • •

0 0 0 0 0

• • • • • ...

... ., ., ...

I

0.6 0.8

• 0

• .,

1.0

~ D

• • 0

0 • • ., .,

1.2

• • 0 • • 0

0 • ...

• ... ...

•

1.4 1.6

Figure B.36 Headwater vs. Tailwater for Grates, Slope = .0063

• • 0 0 • • ... ...

1.8

'.

J::I.J!i. D

I--' 1.0 I--'

2.5 I

2.1 ~

1.7 ~

1.3 r

0.9 ~

0.5 0.4

BAR SAFETY GRATES

Slope = .0063

*- 6.14 cfs • - 8.12 cfs 0- 9.66 cfs • - 11.81 cfs

• • • • 0

• 0 • 0 • ,..

• • • • • • • • 0 ,..

• 0 ,..

0 0 0 0 0 0 • ,.. • ,..

• • • • • ,.. ,..

,.. ,.. ,.. ,..

0.6 0.8 1.0 1.2 1.4 1.6

L.l1! D

Figure B.37 Headwater vs. Tailwater for Bar Safety Grates, Slope = .0063

• • 0

• 0

• ,.. ,..

1.8

f-' \0 N

.1:!.!1! D

2.5 .--------------------l

2.1 I-

1.7

1.3

0.9

0.5 0.4

..

Discharge = 6.14 cfs Slope = .0063

• - No Safety Grates e- Pipe Safety Grates 0- Bar Safety Grates

eO ... 1M • I

I

0.6 0.8

• ~

1.0

lli! D

, • • I

e~ o

I

1.2 1.4 1.6

Figure B.38 Headwater vs. Tailwater For No Safety Grates, pipe Safety Grates, and Bar Safety Grates, Discharge = 6.14 cfs, Slope

i ~

1.8

.0063

. .

~ \0 W

1:J.!!f. D

2.5 , --------------------~

2.1 I-

1.7 ..-

1.3

0.9

0.5 0.4


... - No Safety Grates • - Pipe Safety Grates o - Bar Safety Grates

i a a a .~

I

0.6 0.8

~

1.0

LJt: D

... .0

1.2

ie

.~ .~

i

1.4 1.6

Figure B.39 Heauwater vs. Tailwater For No Safety Grates, Pipe Safety Grates and Bar Safety Grates, Discharge = 8.12 cfs, Slope

i ~

1.8

.0063

t-' \.0 +:-

HW [)

~------I 2.5 ,

Discharge ~ 9.66 cfs .0063

2.1 I-

1.7 I-

1.3

0.9

0.5 0.4

... - No Grates e - Pipe Safety Grates 0- Bar Safety Grates

i i i i

..l

0.6 0.8

i .a

1.0

lit! D

fi£ «j

1.2

J lie

~

I

1.4 1.6

B.40 Headwater Vs. Tailwater For No Grates, Pipe Safety Grates and Bar Grates, Discharge = 9.66 cfs, Slope

rJ. i

1.8

.0063

.. . .

.I::/J! D

...... \0 VI

~------I 2.5 ,


2.1 I-

1."1 I

1.3

0.9

0.5 0.4

£- No Safety Grates .- Pipe Safety Grates 0- Bar Safety Grates

.£ £ £ £ • • • 0 0 0

I

0.6 0.8

£

• o

1.0

£

o •

.il1! D

• ~

o • £

1.2

~ £~

~ £ o £

t

I

1.4 1.6

Figure B.41 Headwater vs. Tailwater for No Safety Grates, Pipe Safety Grates, and Bar Safety Grates, Discharge = 11.81 cfs, Slope

£~

1.8

.0063

HW -D

f-' 1.0 0'1

2.5

2.1 ~

1.7 l-

1.3

0.9 t

0.5 0.4

PIPE SAFETY GRATES

Slope = .0108

* - 6.14 cfs • - 8.12 cfs 0- 9.66 cfs .- 11.81 cfs

• • •

0 0 0

• • •

• • •

0.6

• •

0 0

• • • •

I

0.8

•

0

• •

1.0

~ D

• •

0 • • 0 • • 0 • • • • 0 •

• • 0 • 0 • • • •

I

1.2 1.4 1.6

Figure B.42 Headwater vs. Tailwater for Pipe Safety Grates. Slope = .0108

0

0 • • .I!

•

1.8

.. '0

J1!Ii. D

..... 1.0

"

2.5

2.1 l-

1.7 l-

r 1.3 t-

0.9 f-

0.5 0.4

BAR SAFETY GRATES

Slope = .0108

*- 6.14 cfs .- 8.12 cfs 0- 9.66 cfs .- 11.81 cfs

• • •

0 0

• • •

~ .- *

0.6

• •

0 0

• • ... ...

L

0.8

•

0

• •

1.0

L.11!: D

• • • 0

• 0 • • 0 • .. • 0 • .. 0 • ..

0 • .. • .. •

I

1.2 1.4 1.6

Figure B.43 Headwater VS. Tai1water for Bar Safety Grates, Slope = .0108

0

0 • • .. ..

1.8

1t:ti. D

~ \D OJ

2.5

2.1 ~

1.7 ~

1.3 r

0.9 ~

0.5 0.4


£ - No Safety Grates • - Pipe Safety Grates o - Bar Safety Grates

~ i. .i i •

-.l

0.6 0.8

•

1.0

.li1! D

• t

1.2

a • • I

1.4 1.6

Figure B.44 Headwater vs. Tailwater for No Safety Grates, Pipe Safety Grates and Bar Safety Grates, Discharge = 6.14 cfs, Slope

~ W.

1.8

.0108

..

I-'

'" \0

J:!.!!t. D

2.5 , ------------------------~

2.1 I-

1.7

1.3 I-

• 0.9

0.5 0.4

Discharge = S.12 cfs Slope = .010S

A - No Safety Grates .- Pipe Safety Grates o - Bar Safety Grates

.. • .. •

I

0.6 0.8

..

o .i.

i • i i

I

1.0 1.2 1.4

nr: D

B.4S Headwater vs. Tailwater for No Safety Grate,

~

•

1.6

Pipe Bar Safety Grate, Discharge = 8.12 cfs, Slope = .010S

•

1.8

..t:Ut: D

N 0 0

2.5

2.1 f-

1.7 I-

1.3 •

0.9

0.5 0.4


• - No Safety Grates • - Pipe Safety Grates 0- Bar Safety Grates

• , • I

~ ~

0.6 0.8

t ,

1.0

~ D

i.

~

.i

1.2

• ~

i

~

1.4 1.6

Figure B.46 Headwater vs. Tailwater for No Safety Grate, Bar Safety Grate, Pipe Safety Grate, Discharge = 0.66 cfs, Slope

, •

1.8

.0108

HW D

N 0 ~

2.5

2.1 I-

1.7 ~

t 1.3 I-

0.9

0.5 0.4


~- No Safety Grates • - Pipe Safety Grates 0- Bar Safety Grates

, i , • t

I

0.6 0.8

t

1.0

lit: D

~ • .i

1.2

• ~ ,

i

1.4 1.6

Figure B.47 Headwater vs. Tailwater for No Safety Grates, Pipe Safety Grates, Bar Safety Grates, Discharge = 11.81 cfs, Slope

1.8

.0108

"

APPENDIX C

Summary of Regression Results: Box Culvert

"

. .

DEVELOPMENT OF REGRESSION EQUATIONS CONSIDERING VARIOUS FLOW REGIMES

To determine the regression equations, the experimental data was

di vided into the different flow regimes. Several regression equations using

different combinations of controlling factors (headwater, tailwater, etc) were

considered. As an example, for Type 1 flow regime, the headwater, tailwater,

and slope are factors used in culvert design while tail water depth is not.

Therefore, the regression equations were developed using different com binations

of discharge, headwater, and slope for Type 1 flow regime conditions.

The statistical package program, OMITAB II, was utilized to deter-

mine the best fit equations for each combination of controlling factors.

OMNIT AB II (1966) was developed by the Statistical Engineering Laboratory of

the National Bureau of Standards and uses the ordinary least squares method to

determine the regression coefficients.

The regression equations to predict C were also used to identify e

outliers in the data. To identify outliers, the deviation of the measured Ce values

from the predicted C values were computed and were assumed to be normally e

distributed. The frequency of occurrence for the maximum deviation was

computed 1 n+l where n is the number of observed data points. A normal

distribution table was used to determine the maximum deviation associated with

the computed frequency. Outliers were identified as having deviations larger

than the maximum expected deviation.

Regression Equations for C e

Basically, the regression equations to determine entrance headloss

coefficients were divided into two groups. The first set of regression equations

were theoretical models based upon the energy equation. The second set of

205

regression equations predicted the entrance headloss coefficient from different

combinations of headwater depth, discharge, tailwater depth and slope.

To develop the theoretical regression models, the energy equation for

the entrance of the culvert was considered. The energy equation was rearranged

so that the entrance headloss coefficient was the dependent variable and all

other terms in the equation were independent variables. The resulting equation

is

2g ( ? 5 r2 - I BD •

(C.l)

For the statistical analysis, the terms 2g, -2g, and -1 were replaced with the

regression constants Bo' B I' and B2• The final equation form is

(C.2)

To introduce different terms to the theoretical model, the variables

were multiplied by (~l 5 r2 and added to the equation. As an example, if BD •

tail water was included, then the final equation form would be

For the second set of equations, the regression models were in the

general form

(C.4)

where all terms have been previously defined. It should be emphasized that the

selection of independent variables for the regression analysis must be done so

that independence is maintained. For example, if So was also included in Eq.

206

(C.4) then the variables would not be independent in r::,w which is a function of

Q TW BD I•5 ' ~,and So·

207

Equation Reference

1

2

3

4

5

6

7

Table C-I

Equation Form

C B B (HW) (~r2 + B (~)-2 e = 0 + I 0 BOI.5 2 BOI.5

B (5 )(~,-2 3 0 BOl.5

B (S ) (Q ,-2 3 0 Br;D

208

Table C.1 (continued)

Equation Reference Equation Form

8 Ce = BO + B1 HW, ~ (W + B2 (B01•5)

9 HW, ~ TW, Ce = BO + B1 (W + B2 (B01•5) + B) 'iP

10 ~ ~ Ce = BO + B1 (B01•5) + B2 ( 0

11 ~ ~ Ce = BO + B1 (0 + B2 (B01•5) + B) (So)

12 H~ HW2 ~ Ce = BO + B1 fif + B2 (0) + B) (B01•5) +

~2 B4 (

BOl.5) + B5 (So)

13 HW2 ~ ~2 Ce = BO + B1 (j) + B2 (B01•5 ) + B) (B01•5)

B4(So)

14 ~ T~ Ce = BO + B1 (B01•5 ) + B2 ~ + B) (So)

15 Ce = BO + B1 (So)

16 Ce = BO + B1 (~) + B2 (5 ) BO • 0

209

Equation Reference

17

18

19

20

21

Table C.1

Equation Form

210

TABLE C.2

BOX CULVERT RESULTS OF REGRESSION ANALYSIS: NO GRATES

B Bl B2 B3 B4 Number of

Regime Equation 0 R Points

1 1 .222 -.431 .207 .076 36

4 .072 1.822 -1.132 -55.845 .461

8 -.071 .825 -.206 .248

11 -1.164 4.274 -1.113 36.786 .710

13 .210 2.956 -.842 - .112 42.682 .884

2 2 -.047 6.189 -4.171 -40.477 .943 34

8 -.333 1.367 -.309 .958

3A 1 .344 -2.823 1.154 .586 36

4A 1 .738 2.943 -5.167 .601 103

2 .726 3.480 -4.778 -.739 .605

9 .003 .525 .014 - .153 .653

4B 2 2.720 -36.654 16.641 -31.577 .604 42

3 2.268 -32.40 14.443 -25.911 .572

9 -.832 -2.601 1.250 -.047 .572

11 -.354 -1.664 .827 -41. 657 .779

211

TABLE C. 3

BOX CULVERT RESULTS OF REGRESSION ANALYSIS: PIPE GRATES



1 1 .430 -.384 .181 .054 39

3 .053 2.030 -1. 251 59.330 .453

8 -.121 .977 -.245 .294

11 -1.288 4.542 -1.160 36.741 .791

12 .127 .333 2.111 -.723 -.072 .918

13 .203 2.258 -.651 -.084 34.185 .918

15 .159 7.929 .246

16 .135 .011 7.836 .258

17 .258 .092 .072 8.273 .258

2 2 -.042 6.103 -4.771 .625 .828 32

5 .163 -1.232 2.554 -109.0 .804

8 -.339 1.308 -.286 .922

9 -.355 1.313 -.287 .014 .913

10 -.023 -.061 .521 .598

4A 2 .646 5.105 -2.084 -4.085 .511 129

3 .805 3.162 -1.470 -2.456 .517

8 .132 .240 .042 .543

9 .365 .688 -.0362 -.498 .591

10 .158 .077 .180 .423

14 .176 .077 .183 -5.708 .444

18 .511 .195 .283 .511

4B 2 1.130 -13.674 8.337 3.256 .444 44

8 .219 -1. 356 .561 .273

9 .526 -1.179 .397 .205 .462

11 -.813 2.700 -.554 -123.532 .987

212

TABLE C. 4

BOX CULVERT RESULTS OF REGRESSION ANALYSIS: BAR GRATES



1 1 .321 -.0060 -.420 .675 26

8 -.364 1.339 -.268 .861

11 -.849 3.066 -.755 17.429 .904

13 -.091 1.581 -.196 -.108 16.073 .919

2 2 .033 4.652 -2.555 -.356 .848 28

8 -.269 1. 782 -.470 .941

9 - .157 1.471 -.417 .078 .839

3A 6 .543 -.608 .818 28

18 .059 .137 .744

4A 1 .825 2.419 -4.591 .675 38

2 .747 5.091 -3.648 -3.081 .700

3 .557 6.559 -5.052 -3.707 .666

8 .100 .308 .041 .627

9 .343 .738 -.035 -.484 .663

19 .256 .586 -.330 .658

4B 1 -.571 -1.576 .803 .661 26

9 -.660 -2.039 .998 -.099 .952

10 -.473 .196 .047 .509

11 -.612 -2.031 .999 -19.941 .957

13 -8.193 -.689 4.210 -.421 -12.012 .980

213

APPENDIX D

Clogging Test Results For Box Culverts

3.0

2.& f-

2.6 ~

2.4 ~

2.2 r-

.I:LW. D 2.0 I-

1.&

1.6 ~

1.4 ~

1.2

1.0 0

PIPE SAFETY GRATES

Discharge ~ 9.0 cfs Slope = .0008

PLACEMENT OF CLOGGING

o - Top to Bottom • - Bottom to Top

0 i •

I I

10 20 30 40

0

• EJ

• I

50 60

«(, ClogSing

EI

•

I

70 &0

Figure D.l Headwater vs. Percentage Clogging (So ~ .0008, Q = 9 cfs)

217

o

•

90 100

3.0

2.8

2.6

2.4

2.2 JiWa

D 2.0

1.8

1.6

1.4

1.2

1.0 o

PIPE SAFETY GRATES


Placement of Clogging

o - Top to Bot tom • - Bottom to Top

•

10 20 30 40

o

•

50

o

•

60

% Clogging

o

•

70 80

Figure D.2 Headwater vs. Percentage Clogging (S = .0008, Q = 9.6 cfs) o

218

o

•

90 100

Figure D.3 Headwater VS. Percentage Clogging (So:=; .0008, Q == lOcfs)

219

3.0

2.8

2.6

2.4

2.2 HW IJ 2.0

1.8

1.6

1.4

1.2

1.0 0

PIPE SAFETY GRATES



0- Top to Bottom • - Bottom to Top

0

0

0 • 0 • • •

10 20 30 40 50 60 70 80 % Clo!,g ng

Figure D.4 Headwater vs. Percentage Clogging (So = .0008, Q = 11.2 ds)

220

0

•

90 100

3.0

2.8

2.6

2.4

2.2

J::J..W. D 2.0

1.8

1.6

1.4

1.2

1.0 0

PIPE SAFETY GRATES



o - Top to Bottom • - Bot tom to Top

0 0 • •

10 20 30 40 50 60

% Clogging

70

o

•

80

Figure D.S Headwater VB. Percentage Clogging (So = .0063, Q = 8.04 cfs)

221

o

•

90 100

3.0

2.8

2.6

2.4

2.2

1:!.J!l D 2.0

1.8

1.6

1.4

1.2

1.0 0

PIPE SAFETY GRATES




• 10 20 30 40

o

•

o

•

50 60

% Clogging

o

•

70 80

Figure D.6 Headwater vs. Percentage Clogging (So = .0063, Q = 9.11cfs)

222

.'

o

•

90 100

, .

3.0

2.8

2.6

2.4

2.2 J:U{.

D 2.0

1.8

1.6

1.4

1.2

1.0 o

PIPE SAFETY GRATES




• • o

10 20 30 40

o

o •

•

50 60 70

% Clogging

80

Figure 0.7 Headwater VS. Percentage Clogging

(So = .0063, Q = lO.04cfs)

223

o

•

90 100

3.0

2.8

2.6

2.4

2.2

J:L!!l D

2.0

1.8

1.6

1.4

1.2

1.0 0

PIPE SAFETY GRATES



o - Top to Bottom • - Bottom to Top

• • o o

o

• o

o • •

10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D.S Headwater vs. Percentage Clogging

(SO = .0063, Q = 11.07cfs)

224

3.0 --------------------------------------------------~

2.8 I-

2.6 -

2.4 -

2.2 r-

2.0 I-

PIPE SAFETY GRATES

Discharge = 9.0 cfs

* - Slope .0008 • - Slope = .0128

% Clogging

Figure D.9 Headwater vs. Percentage Clogging (So = .0008, Q = 9.cfs)

(So = .0128, Q = 9.cfs)

225

*

3.0 ,..------------------------,

2.8 f-

2.6 f-

2.4 I-

2.2 f-

2.0 r-

1.8

1.6

1.4 I-

1.2

~

1.0 0

PIPE SAFETY GRATES

* -Discharge = 9.11 cfs Slope = .0063

• - Discharge = 9.02 cf s Slope = .0128

* * t • •

I I

10 20 30 40 50

* • I

60

% Clogging

*

I

70 80

Figure D.lO Headwater vs. Percentage Clogging (So = .0063, Q = 9.llcfs) (So = .0128, Q = 9.02cfs)

226

*

90 100

3.0

2.S I-

2.6 -

2.4 -

2.2 HW D

2.0 '-

1.S

1.6 t-

1.4

1.2 ~

1.0 o

..

PIPE SAFETY GRATES

Discharge = 10.0 cfs

* - Slope = .0008 • - Slope = .0063 A- Slope = .0128

• I I I

*

•

i

I I

10 20 30 40 50 60 70 SO 90 100

% Clogging

Figure D.ll Headwater vs. Percentage Clogging (So = .0008, So = .0063,

So = .0128, Q = 10cfs)

227

J:JJIL D

3.0

BAR SAFETY GRATES 2.8 Discharge = 8.12 cfs

Slope = .0063

2.6 Placement of Clogging

2.4 0- Top to Bottom • - Bottom to Top

2.2

2.0

1.8

1.6 o

• 1.4 o

1.2 o • • 1.0 ..... _...L.-..!L_.....l-_ ....... _--L._---J. ______ "--_-'--_....L-_..J.

o 10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D.12 Headwater vs. Percentage Clogging (So = .0063, Q 8.l2cfs)

228

3.0

2.8

2.6

2.4

2.2

J:L!!!. D 2.0

1.8

1.6

1.4

1.2

1.0 0

:

BAR SAFETY GRATES




10 20 30 40

o •

o

•

50 60

% Clogging

o

•

70 80

Figure D.l3 Headwater vs. Percentage Clogging (So = .0063, Q = 9.09cfs)

229

o

•

90 10<t

3.0

2.8

2.6

2.4

2.2

J::I.JtL. D 2.0

1.8

1.6

1.4

1.2

1.0 0

BAR SAFETY GRATES



0- Top to Bottom • - Bot tom to Top

• o

• o

o

• o

o •

iI •

10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D .14 Headwater vs. Percentage Clogging

(So = .0063, Q = 10.11cfs)

230

. . .

3.0

2.8

2.6

2.4

2.2 J:J..Yt.

D 2.0

1.8

1.6

1.4

1.2

1.0 o

BAR SAFETY GRATES




• o

• o

o

• o

o • •

10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D.15 Headwater vs. Percentage Clogging (So = .0063, Q = 11.05cfs)

231

3.0

2.8

2.6

2.4

2.2

Ji!!i. D

2.0

1.8

1.6

1.4

1.2

1.0 o

BAR SAFETY GRATES



o - Top to Bottom • - Bot tom to Top

• o

10 20

• o

30 40

o

•

50 60

% Clogging

•

70 80

Figure D.16 Headwater vs. Percentage Clogging (So = .0063, Q = 11. 91 cfs)

232

.'

90 100

3.0

2.8 r-

2.6 f-

2.4 I-

2.2 r-

j-IW D

2.0 I-

1.8

1.6 t-

1.4

1.2

1.0 0

Slope = .0063

Top to Bottom Clogging

• - Pipe Safety Grates Discharge = 9.11 cfs

jr- Bar Safety Grates Discharge = 9.09 cfs

.. • • I I I

10 20 30 40 50

.. I

60

% Clogging

I

70 80

Figure D.17 Headwater vs. Percentage Clogging

• jr

90 100

Pipe Safety Grates (So = .0063, Q = 9.llcfs) Bar Safety Grates (So = .0063, Q = 9.09cfs)

233

3.0

2.8 I-

2.6 -

2.4 r-

2.2 f-

2.0 r-

1.8

1.6

1.4

1.2

1.0 o

Slope = .0062

Top to Bottom Clogging

• - Pipe Safety Grates Discharge = 10.04 cfs

~ Bar Safety Grates Discharge = 10.11 cfs

* I I I I

10 20 30 40 50

I

60

% Clogging

~

•

I

70 80

Figure D.1B Headwater vs. Percentage Clogging

I

I

90 100

Pipe Safety Grates (So = .0062, Q = 10.04 cfs) Bar Safety Grates (So = .0062. Q = 10.llcfs)

234

:

3.0

2.8 I-

2.6 -

2.4 -

2.2

~ D

2.0 -

1.8

1.6

1.4

1.2

1.0 0

Slope = .0063

* Discharge = 11.1 cfs

Top to Bottom Clogging • • - Pipe Safety Grates * - Bar Safety Grates

* •

* • * t •

* •

I I I 1 l

10 20 30 40 50 60 10 80 90 100

% Clogging

Figure D.19 Headwater vs. Percentage Clogging Pipe Safety Grates (So = .0063, Q = ll.lcfs) Bar Safety Grates (So = .0063, Q = 11.1 cfs)

235

. .

• 5.0

PIPE SAFETY GRATES 4.5 I-

Discharge:: 9.02 cfs Slope :: .0008

4.0

3.5

3.0 Ce

2.5 l-

• 2.0 f-

1.5 l-

• 1.0 •

• 0.5 • H

0 I I I I I

0 10 20 30 40 50 60 70 80 90 100

% Clogging

Figure 0.20 Entrance Headloss Coefficient vs. Percentage Clogging (S = .0008, Q = 9.02 ~fs)

0

236

.'

..

5.0

4.5 f-

4.0

3.5

3.0 f-

2.5 ~

2.0 f-

1.5

1.0

0.5 [ ~

0 0

PIPE SAFETY GRATES


Placement of Clogging o - Top to Bottom • - Bottom to Top

0 • •

10 20 30 40

o

0 • • I

50 60

% Clogging

o

o

•

• 10 80 90 100

Figure D.21 Ent-rance Headloss Coefficient vs. Percentage Clogging (S = .0008, Q = 9.62 cfs)

o

237

5.0

4.5 PIPE SAFETY GRATES


4.0

3.5 f- 0

3.0 ~ Ce

2.5 0

2.0 ~ 0

1.5 f-

0

1.0 0

b 0

0.5

0 1 I I I I

0 10 20 30 40 50 60 70 80 90 100

% Clogging

'. Figure D.22 Entrance Headloss Coefficient vs. Percentage Clogging

(So = .0008, Q = 10.7cfs)

238

5.0

4.5

4.0

3.5

3.0 Ce

2.5

2.0

1.5

1.0

0.5

0 0 10

PIPE SAFETY GRATES


Placement of Clo~

Ii

- Top to Bottom - Bottom to Top

20

o •

30 40

o

•

o

• 50 60

% Clogging

o •

•

70 80 90 100

Figure D.23 Entrance Headloss Coefficient vs. Percentage Clogging

(s 0 = .0008, Q = 11. 2cf s)

239

5.0

4.5

4.0

3.5

3.0 Ce

2.5

2.0 ""

1.5

1.0 ""

0.5 10-

0 0

•

PIPE SAFETY GRATES • Slope = .0063 * • - Discharge = 8.04 cfs * - Discharge = 9.10 cfs • - Discharge = 10.04 cfs • - Discharge = 11.07 cfs •

•

• *

• •

t • • • • • • I • • I I I I

10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D.24 Entrance Headloss Coefficient VS. Percentage Clogging (So = .0063, Q = 8.04 cfs , Q = 9.1 cfs , Q = 10.04 cfs, Q = 11. 07 cfs)

240

• 5.0 ..------------------------,

4.5

4.0

3.5

3.0

2.5 r-

2.0 r-

1.5

1.0 f-

0.5 •

o o

PIPE SAFETY GRATES

Discharge 9.02 cfs

• - Slope .0008 • - Slope .0128

10

• •

20

• •

30 40

• •

• • I I

50 60

% Clogging

•

I

70 80 90 100

Figure 0.25 Entrance Headloss Coefficient vs. Percentage Clogging (S .0008, S = .0128, Q 9.02 cfs)

o 0

241

5.0

4.5

4.0

3.5

3.0 ...

2.5 i-

2.0 i-

1.5 r

1.0

0.5

o o

PIPE SAFETY GRATES

• - Slope ; .0063 Discharge = 9.11 cfs

• - Slope = .0128 Discharge ~ 9.02 cfs

I

• • I

• • I

• •

I

•

• I I

10 20 30 40 50 60

% Clogging

•

•

I I

70 80 90 100

Figure D.26 Entrance Headloss Coefficient vs. Percentage Clogging (S .0063, Q = 9.11 cfs) (So = .0128, Q = 9.02 cfs)

o

242

Ce

5.0 • • PIPE SAFETY GRATES

4.5 ~ .- Slope = .0008 Discharge = 9.62 cfs

4.0 .- Slope = .0063 Discharge = 10.04 cfs

3.5 0- Slope = .0128 Discharge = 10.0 cfs

3.0

2.5 •

2.0 • -

1.5 - • •

1.0 l-

• • 0.5 • • • 0 0

IP 0 0 I I I 0

0 10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D.27 Entrance Headloss Coefficient vs. Percentage Clogging (S = .0008, Q = 9.62 cfs)

o (S = .0063, Q = 10.04 cfs)

o (S .0128, Q = 10.0 cfs)

o

243

5.0

4.5 f-

4.0

3.5

3.0

2.5

2.0 -

1.5 f-

1.0 r

0.5

o o

PIPE SAFETY GRATES

I

.- Slope = .0063 Discharge = 10.04 cfs

• - Slope = .0128 Discharge = 10.0 cfs

• • • •

• •

I

10 20 30 40 50

•

• I

60

% Clogging

•

•

70 80 90 100

Figure D.28 Entrance Headloss Coefficient vs. Percentage Clogging (S = .0063, Q = 10.04 cfs) (So = .0128, Q = 10.0 cfs)

o

244

.7

.6

.5

.4

Ce .3 I'V +'" \JI

.2

.1 r 0

PIPE SAFETY GRATES

Slope = .0128

15% Clogging

• •

* B

• ....1

Bottom 1/. 3

•

* o

• ....1

Middle 1/.

3


• * * ~ •

I

Top 1/.

3

- Q = 7.94 cfs - Q 9.03 cfs - Q 10.00 cfs - Q = 10.82 cfs

D.29 Entrance Headloss Coefficient vs. Placement of Clogging So = .0128, 15% Clogging

Ce N .t"-O'>

.7

.6

. 5

.4

.3

.2

•

* o

•

PIPE SAFETY GRATES

Slope = .0128

30% Clogging

• • t o o

• •

• I * * o

~

•

- Q 7.94 cf s - Q 9.03 cfs - Q 10.00 cfs - Q = 10.82 cfs

. 1 ~

0 • Bottom

1f, 3

• Middle

1f, 3


I

Top 1/,

3

Figure D.30 Entrance Head10ss Coefficient vs. Placement of Clogging S = .0128, 30% Clogging

o

.7

.6

. 5

.4

Ce .3 N ~ -..J

.2 I-

.1 I-

0

PIPE SAFETY GRATES

Slope = .0128

45% Clogging

• • e * Ii

•

• Bottom

1j. 3

* • II

* 0

• •

I

Middle 1j.

3


• t

0

*

•

I

Top 1/3

- Q = 7.94 cfs - Q = 9.03 cfs

Q = 10.00 cfs - Q = 10.82 cfs

B.31 Entrance Headloss Coefficient vs. Placement of Clogging So = .0128, 45% Clogging

5.0

4.5 BAR SAFETY GRATES • Slope = .0063

4.0 .- Discharge = 9.09 cfs . - Discharge 10.11 cfs ... - Discharge 11.05 cfs 3.5 • 3.0 l-

Ce

2.5 t-

• 2.0 f- • 1.5

• • 1.0 - •

• • • 0.5 • • ~.

0 I I I

0 10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D.32 Entrance Headloss Coefficient vs. Percentage Clogging (S = .0063, Q = 9.09 cfs, Q = 10.11, Q = 11.05 cfs)

0

248

Ce

5.0

4.5 I-

4.0 I-

3.5

3.0

2.5

Slope = .0063

• - pipe Safety Grates Discharge = 9.11 cfs

• - Bar Safety Grates Discharge = 9.09 cfs

•

•

2.0 I- •

1.5

1.0 i-

0.5

0 0

t

• • • I I

10 20 30 40 50 60 70 80 90 100

% Clogging

Figure D.33 Entrance Headloss Coefficient vs. Percentage Clogging Pipe Safety Grates (So = .0063, Q = 9.11 cfs) Bar Safety Grates (So = .0063, Q == 9.09 cfs)

249

5.0

4.5 r-Slope = .0063

• - Pipe Safety Grates 4.0 Discharge = 10.04 cfs

3.5

3.0

2.5

2.0 i-

1.5 r-

1.0

0.5

o o

I

• - Bar Safety Grates Discharge = 10.11 cfs

• • •

I

10 20 30 40 50

•

I

60

% Clogging

I

70

• •

I

80

• •

I

90 100

Figure D.34 Entrance Headloss Coefficient vs. Percentage Clogging Pipe Safety Grates (S = .0063, Q = 10.04 cfs)

o Bar Safety Grates (S = .0063, Q = 10.11 cfs)

o

250

•

•

5.0

4.5 Slope = .0063

• - Pipe Safety Grates 4.0 Discharge = 11.07 cfs

• - Bar Safety Grates

3.5 r Discharge = 11.05 cfs •

3.0 I- • 2.5

2.0 f-

• • 1.5 t-

• 1.0 • • • 0.5 •

• 0 I I I I I I I

0 10 20 30 40 50 60 70 80 90 100

% Clogging

Figure 0.35 Entrance Head10ss Coefficient vs. Percentage Clogging pipe Grates (S = .0063, Q 11.07 cfs)

o Bar Safety Grates (S = .0063, Q = 11.05 cfs)

o

251

j

j

j

j

j

j

j

j

j

j

j

j

.' j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

APPENDIX E

Graphical Results For Pipe Culverts

:

.' j

:. j

.' j

" j

. ' j

" • j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

I/) (\) .... 1'0 ... C!)

.c: ..... ~ (0)

N Vl Vl

1.2

1.1

1.0

.9

.8

.7

6

.5

.4

.3

.2

.1

0 0 .1 .2 .3 .4 .5 .6 .7

Ce Without Grates

.8

LEGEND

so=O·0007

.9 1.0 1.1 1.2

Figure E.l Comparison of Entrance Headloss Coefficients With and Without Safety Grates Slope = 0.0007

1.2

1.1

1.0

.9

.8

I/)

Cb . 7 -lIS ... 0

6 .c: -~ 011)

.5

N V1 .4 (J\

.3

.2 f /

.1

0 0 .1

Figure E.2

· . · .. . ... · . ..

. ...

/ LEGEND

So=O·008

.2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1

Ce Without Grates

Comparison of Entrance Headloss Coefficients With and Without Safety Gra tes Slope = 0.008

1.2

3.0

2.5

2.0

HW 1.!S -D

N VI --..J

1.0

.5

o 1.0

~ ~ ~ ~~ ~

1.5 2.0

~ ~

~

2.5

~ ~ II

3.0

Q -D2.~

~

~~

3.5

~

~ ~

• o

~

LEGEND

SQ=O.0007 • Grates o No Grates

4.0

Figure E.3 Headwater Vs. Discharge With and Without Grates Slope = 0.0007

• o

4.5 5.0

3.0

• 0 2.5 ~ ~

~ ~

~ 2.0 t ~

~ ~

~ ~ ~

HW 1.5 ~ ~ -0

~ N ~ ~ l/l (Xl ~

~~ 1.0 ~ ~ .

~ 81 ~

~

.5 t LEGEND

So=0.008

• Grates o No Grates

0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Q (i2.!i


3.0

2.5

• 2.0 t ~ , 0

8) f!

O~lIl!1 • HW 1.5 - 110 0 • ~ • N ~ V1 \0 ~ ~

~ 1.0 t

~ ~ ~ ~ II ~ ~

.5 t LEGEND

So=0.050

• Grates 0 No Grates

0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Q [j'2.5


N (J\

o

Ce

1.25

1.00

• 75

.50

.25

o o

..

.5

•

o •

o O· •• 0 .0· ~ ~ 1bIo0. 00. 11 !jOt

~oo • • o .... ~ .- .. . .-. .

••• ftn o'b o •

o 0110 •• 0

o OeD • • •• .tib 0

BI' 0 0 • •••• 00

o rEO 0000 0

o

1.0

o o

HW -D

1.5

LEGEND

80 =0.008 Types 1, 2, 4A, and 4B


2.0 2.5

Figure E.6 Entrance Headloss Coefficient Vs. Headwater Types 1, 2, 4A and 4B With and Without Grates, Slope = 0.0008

3.0

N 0'\ l-'

Ce

1.25

1.00

.75

.50

.25

o

•

*

o .5

Figure E. 7

• •

• • • •

• •• * ** * •

*** *

1.0 1.5 2.0

!iYt. D

LEGEND

So=0.008 Type 1

• Grates * No Grates

2.5

Entrance Headloss Coefficient Vs. Headwater Type 1 With and Without Grates, Slope = 0.0008

3.0

N 0\ N

Ce

1.25

1.00

.75

.50

.25

o o .5

Figure E.8

, •

... *

* LEGEND

So=0.008 Type 2


1.0 1.5 2.0 2.5 HW -D

Entrance Headloss Coefficient Vs. Headwater Type 2 With and Without Grates, Slope = 0.0008

3.0

1.25

1.00 ~

.75 l-

Ce

tv .50

'" W

.25

o o .5

Figure E.9

1.0

•

*

!:t}!L o

*

• •• • •

* ** *

1.5

• *

* • tt •

• •

* * * *

* ~.* t* * • * • • . ..

* •• * • • * * .* * • •

2.0

LEGEND

So=0.008 Type 4A


2.5

Entrance Headloss Coefficient Vs. Headwater Type 4A With and Without Grates, Slope = 0.008

3.0

N 0"1 .t-

Ce

1.25

1.00

. 75

.50

.25

o o .5

Figure E .10

1.0

• • -.. .

• . . .,.. ;.

HW D

•• ••• t.t.·" •.

• iI • • • •

1.5 2.0

• •

• • •• • • •••

LEGEND

30 =0.008 Type 4B

• Grates • No Grates

2.5

Entrance Head10ss Coefficient Vs. Headwater Type 4B With and Without Grates, Slope = 0.008

3.0

1.25

1.00 ~

.75 ~

Ce

. 50 t N 0\ VI

.25

a a

[f

• 0

• 0

.5 1.0 1.5

HW -D

o· rJI ~.

0

• • • .. ,,·0.0 .. • ~ 000 0 • ~ .00

000

2.0

LEGEND

so=0.0007 Types 4A and 4B • Grates o No Grates

2.5

Figure E.ll Entrance Headloss Coefficient Vs. Headwater Types 4A and 4B With and Without Grates, Slope = 0.0007

o·

3.0

N 0\ 0\

Ce

1.25

1.00

.75

.50

.25

o o .5 1.0

HW D

• 1.5

• • ••• OO[]O .!J

[][] []

LEGEND

30 =0.0007 Type 4A

• Grates 0 No Grates

2.0 2.5

Figure E.12 Entrance Headloss Coefficient VS. Headwater Type 4A With and Without Grates, Slope = 0.0007

3.0

1.25

I 1.00 ~

.75 ~

Ce

N .50 t (J'\

-...J

.25

o o

0- 0-d'

~- 0

tit --'" 0 0 O-r.

I:f 0

-0 -0

LEGEND

So=0.0007 'lYpe 4B -Grates

0 No Grates

.5 1.0 1.5 2.0 2.5

HW -D

Figure E.13 Entrance Headloss Coefficient Va, Headwater Type 4B With and Without Grates, Slope = 0.0007

3.0

N 0'\ 00

Ce

1.25

1.00

. 75

.50

.25

o o

•

o o

, I . •• ·~O lh. • o·

••• • IDl 0

o 0

o " 0000 0

1.0

o o

2.0

Q -D2.5

~lffIJfIJ

j ~ @! ~i ~ 0 ~

• •

LEGEND

So=O·008 'IYpes 1. 2. 4A. and 4B


3.0 4.0

Figure E.14 Entrance Headloss Coefficient Vs. Discharge Types 1, 2, 4A and 4B With and Without Grates Slope = 0.008

5.0

N

'" \D

Ce

1.25

1.00

.75

. 50

.25

o

•

*

o 1.0

Figure E.lS

I

• • • • • • • *

* * * •

* * * *

LEGEND

So=O.OO8 Type 1


2.0 3.0 4.0

.Q. D2.5

Entrance Headloss Coefficient Vs. Discharge Type 1 With and Without Grates, Slope = 0.008

5.0

N "-I o

Ce

"

1.25

1.00

.75

.50

.25

o o 1.0

I

•

t

* *

2.0

Q -D2.5

3.0

LEGEND

So=0.008 Type 2


4.0

Figure E.16 Entrance Headloss Coefficient Vs. Discharge Type 2 With and Without Grates, Slope = 0.008

5.0

1.25

1.00 ~

.75 ~

Ce

N .50

-....J !-'

.25

o o

* *. • ,

• • i

* ItIc

1.0 2.0

* * , • •

•

Q -D2.5

* ,

3.0

LEGEND

So=0.008 Type 4A


4.0

Figure E.17 Entrance Headloss Coefficient VS. Discharge Type 4A With and Without Grates, Slope = 0.008

5.0

1.25

1.00 ~

.75 I Ce

. 50 N -.....J N

.25

o o 1.0

Figure E .18

* • • • .. *

ttl . i * *

• •

I • •

• .. * • t

2.0 3.0

.Q.. D 2.6

* * • • • .. * * •

*

IEGEND

So=0.008 Type 4B


4.0

Entrance Headloss Coefficient Vs. Discharge Type 4B With and Without Grates, Slope = 0.008

5.0

1.25

1.00 •

.75 J

Ce

N .50 t

...... w

.25

o o 1.0

Figure E.19

• *

•

• * *

2.0

Q -02.S

* .. • • •

* • • *

• · I * * • * *

3.0

LEGEND

80 =0.0007 Types 4A and 4B • Grates * No Grates

4.0

Entrance Head10ss Coefficient Vs. Discharge Types 4A and 4B With and Without Grates, S 10 pe = 0.0007

"*

5.0

N -....J ~

HW D

2.7

2.5

2.1

•• o· 1.7 .. 0

1.3

.9

.5 .4

De •

• ~ ~. •

0 0

.6 .8 1.0

TW -D

~

o.

1.2 1.4

.0 o

I:f

• o

LEGEND

80 =0.0007 Q =5.6 efs


1.6 1.8

Figure E.20 Headwater Vs. Tailwater, Grates and No Grates Slope = 0.0007, Q = 5.6 cfs

2.0

N -....J VI

HW D

2.7

2.5

2.1

1.7

1.3

.9

.5

• 0

.4

• • • 0 0 0

.6 .8

Figure E .21

~

• 0 • 0 • 0 • • 0

0

• • ~

• 0 0

LEGEND

30 =0.008 Q =3.6-3.8 cfs

• Grates D No Grates

1.0 1.2 1.4 1.6

TW -D

Headwater VS. Tailwater, Grates and No Grates Slope = 0.008, Q = 3.6-3.8 cfs

1.8

•

2.0

N '-l CJ'\

t!Jr o

2.7

2.5

2.1

1.7

1.3

.9

.5

e

.4

• •

• • i

i i

m •

e e e II

LEGI!.:ND

50 =0.008 Q =4.5 cfs


.6 .8 1.0 1.2 1.4 1.6

TW -o Figure E.22 Headwater Vs. Tailwater, Grates and No Grates

Slope = 0.008, Q = 4.5 cfs

1.8

•

2.0

"

ttlY ~ -...J D -...J

2.7

2.5 ~

2.1 ~

1.7 ~

1.3

.9

.5 .4

~

i

• ~

• ~ ~ ~ 0

.6 .8 1.0 1.2

TW -D

• 0

• •

i

1.4

• ~

LEGEND

50 =0.008 Q =5.5 cfs


1.6 1.8

Figure E.23 Headwater Vs. Tailwater, Grates and No Grates Slope = 0.008, Q = 5.6 cfs

~

2.0

, .

APPENDIX F

Data From Culvert Experiments

."

10.0 1 :I

10 1.0 C\I -

./ ~ I- .. I

F

B

" /'

>-

: ~ tv 00 ,.....

'a /'

>" 0.1 ~

Y c , ft Q , cfs

0.01 I II II II

0.001 0.01 0.1 1.0 10.0 100

Z/S2.5= ~ /S2.5=Q/32.1

Figure F.l Curve for Determining Critical Depth (Y c ) in Box Culvert

Table F.1 Data, Type 1, No Grates

D :; 1.25 ft, B "" 2 ft

C HW _Q- TW

-D-BD1 •5 -D- S e 0

..... 1)1» ,1b5.0 1.864") .J ..... ~ .'~13id

;""8' J;28185 .,

~,J"JG8 .,.,e.it ,0PIJIi.4

,2"'" t,"'.' ","''''~ ., ..... ,.' t 3~" .Pl813 ,11588 ~~"34'2 ',I~e •• • .. ~t1ft

:, .. " 4 • ,9'''68 2,411'" ", ..... , •• 1J.

~~ql'3 .,.'Hee l#>57841 ", ..... ,"S3' .. 2Q,., 1,.R3~A 1,.';n97~ I, ••••• ,.eI3' :221'" ,91?,tUt ~:2f\158 ~ ,0ftHHU! , M'2J8A

:22"~J _, C,A~:>'~ :::»:5S5~8 d I ~~~~J.' ,~H'~'H~ :l5&56 l,illdh' ?:16111 It', ."h-~ ~ V'! 'I ~~,f6"1

:Zba4" I ,'~Y.8ii! ?:91!JI)J8 (', .Wf4~~1 .;ii9.l£lA~

: ,,91J3 ,5(}12~ 1~18755 ~, !-'tHhH.t :l!\t~A~ :lJiJ80 ,btn"~ 1 .. 334J7 d. (l;1iJ~f : V.(,HR~

:.7385 ,7dbfl' 1: SiHH"3 ~ ; ,1v~ ~H'i,~ : ,'H "~ R~" :i~192 .17" • .:771')2 yII'1.t! ... H~1d ~-1'~.J ~ ,l ;13~45 ;e336 J 1:'19171 ~ I "f!~fltJ • ","'H'tRI' ,211 195 ,e9ZA ,~ 2::9822 ;11 ,tt~44dl' :IN~1HLl .22q65 1, 1 ?(.~'.j 3:tt;1l1 d: 9~';A;1 :,'~.~8\~ :l~2Q" .89!HV ? :23,114 iii, " >j.I"'~4 ., '/'11 ~A VI , "

:Z6"4 ,9t11?' 2:;"lH7tl If t "'~;.5.," .; h) ,~8U

:2b45~ I, 1ft Il/Hll 2:9a538 rtt,tt~Je~, ;~HHIAP :.Q1'1 ,S3'!~f: 1:17.-72 PI i!/'J" ,., .~ .0l-H,30 , ~,,',

:l9014 f 6t'?~·..:.' l ~3.., 176 ~, tHH,,~,' >'4b31ij :5 ("1645 ,07.h . t : ll~! /) ~ ro4,l'f~i~:li~~ : ;"~. b 3~' :37899 ,1~8(q 1 :',AQQ2 ti • ;;h'l; h:11J : ,:H1t,3~ ;lS.,j4 7616:~ 1~"qo2q ~:'i~,'''''' :\H~63" I

.?:1l~4lt .

~ d1863 ~i .11Q36 8"1'''' ':' • ,~:,' '; i" ~ I t ->' ,'j

:1~6'9 ,~76i'" ,.\ ?: :nc!l r .. "'; i> f'~~~·" • ~~63~1 :-?,QClo 9" ''''1' ?:o::.bJl.4j ..,. :·h.'Yf"'0 ; \t}~h3'1f I ,. ...

:,62"1 _, tj'93fl ~ ;>:79696 oil ; {c j.H4 rl" ,Al"63~i

;.100.' J, ft5l.?" 3>:3914 ~,~J.HM ,~0030

,2)2'~ t,1216'" },,28917 ","~.iI"'.6 .;:ab3~ , .1, '9 a ,8~3e" 2.,105t& .,e ••• " ,.,63" ;,52.' 1,.,.t14S" 2;.,.511 "," ... ."e618 ,1)4'5 I," 12411l 2,9.~3" ., ....... ,".bJ" ~215.3 I.I'lb. J.l.I1J1I11 '.18 •••• .fI .. ~J"

282

Table F.2 Oata, Type 2, Pipe Grates

C HW -L. TW

S e -0-B01.S

-0-0

, •• lJ. , ,1.5.~ l,86QS3 e, •••• ' ,IItIH3t!1 (\)7'3. .,I!Zo8 J,'A285 ", •• ,.A ,".138 ,

-21_11 ','7118 ].]9.7. . " .... ,., .ft!lfU 3'" !".58, .8t~2t) .2: ~Jlt.lo2 :;.t .... ,.,"tt'& ; _H1131r!1 :"'217 ;'1~2'8 2: lI illl0 ~;~"."A .~113'" ; •• 8.5 ,Q58?~ 2:S7A41 Qj .Uh'iti : .HH:Skl _125,.1 2;57847

, ;!HHllr!J ,'ft§868 ,52833 ,._.4f,l1

,958'" l,578'7 ,52811 ,"13. ,1"7" ,958b8 '.57.,1 ,55313 .'"'''' ,"',e. 1,'Un8e 't·3

." ., .... , ,.I.Sit

,1181' , 89'1w6 ~,1'8Z2 387Z. ,.IIfHI • iH S4Q ,<;It'4~ 1.2Al~8 .,:99f1.1lJ , " ... "'., :i?ZI54 .982fL; 2:')5520 104. i9tUH'"'' • .u*8 EH' :26316 -..

':76tt3 ..

: O~8e{i\ t.~~41b "!' ;J,~~ :':4 :3.249 i: ~'I~(.A! '.? : <J ~, '5 "' 8 "i, ~~"hhh1 ~ ;;0£1 8'" :;"97J3 :Sq12~ t:t~7~'" ",,~I~'h~(~ ,~0"'8(' :1 11 76, .

1:33 /H1 • ott iHh, :1!,~0IHHJ .~~I1JA:~ :15.b~ :7itSbv. 1:C;1l\j41 t'I, ~~"fllr.~ ; 'fl:H'!IU :.2676 :17214;.:; 1:711S2 " . 'i ,~hi ~ t\ • ~H'!(D8'" :15214 : J33SM' j : "19 tTl M· 'H~P.;,ft~ : ~3r.t98e . ~ ."

:~/"1'5 .. 59 >P'4 ~:t'9822 ~:;1"HH4~ :~~ff8" .. ,. ::;".)9i" .; .. 992:;) ,::-qtlS~8 iJI:i'l00M~ ; m'1.980 • :27 .1&9 1. !IAC;~") :>:'lJS'SS : 57 t 'S3 .0,;10A0 :1121" : 5'~2w\" 1~t2'.f72 ~; i' JJIJ)Vi

.. f~H~63n

:~?t.84 ; i: •• ,'~!J"f' l::hH 76 ~,-" ")J.lp..j ,~ltIb3lA .16751 .0"'2,1'1, .:'l91"1 .;J. <'M"'~HII ."~63$1t ;](6)'1 :7')68'" 1:&1\992 e; ,~ ... t4 ~ ;0063111 .. 183.6 ; U.,S2;" t:896;tq ~, • ~ ~ ,i"1[.' .idQlb3~ ;18330 ,8?26i.1 2:JI.I;41:1 ~;i'hllo1fL" ~ '1:""6]0 .1~8,. ,e18!"".~ ?:3~2t' "', 0~~~~~ ~ r.tj'ljo 3t~ :21373 QO:;"A', ~:561"'1 '" ,:" ~H' 4 ,,' "~lI630

:,,76.-" ,>

,:7<'1696 ,

"qoR.:' i1,"~0~1d "ih'163tlJ :.82I1i

., ,:eV17l1 1 ; O:;l6:,~ d.0"~~.:.' • t1~63i~

:2 (J~.S3 ' . . 3:,..,Q911 ~~f,fhHU ~dW!l630 1.i?/:H\.;

:126'1 ;g'1I4~ 2:t6516 " f1Iff""~ I tJf\630 :.52.1' •• ;..q(18~ ;t:9~S3a '51.1913 0\jb30 ;121.114 ?;'It9S18 ;'4973

, !,,~ ,,,.,, ,dtl630

,It!'3 &,17168 3,4;''17 ,511 .71 ,.'.10 .. >.!6! a.1716. 1.4!417 .64'7] ••• b!.

283

Table F.3 Data, Type 1, Bar Grates

C HW Q TW

S e -0-BDI •S -D- o

t··"1 ; b6J2J ·t45l97 • :~~WR'" .,fI!~I"''' ,'l'·1l ,7IJb'. 1~619" .. ,,, .... ~IJ" •• e ,"," ,7'16' tifl4J' " ..... ,"'8' , ,1'2.' ,~a~4'" 2,f8"'" ", ..... ,B.elf) .114'. ,e"~8' 2)28118 ., .... ., , •••• 11 ~'12.3 , ''J 6 .q IH'1 ~t1j1466 ~,""tt!l" ,.'l1li8 ... • 28b89 1, .·VUI" • '!:717J2 '!I,e~lf"ilt ."""'80 :'28'3 t., • ril1'~' ?,~986JS A,~"A'A" ;00~8~ :IIC;". \ I QIH.1 3.;'181& t;f ,rl;4 ;f~tJ t l~"I"80 :3'5.'3 j!~IH2ij ~:R9q12 2 ~~~iI~ , Vhh'8l' -3.31& l , \.1856 1; ~:"q~12 :S7i353 , HI",80 ~27489 ,~376~ 2::H522 " , ,." .... 9*) ~ ,·U-,tASVl :21.4211' , ~ 116 'l 1:"n371 f\, ~~10~0 .l1~88~ :UrJ:51~ .5Qb8l'f 1:~1417 V'! • {<HI)lI t- :~d630 :1'5.15' ;bb'?~ t:SJt5Jl · : "~'o3@ ~,IlI"'lt\~'" :1 81.' 7"'Sb~ l:TI)o12 ~1 • '" f., .; 'Ii ~ :\\91630 :lb488

' •. t.:

l:qbS~" · :~"'i>'~ , 77~4. .f , (-1 ¥' t; ~ .l

:23.1' ,

.8'524'1 ?:t8161 '. ~,-,~"q :"".6,0 ~ 1 ~, .

:22"4~ ;~Aq~~ ":-hl ,, 7 I 0, :\10,r1,.:. ~"~6'" :2U821 .q6'Sb~ 2.blo9J ".'~ ·h·""~ .~WJ61" :2b2~e ,;03,ZCH ,:1\1512 · :tldblfl {-4 ,t;itHh~8

: :\lSQS 1.1917':' 3~12""8 .... JrJI.-'l'It'l :..,:J63" :21!61 ....

3;158qlJ II ;~'d':;~:-! ;~\'Ib3e I.1A92~

;22016 ';"'26 •• '19.~]1 ,54973 , ••• 3. .11 •• 5 ,e~zIJS l.IQ82Z .. , ..... ," •• J8 :2~63b I. ~?P"ii 1:9.5JI ..••• tIt. •••• Sll

284

Table F.4 Data, Type 2, No Grates

C HW ---.2. __ TW

S e -D-

BD l . 5 D 0

:2""4 -. 1:l~285 ;85333 : (UH 30 !,1 1l t'b8

:268q3 1,17l.166 ':JlHd 8 ,828\J" >6013'" : t1 ]'3 ,~19.e 1:ru 14., ,58b67 ~ i'>1113~ :2lIU~1 1,0QQ48 'I~JCJ"" ,Sft",,, .'.13" :?6f17i ,q"l" :J.2"31' ,!,.!] ;"88' ;~'2J8 ,'.J2' ~~'-'374 ,""!] ,''''SII . 26489 _,".41 2:2.31 • ,'''''5J ,0'8S1 :32911 I ... t.4 llll .~, ?:?~374 81"5 :s • 1~H~~h" :s~2~i

-, 2: ~~3 7 '~

, :"'(~"8~ ! , ' 1 -l :.- :- • '-I87b'

:27 1 /1 9 , tA'-~~ ;J: 911531\ ;67"'-;,\ : ri,HHht -I .., . ;:Hl;-a !, ~;W36i.l i< 'JlIf5~R ,77053 ;~(l}~~0 .318q1 t 1":;'5)-' '-:'-?~)5.sR .87~'53 • "V0RA :J88114

-, ~~: '"' ~r; Jp. : q'hJS3 : ;i:'~'~'80 • 1 ~".~ " " _ c •.

;26 11 71 ,"1 It,?' ?:.'~~!t1.'.l ;57~S3 : ~qlt'89!

,2"238 ,~ ":J?'~ ":)'37~ .67?'153 : i.H'(l!RH .j6~o19 .,9"tI 1l, ;>:">;,4371.1 ~77lif53 ~ ~"iIll8il! ::\2'~1 ! t~ ''<~ 4 II '# ?: ) .<'5 7'~ .R7'{)53 .ep08~ ,., .

:S?2?1 I , 1 t -~'~:' 2~2~31.:J ~qR7?'" ;1d"'08r( :l111J~ 1.dfi'56" .~.~IHBA .67",53 • ~tH1A!.1 :?12)8 j ; " ~ 5 I,.~ l:qtr53~ ;17~53 ~ ~~~1~~ :.H ~91 !,J~S2~ ;>:9~5~,'i .87~53 • J'1~8~ :21\6444

. ;q7~S' ~ {.~~f.I!A0 t ,Ii;, :H'~ ?,!(053R .. -

:~94~0 tn ;>,I.:~ ?:1()!3~~ 5bb fJ ,\ :.~~63V\ :t?1f13

J . - . 2:1q~?2

1 ;"'1r..'63~' , 8~2r"il • 6 flbtP1

:121'J • (1, 3 .>~~~ ~:tq~22 ~1497l • "06 3~' :18ftb' • e I~ 'I ~ ~ 2:lq~?d ;84q73 : ~~b3 '(I : .~~542

, ?:tq8~2 • '''1lI b ~ " ,,'>.,..,1\, ,9 L1973 ~, . .' ~- ...

:!?I\&& t .~ iI?', i ;> : q t; II>" ;. • q" ~!~ ~ : ihH.~'; :t34 15

-I . 2:,)~S38 :b/~q73 · t ~ ... 2 l l:" .... ,6·H~

:131.115 :.., .

?>Ur;3~ : 7/JtH~ :8~b~0 !,"'!,ll::' :13447 5 ?~4HII~38 · ;."b11 ~, "20t) ,84973 :14355 ,.,;,,11«, ~·.'1"538 .84973 ,8eb,e :176'1 t:'~lllil" ?:'i'851e :'491J .f"b3~

285

Table F.S Data, Type 2, Pipe Grates

C HW Q TW D BD1.S -D- S e 0

: "1'i8J~ 1~' ,156ij .312Ai!~'3 ~85333 • tHlJ1 'J~1 : ~61 ,., ',11/168 ':.34~P\ .R"J~~ ; ~HH 3~ :il7", .6'4,8 ~;'~4'? ;"813 t"tt" ""'3ei ;q15G8 )"4114. ,'.llS ,"1" ~241" !,,,q,.e ';'J914 ,18'67 r Itlll 'I :486.5 ",,051. 2,t()82l ,'7''11 ,".SEI ;1'IJ~ ,9M7'" ?~t~ft2&t ,~e,~ .. !"'''~~P .27961 t,~'5'?) } ~2~ PH! • (.1'3 7 i?:~ • :'0~l:\e ·?'}7IJQ , QS'5.?ii ?':rH ll'.l ;'hI 387 : oHhH\1 · " ?~23144 : "'~j08" .1~465 ,917b~,' ,72887 • ?6!;Hi • ~~11 ?~ 2.2"!!17(1 .57~51 , n~'t;l~~ · -• ~1I1 iJ 38 ~ .~ -132 i~ ~~;~~n74 :67;:tS3 ."~V~R~ , - , ~ -

,'I) LI tl9 q IHI IJ" .,. ?,., 1 ,'! ;77~S3 :"0~8~ I 'J,2 Wt 7 -, '-1'

;~q~~\1 ,. '. !,f.r'll"~;6 ~.~t'.!71j ,r.7!1i53 ~ r;f\9&3 t U £I"' ;:;U37~ ,C'Hn 2\1 ,"i1~80 _, 'F,'

,:?7!/J9 !:.'~;b·: ,:q 5"'8 .t>7J53 • r"(,~~t.~ "72"$3 1, .1f'b6· ?:;';5~~ :77'~5:S : ." 11'10 A!~ ,~ ,

,318Y7 ! , H' 'j '-:) (' ~ 9,.15'8 ;H7~5J ~,AMHH:l • ;; A Ii It 4 t l~'j~'!~; ?: 9,1.'518 .970'53 , ~9t~8&~

:!3 h 7i 1 .'

~:1IlS\~ · 5~"~7 ,8~1{-'" .'JI36'~~ :t361, ;?: t 6S U)

, ;S~631;~ : 8~ 7/, ,6 11 9 7 3

:iV'15 , 817 6~~ ;,»:16516 .7~915 !-41>'lb'VI l' -,. : .)T35~ e ".~.t 2:16516 :'HIQ73 .~"&3;l :q~ 12/\ ' ' ~:165t~ ;911973 : 1ll/l>6 3~' 92t2~

· ! 521h' ~, '

;>:'1~538 :.\~63~ I .. t '18 '\ ,64973 ~ ,,' .. ,

2 >n:S38 :~0b3~ • \ 52;-'"" 1 ~ 1 LI,IP • 7/~q7J :!'J21t .{

, ;< (h:'5V~ ~ ~L\973 ..

It''JIII'~'f ."'''63@ : lIl'583 1,"'13;>" ;:< <}Wf5JA ,cnJ'J7 : f· t:lt:-:3 te' :i:!> tl 7S ~ '·t"Lo' ': 9'·538 ,6<1 9 13 ~;~ "0 ~V) :13lJ1~

., , 2-9lo'!S16 ! '*12 Ih( , 7'~ q 73 ,~li'!& ,,\-~

;13 1J 75 " -

l~""51e : ' - '

1 .... t2 4 .. ,8"913 ,"fib]" ,~t563 " , 17 1 b" :1,.-4'5477 ,14913 ,lilf6]1 ,~15b3 1,1716' J,.15477 ,84973 ,0n630 .~11563 ~.17t6~ ~·.1J'Jt17 7 .9"913 ."'?b30

286

Table F.6 Data J Type 2, Bar Grates

C HW _Q- TW e -D-

BD1.5 D S 0

;J.~1I8 t ;.,'10410 ~~Oq9J2 ;~622~ : ~~v.HHH'J .. 1.1I b 1. (4856. 2:~~4IJ12 ,"S72. ~"'8" :3.1'b ';""56' 2~6993Z ,61'I!J ,.'tlA" ;46411 1,15688 2';.1'9912 ,Q612' ,""8 .2tU!1" ,,9'8" l;1IS'2 ,i5f)l211t , ..... ; :S34'l 9~A~,F" '.!1'122 ,"'41J~1 ,"'''''' ,- .

.3111." • ;1i.l1 r~~ 1:31522 .75361 , ~11lJA0 ;3~311] ·vR7'Y ?:'i522 ~817?~l , r"008(1

" .

.5 t'190 1, t ~i 6lJ.- ?:.l)tS2? ,CHH~IJ , \'tilr.-I\~' :)6ftr~ ,7.'S>iA 1: 11 1117 ,579'S] ."0flt89 ;S~.8t , 772,ti.W 1: 11 3171 ,67053 ;09918" ,59.Q~ , 797'1ltf 1:WJ377 , 77 ... ~1I)3 , f'0elH' .8!3A3 ()~~e" 1 >'3371 :R7QSJ • Vf'!!I8~1 I ,.,

:821~14 I ";;>'j r" 1:"J377 .97Ar;l : ~W'J':'''t4 , ' .",.;~h

;il3b"5~ ," ~~;":,.,.~ 1~(J'371 ; 57 ~"'51 • "Ylti0IU~ , .. 3'i7 QQ ,7~blJl1- i. 1I 'JJ71 .65387 I ~"00AfII : 1'1.£15 • B 11 ~ II LlI ,)~t9R22 ;5 11 q73 , 0~b 3 It) .174'45 .8ll?lll" ?_J<~A22 .6 11 <171 .~0630

;11(ij5 ; 8 "L?It' ?:t9S'?2 ;7'.97.3 ;W<1lt63~ .2318n • ~J.:;2lH.4 2:t<')~22 ,B1i97l ,.J.~b'''' :l'S"" ·t:it"~Ai' 2:19P.~2 ,9 /1973 ,0063'-' :;t~636

' ... 2:(WS1~ t • t';;>':I;,}f' .6lt 973 • :i0t')3r

:22636 :; ~2H'1,iJ 2:9ff538 ;7/J97' : ',"'I:> 3 '" ;226!6 • t "21,.", t':~.'38 ,A4973 ;"'1" ... 21145 1 • ~.?thl" 2 ... Q ''5'8 • 9'9'3 .... , .

287

Table F.7 Data, Type 3A, No Grates

C HW _Q- TW

S e D BD I •S -D- o

'!: 0.86 ~ t'3~ 4\; ;; J ':~?8'S 1 1\,'H~0J ,~'f2R~

• 1C'J4'9 .d6b··:. 1.'773l (1,k\.HPI3 ,1t12R0

; •• 'ff" ;532 4 • l~leJ.r; ",'8 •• ' t~H28" ,llall0 ,"H~~W :t~tj6082 9, ••••• ,"12&111 " ".Ua a 1/0)la 3:6.,51' iI,_."" ,".281 ., i i 4hj~] !, ~IAljtl "" J,1.g7Sa ~,"'" ,'12S. .ltt211 :,t?'2-{-' J.3t447 " , ~ ~~ ,;',JI ~01?M'! - "'48'~ ./'I,.B.< • : f\ 8 .~ '5 'l ,~. !'II~ 'HH) ,~Jt 2Ar •

·'ll4 ;6136:· 1:f~'9163 A; "~'0e8 .~·t2Io\Qi

~:'!J7"4 (~q 1','; 1:77'52 til. 'H;~HH~ ;~12A~ : U15'11 l' 'V' . It:.'4"5' l';;) .jtPlVl , ~~ 1 2 8 ~1 i ~j .. ":!

:lJl5£12 . ,

?»~qbb 1 .,.~. "', .. ',~ , v~ ,,' VIr: \I) .'112Ma t .. ,. ,

;: 'Sa 4 .,7 Q ,tJi J .l:t~b81 lA,~"'I.J"/(\ ;.H2A0 .1'9753 I • S I~ 6 i' .~ 1~.t915'" '.I.01if0J1,f1ll • ru 28" ;(931i ~ 'J/.. 'I A .~ '»7~22 ~; "J,.'y}lH' ::,. 280 , ,

:~:B5:JB~ ,atlbb I , :i; ~l 41 '. J"it';"'" • iid 280 .. .t95"e I.·~ :'~" " 2: 'flH''; 3 • 1 til ~ r. .; :~J?88 ~

!0210 ; S? 1 ~ • t:13l9B ~I: ,,;,c ~hll' :lI!H~8" .. ;111779 ',9 11 fl' !:~t57" III ; ,:, ~,~) I' ", ~""08" a ,,2C"1Q4 " C 1: 5,,/);> I ""."A(,.l~'" • ,~ I 0 A fI • ';t::> Jb· 1

• ·87o~ • ':.i~21.J- ~ ~7 ~5t2 VI' r1' ~~.,. ;ql~80 · , .- . t "(1, '.

:12058 ,7<)So<,; 1>/12Iq ~.~,4~?,? !:" hH~" :ii,lQ6Qli ~ .• -'l!l " ?:1?6~1 ~: r~~ 1'", ."l~AIIJ : .. : li2'1 41-'./~1~1.l;~ ?: :',l.l9~? ,1 ~ 1'~~\.~0 ::~t~~r, :156.5 'Q~C;'" ?:1)78t17 ~. ".M.t).Q : Jl U~6111 ,. -: 1811§iI C,q7'~) ?>q I~~n lIt'IIt~Wi! ,!,}~06P1 :

'>,,,,)A?? ,~ .. '

:?I:ttQ I3 • ~' ( I~ A-:\' ,..I:t~l?C~'. : ~ I <'181' _ , - J .•.

; ,&bo'.; 1 , r t '! :~ 3:1.~Atll ·~:t~"W"'.~ ! ,q ;"h'!

.tS53Q •• 2~~?1. ~: SI, I~S J ~ f~';ili~"~ .... t ~~ 60 t' .. : 1 '12b3 .i; lq 11141 ~:();>7tq A, ,.,1',tlllli" :,q"'~A • J 6 7~'" ',5'51?c1 II:! 8469 ~, ;'t"~Pi:': ~ \-': 1 :.H~~j • 94? .f~'C,)lI\~ :q3ttll~ .,8."1" ,.'''AII' • 1 .. 1 ;1l.1'hlli» :B37tt·· 1~tq-'l2 iJ,PtUII' ,8.IIUI

t85.8 t;~136' ,.;q.~18 104, •• e.iiJ ,~1'8.a :zeOll ',173'-8 3:11t;077 ., ..... ,",.S .. .1~6Q6 1.'S.>ttH !I:'?,)R~ ." .... l'f!~e • ;H fl8A

288

Table F.8 Data, Type 3A, Pipe Grates

C e

.. bill : AH ~'5 :i'r1~13 ; I :;j, J ;»b .If\l~fl :16i~39 :a'J7ll • '6'.80 ~ ,',',6&8 : .'H84 :1 t1 BV>8 : • • :211 f : S?66 :., JJ556 '.)~~ 6~ 3 ~,q395 .1 5i1tj :.olI1h' : ~ 'H 97 : 3313 ... , ~'16;"> : J.5bb<', .. < • 'ISS . • "~~7 ~ ,6i1S9 :!9l>Fi3 ::;t22~~ .!,tlCj, • t q 3 i'l

:153(113 :?Q~3 :2~~t7

HW -D-

• IJ 7 ' (, " : g ~;~ 4:'1

;5J3f>~ 'Ilil'fl'l'.l

1 ~3'1t~A<' ';"9;;'4e 1.",6.-1'

; l3i: .. t:, • i! 1:\

: '} 0 'J? 1 : If ') t} {

:;;9 R ,

; 7 <i (,

, .. '5 ... fYi'

:'-1',~6i.' y': 315??· 1. : .~ ) ':.~1

: -; ;:'.l? ',,~r.::., • . ,.. ll,'

.. /);:t"')tl~" .. ' ,

:(,<?c.~ : 7~J..q, ; 8 I '(1 .i\hf.,;')

.. ")" '~l t!

:'}(~.," ,: ' (,I $:\, •• 'jI' , , 1 (,' <:: ',;

I.'l"q~,·· t:lt476''1 ; ~ S 18~ 'I

.!.I1Hllf

-.2._ BD1 •5

".i~;'?~')l

~:~n7H 1:181i5 ?: 4:)0682 ~:(,7'5,q l:?J118 J::H441 t. - "I H ;~ '51~

!?

! .. 119 t 63 !:1715l ,I ~ I'\J'I'i 1 7:<"I)96b 1:i?blll Ij: t <) 1 S tl ~:fJ1222 :~ : II 5 3 R 1,-

?:'~~45' 1:l339~ 1:~!'57;1i \ : S<~62 t t : 7~~5 l 2 , : ~ f 7 ;·19

? .. 1~6AI ;::3 tl(H:2 ;l': C; 7 ~ 'I 7 ?>~!r~qJ 3: ,,5~?? ~,:3';8tq j: '5{,~S 1

3:~r.7tq 14:18 1169

: q'J~/15

289

TW -D-

_~ • '1 ~ V .f, ~

~-"""""'J~'_~'l ••• " { ¥ •• '

.,; ... Md ..

~,~"'~.;~

~,"" V':HJ ~, ~Ih)l'e

.. !' IH,e.U'1 'i , ':~ ... " '.'

·4:i.;'tl.r)l~· . ", .~ r~

~': : ;1 "."'.

,'" • ;ID .,_"".,0,.;..

y; ! .~.~: '~),:.l

'1,' , ,.~ -t L t~,/ ~J. ~': l~;-lt~

i' • '." '~. ," "1'1 , 7,.- \.)- ,'~ ','.~ ,.'

," '}. "4" ,-, . \' I . I ~ <~, ,.- ~"

,.. t '1'''' ,II '" ••• f' ,:;.~ l;:

:/ : .;~ "'':'~ ,to ,,<~ V,, . ';! :.:~~, ... 'I! A

~4:' , il:.~ \1 ~ ~ ,.4 If 't ,.. ~

:.. t

• f\" 1:'; 1" ~... l , .

~ (: 7~

') • ~_~ 1. :.,1: l .t~

tt: .. ~H ;;J~ .,' • il-I' i"'}''''' .. . '("

~ : ~h~~~'" j! ~; r)thU,QJ

~,"~~;Ji6

"'."'!3ItlfI98'J

s o

.~. t 2~~

: At 26~' ~:'H~8~ ,-'1281 ,'12AM ,11280 ,'1281 • ." 1 ? A>,' ~lt2t4,,~ ; I' ,';> 8~"

• t 1 ?~h; • -: , "I" ,t • ,,: en it.'

~;;'281!' .I!H?A~ ::; t '- A ~1 :n 2~;:tJt?A"t .:/Ii lM\~

" "~ V1 , .;J ' •

.~.t\jB~~

;:;'\~~8i ~·~l,~~lI

!Jt~A? • t'{, -;.!~(,.

'ItPA~_~ · ,. ~~"'·A.l. :Ol,..,A!f.; : 1) L"S\." • 'J t "Po!< I' " Ie

,"tt181A t·lae~ .It;.J@0

Table F.9 nata, Type 3A, Bar Grates

C HW _Q- TW

S e Bn1•5 -n- o

~ .. 1:3~ln7 ~f : t:jfllV"U : .. "'6 ~~ ... it;{( 331 .. 5<Jt,Q;'

:~5b5' : &(,3;».c, t:StlSJl • ~~'Hb3~1 ~ ~ t1f'J .... i:~

:181'~ • 7?~ 6''; 1~115b12 ",.~n~~i\ • ~H~b3"" : . ., . :16~88 , 771HtM 1~961J'5 '~."1J8. ~ IH'''3t6 :c?3.~1 .652'10 2.18167 lit ,IUIHI." ,""630 ;22t4l ~..,tl9~e ~:4'571 ',"'"'' ,""b3" • 2.6 21 .q63blt 2~'-'36ql d, ....... ."e63" :.;:>1;)25'" ~; :~3::t4" ':1.!151~ 111.-.""" : lUI 6 ·UJ :~.5q~ ~. , ~ .',1 ?.) 3: t ~.iH~ U;:..l~~:Ji) : -'\t!b3'" :;>1561 i, 18f.J2';' '\: v;~~ ,j " • £h·, ih,j n : '4H6:V4

.. ?S34l t , :s 7 ~', ijo: 3:67539 .1,; ~Mt~H~ : .f"bJ.' ·~1.I684 t I ~{-; Ii "'. !.:tiA7tll f,J : itJ '.'1 H P '..-} >J.,63(lf

~ !~q5'3 I ',,J,llfl,' 1I:11PH ;4 t tH~.h1b ; 9;;16 3 ~~ , - ~ .

.. 825" .!j~'lP.·';; ,:a,'T'il ,.~ .. 0'J!..t ~~ :~ ,.IJ t fl/H~ : t 3 1.&1f8 • ... 113'· i:2A781 .J ;,,;. •• ,,~ '.~ ,"h'i8(' , . ,

:l23~~ .6'U) .. J:q77~9 :i • ~I Iii 9J ~,W • .,fGil8f4

!.~lt13 "IQ',l, !:~)7ll7o o ~ ),H'fll!qC' >'lNW " , :1r,:1I7 .7'5;.j 8:, t:H~"'Sfi ;), "'<P(~~'fi ~.q ,Hh' ,. . .p~f.\Q' ;< Itllq ;?, ;'4tH~3 "

.~ t ',4{J.,');~' 4 ~.J'~~8J

:: :.3672 .. Sf):, /I,' '>:)1'52) l''j : ~ fi, ~l 'f' , .. ," !~ Ait:1 ,1'155 ;<f?I-\~" ~ ~ 5lf V)'~ ~ • i]~ 'f ",1] <-,1,1 : ,'1 S-18~ .

;': 77"H2 • ·'85ij9 Q I' (/ LI, '~~ ,. ~. ~'~ .,~ ~.s~.., ~ ~11 ,,;~,~ ,.- • > >2 LJ.; .2'" 6 ~ t t • :.~'j ~,jil, .oc\. ~t' ,a;'1 ~~ !" .·H~R0

:;n 574 ! : t ;l H P. <, ~:;>7i23 · :o:.H;J:\'-' !.i"" •• /~ _tit " "'" ,11

Jq 71 ' .. ?"",l6 ':'5~51.5 .i; ,f'J""!~ ., • ;II t v'l A Ii! '." - " :I1'Q~" ( ~ 'J 1 iHnl ~:7"719 :ti,"dih~i'I .. t611"R~

;tJ151?' i. \G96.- '>~~77b e t fhJ1~ ':Hi ~aI1)8t'1 .~2q5C i.~52"( IJ:;lriS24 ".~"I<t~~ :81~8t)

290

Table F.1D Data, Type 4A, No Grates

C HW -L TW e -D-

e1.S D S

0

i· .. ·' ,,'~:S" !l'~'" 1 ~ Ht'S} ."0B8., :'.,.S 1,··16' 1,9"" 1.21;J1)1 : 18"lH~ ,"," 1,1J'I' 159""

1,37053 ;2'0880 ,85714 ~.849f»1 3 .. 92729 1,45387 , " •• -88 •• 3e. 1,']28' li"Y" I ,5!S87 t····· te"11 ',""" 3J"'" t,.".1 , •• 8.8 i" ''! ','Z' •• 1"129 ','8JZI ,.8 ... 1

,"'8' ~11'28' '.927" _,81'5S ,"'8' .• , .. ,1 ~:19l~g 2.2,U74 l.i711153 • fiUlli8111 :686'" 4,iQbth; 7:?,d74 t;l A720 ;890"" :"1" 1.4284" 2:'.]1~ ',32853 ,"""88 :8,8.4 1: 4A 32t9 ':2J1'37lt 1, 39587 .1li'M88 :7'11)' -- ?~2'J71J ;~fm8" 1 .. S<FiA" 1,537211 :6"'" i:tJ761H l? ~2.3711 1,55387 • 0001HIJ ;95215 --.

?:~it374 ; "ft)~H"'J ',774;'hl 1,65381 .. 855.8 !=qU?~ 2:2-'37 (~ ',778-53 ,,,,,e81 ;ss,.i 1,2R52i 2:9"538 1,811153 ,:;''''080 .,,6'2 J.:nqMt l.9('}51A 1.1795:5 • ~H1H!l8" :bt,3l8 i;.'528~ 2;916538 1;27~~53 ~j"'060 .. b 7244 !:5A2firl ~ .. q.538 1,37i953 , '80tHJ :6785'1 1,~186" ?:qllf51A t ,/HI,IS3 ,(111"80 :~6"15 1. H"S6':' ': 9~'3R 1.57""3 • r'h'~8'" :""'3 ,:87biit,J ~:q"518 t:67~53 :~e.H\0 ;6J'~1 • ?,; 9-'536 1 ~ 77~51 ; -aihf8~ 1.,~q2,Q!\.t

.812'-' !.t'U\5~;.'l 1,,9.?7(!9 t,~812\J , iUHlI80 :3652j I ,fI'l2"~ 2;.ttl822 1,1<14913 .~t63~

;3.131 ':~626~ 2:19822 l,t1l973 ~lH'l6'Vl .'51,." 1.r2~~I'h~ 2:t9822 1,211973 ; ~~63.' :l4'Z1. .I. :S~84l>:' l:19A22 1,34 971 .14"63'" :z'4i" ! : 4 i ~ ,,::~ 2:19822 1,44913 :'''6321 :61", !;S2J6Jf 2~lq822 1,511 973 ;_.,63 111

-7'''.i 1 : b22.;,.) 2.19822 1,64973 ."9b"5~ :/~9a •• J. t OboE'. ... Z:19821 1,74973 ~~oo30 .. 28'.1 '.58ftS" 4:?~56'5 1,:;0'111913 ."8b30 ;61!il j; J.t7'iI,~ <I ~'2581 1,,1 :ne7 ;""o]A • 89112 1,52 118;' W;.22583 1,233'7 ,d{463~ ., .. " ~,b308e 4:~25~n t,34973 ,~063'" :8171' 1.1 1Si'1t It :n.S83 1,39973 .""63!4 ;7.8,. i; 7928" Q:2i!583 1,49973 ~atl636 .~J'22 .,~tRa..'1 4::U'5R1 1,610 11 " ,,8863P :79_.1 ~ ,'5'''6\1 It;22583 '1'33~7 ,".635' ;2."- ~: 111796,:' 2.9-5"" 1,BI.t~71 ,""6]10) .7612. 1 .. 2512'9 2: C,45 CltJ 111 t,1 t1 973 ,88630 -3)121 i;2&7h~ ?~95IHh' 1,2~97l ,~"f»lCII :49'6'1 1,38166 2;954"" 1,3"'-173 ,0963" .5811' 1.481i8~ ;:>;.fI'SIJ('IP 1.44973 ,fJrlJ630 :b"'43 ...

2:954\11~ 1;51.1913 1,0Ib4:;- .!d;'63~

;629 ... i !,7~5'" 2: 9tr;/HU'I 1,64973 ~0fib3~' .. 66,,9! 1 .. 784BJ 2:9514"'" 1.14913 ,,"3630

291

Table F .10 Data, Type 4A, No Grates

C HW ~ TW

-n- S e Bn1.5 n 0

;. 783' 1 ; ? L ; :1 A ; i 3~/!~117 7 t~.,LJ\/73 .,irl()3~

.Sb86f.o h 2t11 ?" ,>15Q 17 1.1/1973 >~6~t1 ; :';Q7"8 ~ ,~8/1 (j • 3 >~C;477 t:2i1913 .~",1}3" .f)C;5'\5 t,~17t'" ,: ·:1 iii II 7 7 I: 3'-lQ73 ;""630 ~711' ~ II ',5R7'·j 3~1l5477 1~q1:1Q73 , ~l~63~ .. 62517 l.6b7(", '>5 1-117 1.~4Q73 .~061QJ :77614 i;7 q 76 H '>I'5 fH " 1 :6(J97~ : 111061~~ ;b19~f1I J.~blb" ~:u547' 1;74973 ~kJBbllt .1,8't. ~;~".e., 2;'1.518 1,.a973 ,'~6J" ;b""ol 1,16q~., 1.19822 l,l{l413 ,IUISA .SQ3Q5 J,17?4H) 2~19822 1,4'41l ," 1 "'H' :561" t.4Q",,. 2:19822 1.SIQ n •• 1"~6iI :'5Q1'. 1. I :s 4111/1 ,J. '1~b5<.J i • 3~c! 'I 1 1 .t:ll~A~

:t)lOt e a.ll!),flt ?': "{Il6S9 t;lI:;lIJ3 :r.tHI 6C\1'1 : QI1 5119 i: 6;t;~; ~. ?:9li6SQ 1 • '5 t:1'j 1 3 ~a10e21 ~6ttel? l;Ol>bfi.f ,,:411659 1 ;6{~ln 3 ,~ hUH'I .7l8~4 t t474')~ 1;111012 1,3'413 .IiIUUUJ :7813.2 1 c.552111 '.~Qllll 1 ,4"'H 3 ~.11il8" _. : :e!i771 1,"67;- .. l~3~418 1,5111"13 ,111180 :71 .. '5 ;,7816t1 :h3".18 1,61 11 11 ,"1'18' :Ab45~ t. 8711/hi 3:3A4JB 1.1eQ13 .311-)8B

:87199 l'~f"IA" J:.,~q18 1 ;~,J(~ 13 ;,:,t~lUt . , .

":'71"" ·79:5511 1 • t> ~ 5 f. ~ 1.3p 41J • ~11081!1 '77811 ',; 7 ~92<' il:l7!~1 t;.(!f,1113 ;V1080 :<137 t o ' e'f,FI ~ II: 1 t962 1,5f1413 .~1~~~ ., ..

.1-\8988 1,Q'4~" 1I: 1.-,Q62 I • 69 (~ 13 ~dt~8'" :R76J2 },~J2b6 ~:8538~ 1~b2A33 .ltIut3f1 :b7b9. l .. (.f.,'~fIJ <H.,.,9f\ 1.28b67 :"'~t3A - Y91.109 ?' 11: .;(' ~ 4~!~531 1;7?833 ~ ~1\4 t3~ ~781'b

, ~,f\ 'nf,F1 " .... 'it';.; 1.'Ulsnf::- .1.:11tI130

:,,~tqc, : .. 7 S');> 8 i:77bbtt ':712""" :(J~13~ :,:>0Q9:S .1; '5'-11211 3: 2~ J I? t;3Af,h7 ~64~1391 :~~9'8 f ,6\'MI !>I;tC)J 2 t.59sa~ .:"P,13~

:681.#1 6 1.1il9HIj "5:3l3 lt 9 ,:5;167 :.,013(1 :".;11" '}"JII2bR < qa911 1:9Rbb7 : P;iI t3~ :~ .... 79tj1

, ..

;:<,H.S9B 1:6tOt333 : 101'; 11'" I r 7~'&;>8 :~'5Jbtl t,8f"!i~ ~: ~IJ 3~\· t~15333 ~.HH 311' :-':'5260 , .5 11 ·;-2d ':~i!lI9i11 1.37UM~ .kt,.t3~

:78L1~? 1· 77fJt..' 1:~Q~~'3 t:QZ1-l53 :fi128 .. :'5&8&1

~,

?:l49.,,? 1:5'5387 ;';i28'" s. ]q?~" :Sil995 1;135; J:'b~66 1:S8721D ."'12~0 :1l43.,e l.,17() ".~ ?:SS52e t;q~~'53 ~ e 128~ :7258. 1, S73M; 3~h7539 1,5171'l1 .ioJt280 : 15/13t~ J.J;tl?t" ,\;.. 3 t IlIl7 t:51)~~7 : ~ 12A0 :7t26! 1;5,8.,;" 3:?7"23 t,5'5~6·' ~aJt2"l-t :81 824 117URlH 1:7q728 t,Q5387 .~I?A~

:63·,il! !,b,4?y, J: h5J2 1,83720 ~rtt2e" - ~ 3;:» ~fI !, A7 ?..,,:J. :r.:Qll776 2,7A5'53 ~r.t2~0 ~'bl~J t,3.~6" 1;~9932 1,t4622e ,llIf2691

:.,"31 ;, q?" •• ~p 9115. 1,8ii38 7 ,"12R~

·e"" ;.,,.l.1J l.O"'. Z.12.-.53 .'U81

292

Table F.ll Data, Type 4A, Pipe Grates

C HW Q TW S

e -D-BDI . S 0

#761 8 ' l;'I ... ·.?d 3.',"1Ih l,(,'>8,B t"Ml1~' .6'J286 , ,fJ:t'nM II • t' wI 7 IH\ 1,28067 • .~~ 1 3" ~"e2~7 1,1!f6 7A fo.8 I~ >'S';-H t,7?~:n ;~"~\'3'" .784" '.rAJ lllR I,' .;> p' , W! 1.1.16'6"1 , ,",H 30 :?19"Q 1.7"62R t: 71bbtJ 1:1ttfo.7 .1:~J' 1 3e : 5-11';,,5 -.

:\;'-111111 1;3"58~ ~I!'~ll~ t,~. "I11S ~5.,.d8 l,e:B<f6 '.~?9\':! \,'58&67 ,.~U~

.. I.IA751~ 1,7'\468 3::n,,,'" 1 .. 524"" ,iI" Uti :qCJt~6 ".~~2b8 1 : cHI'~ 1 t 1;~"667 , •• H 3i11 : '!f) 7 qr~ !,7"*I;»8 ~: 36':P'i8 1.bi1J'n ,""13l!! :Sl5tba 1, Atl }Aft :>: 5''H6.~ I ~ 7'BB • 'h' 1. ,,;.t : >'-Uft 1~'11lAA ~: ·".1<)·~' l,37..i;.iri : llwt 3~! ;*\12C1S t" i7iHj!~ ':1111\22 1,1!I7.Ij'iJ ;:Jtl0f\1'! .71678 ~,t?«\36"" ~.1·iA2.:? \.\7u rn • \H~0fHl

: ~~86o' t. Hb'\'!;\ ,): 1 q8~2 '.27~'5.s ~ 'h!'~HH~ :S3-53a ;: :116J" ?: PP'2) 1:"H,''53 • "hiP! ~,.

:8\78S ,:f)ln.· 2:t9872 I: l170f) 3 :P¥l~R\l ~l~~l!Il t' 7tH,,'; ;>:lq~22 t; 5 7'/153 ; Iolf/''-H\v , .7d65S 1, fj . ..,,(j,,,,' l.1Q""? l,b7;'SJ , ';;~h;1f\~

:62e.6t 1,8 o filbT :?:i!)"2? 1 , 7 7 ~11i3 • "'~HHl :4287'1 ,.,'<,&:>" ':'91'\7.2 t .87!'1:)~ ~ ~1 ~? A 1.1

:1,n93 ,~; .' 'I~' II. ):lq~2? \ >H!l,)3 ~ l(>,,'1 H I' :!167h 1,,"'1'2 ;": '1 ,'S'~ 1;i:bl87 :~I!'l{l8'" :fI9 R17 1 .3' t ;t. ;>:Y~:5J,8 1.t'.l,3~7 : 'hHHh' : f:.t:,'YH 1~V'\7b"'; ,): 'H'Bll J : t7 .It'):; : 'hliHh'

~()t7\lt 1,.:.I"'>8~ .~- (;>45J~ t ;215 :StH :>i(.~~H~~' ~ ,

: " ~I ,~A [' .88b1" 1.5~12~4 " .~'!'5 3 R 1. :n-u:;, ;8,,/0 7 l:bP.l?'\ ;' ~ ~:;Ii ~ii I >7~S3 : ,J,,"~~~~~

• f\~R"'jI· t.7lj'II\' ,< 9,!~ SR 1:5'5]81 ~ "'_- ··~'R ~,~ ·78A'~14 : ;1'7,:),. ,'-'i",,1)~5 l; 67.;S3 " .;s \~ "H~~' I :r - ~ ,iHH\ ..... .#'7621 1) •• ' ..... ,!~,' <!.~,!5J8 1..71\72fl , :bZqq,) ':"/>24j ')~'k~"S8 l:At;J87 .'I!I!IA~OI

;15'515 1 • .5q·~6'~ ~ :1~ 115 q 1: n:"S3 :~~'J~'" , , .5?q21 liScH,,)" '\: 7 ~ 115 t l t~un;>J : J'hHh~ :"1'f9'59 ~,'jP'52'" ,\: 73'15 1• J,?f:t?2J >~~"'80 > .. 17~S ~: 7,' pi :3 : 7 3 £I '5 Ij t,. 3672',; : ,>'.HHhl : 717.Qfl 17·''St.,;:: ~:'S(h7'5,~ \.45387 ~ .~ .H'lIon; -, : 7tI?46 l,<tl1jf,J ': 59!-H),'l t:6W~87 • ",e,HI8'~ :76239 t, v<,7tJt' :'.:c:;q.,C;oiI t;b62?~' • ~"',, t\;~ -< ':SCf ,"~;'

' .. -: 7S?I~ 7 ',*,'93t-;' t,,7'H8 7 , ~'H~8ft1 :7~217 ',22?/,., ~: 5(HS" 1./Hq2~1 • ."HlI~~ ;AI2t.iJ 1,1:tb' :r. : "Q ;., 5 ;1 t; 9';)387 : ~:..HH" .. 6t!H 74 '.~5:?~f' l4:n5$\'\ '.5~72" : ;d1,,;ffA ~ "7tDbS ';11I>R.' I~ :;'''51\ ~ .;r.7a53 ~~I/JMH' :A1281 , ,2S~'$c) "1 :~2'j8 S 1.77~'n • "HHHI

;8:J77 Q I 7 ?2<Li i\: "2SA, 1;2711153 ;~'"8''' -, <n58; ",H6l)&1 1, , ~ LI ft. tJ;rl t.37>fS3 .+1I~rlA~

: 7tH i b 1,?-:;i lh' <2?5!B 1;1.j7~53 ~ .tk)~lh' :8 11 611 i.5(11.J~-b .;j:2'58~ l:?Hl'5J .e"~8'-' : 7~1i S8 i; .,'561,,; 4>t'58' 1.17>153 ~ :'~ij8l1 ~8'5~e ! 1'5 H'-·,' ~~"In2~ 1;17~5.5 , ltItH~6" .8.7,11 1.bfll~. 1.9~729 1:21.~! ,"18" :8'717 J;178I1lJ 3:92729 1,37"53 , .... A8 'Allll~tI 1.6lt9b'" ':~272q 1,45387 ,PI •• e"

293

Table F .11 Da ta, Type 4A, Pipe Grates

C HW ~ TW

-D- --D S e BD1 . 5 0

:etl4ii1 ';:<'5 n •. ii 1:9?12q t~6Cil81 ~W"R0 ;&84.0 ,., I.;t b' t. ,:9,"729 1,7P,7?~ ~"':'I~R'" • "'5IU ~l()28!1 3: 9n2q tf~1"5' ~ ":",, 'H1 :""56 l~ I q?.,~ ?~ ~t13 74 1.1l7~5~ • .,,~~~e ;b8f)1!1 l.lqb~., ~:1'.'l1q l' 1 R UI~ : "IJ~VJ8~' : ' . .'11;"7 i : 'I ? $3 l\ 0', '<~""J 111 1.12(\53 ; rl~8!\" :e.894 ':(.~J'J .>:?n74 t~39587 ,~~r'!8'" :1,,,~q ,;<;q"l~d 2: .,;)~H 7 q l,"37i?1il • f'~"'A~~ :1,17~Q ~ t ~j 7 t.. 8 ~ ,: ~.d 1'~ 1,55387 ;!HHHh' ~ 'I1i2 t ~ 'rl~QWIt4 ;'~l"HI.I l,b5187 ,,,'''80 !81''Ie 1. 9 1'UI 1».211'. 1,71853 • .,tl!te8 ~,)5ql\1 I: 2"52- 1:Y8538 t,"7'~3 ~q"8~~ • ')1 b'? i, J~QtI--' ~ ~ c:,·"5~e ',17.53 , '''''(11 ~" .Qb!ila f .J~2f!d 2 >HJ5'J8 l,27853 ~ l!hh'lft! .: ' - . :672Q/J f,O:,..Ol-'. '): 'I . 5"3 A "r37.~'53 • ..- ~~ i'·, A ')

:h78~1.1 t,r)71:';~" ? ~ '",5311 l, 4 '1',11), ~:I ~ (iA'~ :>i()77'5 ~,7{j3b;} ?:~."H I • 57\~53 • "'~HHH~ : ~t!lqcn ! ,13 1 ,>",;n :.>~qi'1'5~~ 1;~7"5~ ~ ~"PytR'" :b"Stt? 1,9'1;>1"" .... ~'I.t5,H', i,77¥l';3 " ;h4;~80

:q1748 1 'S 1 -,.A" ~: 9?72q 1 ,~.,P,S3 ." ~'Vl8'" :~l2t'6 ' " " ~:'n72q 1,J.IH~·' • ,.",.";I..~ 1, ,,"~( .. , ! "- \ .

:'837 /1 • Q'I " i',' ;< !651 t:I t ." "3:.:1 .Jfi~.3~'

:_s9M'I1 ~;1A3? ?>f."il6 J ~ 1 H~ 7 ; "\f'6~0 '~4'S1b ~,??!(q" ;;:tq~.?? 1 • 2 /t cJ7 3 ."~;>&J~ 1-

J:lq82? 1;31~913 ~,', .)6 ~p ,:P"I'3 ~,J;7? .?~C4~? 1 • 3~,-'~,,, ~ > <f82? t.'14'713 .;A;,16ll1

:S93QS t·~rlF3c. ~<19qn l: 54q75 >.,6::\0 I ".,

;6111.1 !, 6~.56': 2:19tJ.2? , ; 1'111 1.173 ~ ;;'.6:U .:'83i'Q !,71'l2" 7.:19822 1 • 7'1 q 73 .~; ;'630 : 2 i l 'Ii b i.J"1~ .. ~:'I"'5'8 1:\1h64~ : .. )/tbl~ ~ :> ,.,,4 i"lQQ?" .< tI :)'5.3 t\ t;16h IU' :C)Hh3t1 , - ,·1

~:'I"'5JA ; ''''6 Jet .1.1I32Q3 1.?~ ,;1-\' 1.211973 : '5('!7~6 1; 3~B~;: :< 'J'!}') 'JR ':333~7 ,1ilJ0963C'1

:~b55Z 1."111,., ~: 91t538 1 ~43H1 .~d63'"

:5'5930 !; 6l""~" ?~q~~JP, 1,5111 13 ; ';'.'61", :727'6 ,1,tlll. 2:',1,''538 I f,ltq73 .~; iH, J~' , , " (,').,Q7 ' ~h';? H " "'-9't-53A 1 , 7 11 q 13 · ~~~Ji1

:5;'652 ::., ~ . " '. A, 5in ?~ Q.22S~~ 1,11.1913 ,~f'b30

:609~5 1,~17? . <~~rs61 I 2:J9n ,H~bJ~ 11>'}S8J

: :7b4i 8 l,6'7!.1-1 ',Jl.I<Pl ,~!Jbl"

:R1'"']3 , 7864' <2?5 IH ',lIflQ 1 3 .""6~r. - , 4~~?,)83 :iII:~b30

: 79 1" 1,"512., 1,SQ'173

:6811' \, Y4~U.' 11,2258' 1, b /lY73 : .Hj b 3;,1

.788'~ i!, ~6"~U 4;.;>2~81 1,7'1973 :'~l4b30 ~?~q~7 ,,18~@~ 3: 115q71 1,';'J31rJ7 ~ ~HlIb~~ 156127 I 206/j~ ':"'i'l71 1,1 Hili 7 ,1tt~b3!l1 .,

3>~511'77 .51l1) !,15~e" t,2~~f.l7 ,~~03d : sqq,tLl i,456PJ 3:4'5"'7 1,:B317 • .. h~61~ :b3l77 ~:S67?'J l:"5~77 J,41];.}7 :8;)030 ;b8l.' ',7l'(\/' :<q'.!;tH1 .,51'3,11 ;i1jf'lblA

.7'\tlb~ ,.8,q~0 ~:q'5477 t .bob'I 3 • ""b'3l11

294

Table F.II Data, Type 4A, Pipe Grates

C RW Q TW

S e -D-BD1 • 5 D 0

:67;.t5t' t;e92i\t, ~ >it§411 1~14CH3 t ·j~b~Y'

>S6J1 l,2{f16! 2: 1 "HI/>2 t.l"'113 ,,I!BHh' :bfJ85~ , ,11 f4.,1"/ ':19112~ J;4~4t3 ,ll f ~8'.,

:1'J78tf J, 'i~ 7?j ~< t '9R22 ',S~Hq3 ,"UHW .'Ufi76 l:S~S~' .?~t9822 ltoell13 ,j.@SiJ ;b11e ll 16"44" 1:ICf822 ',71'-'U3 , Itt ~8~ J .e,,7QlA it78q~. :?:.,S1i i,88""13 I"J8~1I ;b1 G15 !,35&Qb 2~(H'518 1,3t"'13 ,klII8el:'! ... bb"'H'\ \,<472'lt i\ ?;,.Q"l§36 t.l\fIl~t3 .!:.4HIM! :7lf656 J,568tlJ ?: '1 ',"S:SA 1;5~f/~13 >qt'lq~ :7,)3!l1 1.t,1t4\.4 ". 'H iii 3 Po l.6,Hll' • ,. , ~' 8'~ . - , '

:7.8q~ t·':'IIL' 2: "l.}5 '8 1,7~1113 :iil1 i1AI7I

;/~1b81 ., ?: chJ fB8 1 tt b .&, (t ::' 1 litJ 11.13 , [," 1 ft AII!I -. -

~:ltt\.'171 f .. M,. 8~ t.o~f~R'" l.l·HH3 .~q~A"

:b~253 •• '\~ ,;>, ':/ISij77 1 : ~'"' II n ; {~I ;-t8~ • I .. ",' :71 8 "7 I , t, '5 7 ;?,;l -':!15 /H7 , ; ~ .,' i~ t 3 .\ 1 :'8P :b83S! \.75~t:hJ 3;!45a77 Jtb'~ll ;11880 :&4 8 ;»6 lt81)~8" 3t'~'S417 1,71413 ,.U'8~ :b229Ci J."It)36.-! 3 ." ~4 71 1,8tt4 13 ,.I~~e

:~~~:! j ;I;dltb~ 4~2?5fn 1,3111l1J ,11~.80 I J 7·:i·'/1 .~ ,~ .. ??5R~ 1 t let 'll .3 ,':" I \lA~

.797lJl J.g?17" 1.I:1~S8' t,5l~IJ', q ')RA l' . : 73,,11 ~ ; : 9!t"'Uf J1:2?5~1 1.6fli~t3 .t'tt8Y1

295

Table F. 12 Data, Type 4A, Bar Grates

C HW -L TW S e -n- Bn1.5 -n- o

ai_i.,. r··· .. It"T" ,;.,3" , , ..... i,a1.3 t~6jl'" 1·"'~' 1,17." .... ,. • ".13 1,6"'. 1' •• 72' , ,J7'~' ~ ..... .9I.1tt"b 1,''''''-' It"7P' 1 ,17'5J , ..... : 9,14& t,~'-."" 3~'212'1 1,47153 , "" 11IUi'1 :811225 , ,"U'." ~19'-729 1,58'2' ,''''88 :1\9J97 ~,'9811" 3.'1'-12'1 1,&1.,53 , "tUJ e., -'4517 ~,21fj.t' .. 3;9272'1 \,7T0~] , l"'880 "S112b J,?'15)WI ?',69912 1,~872ft!1 ,"leAf' ~5I1)UI 1,]QS21!1 ih,St932 1,H~12B ,"'''80 ;~5HJ " 5~£I1:1.1 2:89932 1,2~72! ,~'0f\t ,7'80' 1,5f\~4. ,.;89932 1,35381 ,PlIi'08f1

."1-' t I 674" i!~8.':U ~,4IS'" ,1 .. 1. 1····' .,'116' ',8 •• SI 1,56'" ~ .....

,71 6" 1,'1768' 2,89 1'll ~,1IJIT ."'" .'21"P z,2GUe 2 .... 931 1,".~S , .... ,

:t:91.1.8 1,l3t2P '~3\522 'f~8'?;' ,"""1I!8 :b3Ul , ,'.~M'" ~·.3152:? l.tI53~1 ."e.08~ :7CJT6" ~, 'UhU" 2~31522 t;25387 ;""0~1! :66'.7 s,5'~b" ,;3t522 1,38721 ,'0080 w7~"l!l ! o'HHI~' 2,3l522 1,48'20 "eMR" II !:1~:5btj .667,8 '.31522 1.5872\1 • "flrJI"0 :744311 I,Q1611J" ir:liS2l I ~ 71'51 ;"8'U'"

1 ;",., 1,1 8 168 ;';3',522 1,~"e53 ,1008e ,.i!71" A,9'l66M" 2,,~'1822 I,J4973 ,~~630 ,,3161. 1, I. ?5~~ '):tl~e22 ~,2Q973 ,,~~b3M

,38811 ~,2V~"1et 2.1f.J8Z2 ',3I1Q1J ,lItflb]8 .5']91} 1,391111. .?:19~22 h 44973 ,,,e63e :o~9"!1 1,4Q7:»e Z;if.J822 t f 511~n ,."'63" : 9"n~ ~,b~q6" 2 .. 1'1'122 1,6 QQ1J ,"~63'" .44,.6° !,(J~befJ ":IQ822 1,74973 ,~~b3P

;661" &,44!!1Z9 (I: 2t'~iI\3 1,141913 .111631 .~81!' £,1,3761 4~125B3 , ,24 913 ; "fl63S11 :S1l1h ,,72"8~ <n583 1,3491 3 ,i'fl6 30 :81S1,e I 7~t61,! 11:~2583 1,,q aQn ,'flb30 :8464' t!eMU 1.$;?25ft~ l"a971 ,'°630 :75Z6e t 97249 4.21583 t ,64Qn ,tt.63A :7ffI$" 2' "8Si'. 1l;225A3 ',71.1cr1:l, ,"063"" -. ;64"'.3 !,21.76Y! 3,1.1'5477 h 1 LII'~7l ,l}ft618 ".71 1" ),39]60 ~;,tl5n7 ',24nl ,~fJb3"

7\ltl!l 1,41:>2111-' :5.45471 1,349 73 ,""b10 ;73 •• ' ',b292P 3~~51177 t,44913 ,.ef,'" .b~b4e 1,7"2U 3;"5417 ! ,54'73 ,~0b31i1 ·b29., 1,'"60 ... 3;.~5'7' ',64971 t,,1/iI63P, :6661' 1 .. '!UfJ 3~1I5q77 i,74'73 ,""tl39

4114'1 "'12." ~,q.S'JR ~,1.973 ,.e6S1 ~5.2'7

.. , !,J.I ue c. '1.538 1,2."1 ,.'!fUIl ;,., .. l,'2l"4e 2:9.518 t,3""! .""63" .'2.U , ,18Z." 1.'-'" ~,t"'J ,,,,.631

811{3 t,el'" ",.,se l,"'1J ,"'" ~.""J .... ,. a.'."1 ., ••• Tl .... , . 296

Table F .12 Data, Type 4A, Bar Grates

C HW Q TW e D BD l •S S

0

;75"" ,;84 .. 48 1~~e53" 1~711'13 "deO]" 21316 \,I5MIIW Q;7~989 1,144'113 ."1638 , ",v"54 .1, 6 36~;'? d,?RPAQ ',21:1973 ,"0b~0 !~1753 t.6QSMI !t .. ?R~fIIIQ 1,360Q" ,"Db]1 :8'5bftQ .';7~M~'" l':l8tj~q t,IH.f973 ,~fl6~" :Rl2'~J , ClI;;IIi"T", 4 ~ 28ijH~q t Sln .. 7 ,"'(li6]~ -, . ,

,; 65~/UJ .~24458 , •• ~~~ 7 *'''' IJ .;~"8q " ,,('t~3l'1 ;'-"1bbi! 7: I t l{ll~ 1.j~;"~iit.iAq 1.7 4 113 ;311'638 . . .7u63b .;2q~l!'? ':1<)822 1;3t,4J3 ,iilJUHU, : s 3S'/~ ! .37~·;;'," 7:lC1l\?2 t. IH.I;:4! 3 .:At~8€

;87135 ...

2~19622 1;5fJ4t3 ~."8. !,4~t2t'! :76CJ61 t,5716" 2~.19"22 1,6t'4 13 t·~·8~ .34322 .. ,~~t6~ ?ttQP.22 ".,"4J3 ,"18"'511 :8'5530 .,81 .... 1:'<)822 ',8"'413 , .. ~e8'-' :bo7tS7 , .7" P.4':: ~:~qt:"i' !,,]1'1! 'H] ."'t!l1f'0 :'J '553& ,- 301'10 ., i':19~2? t;4PQJJ : ~ 1'~~~ ~ ... . :7~Q]Q t • II ""':.> ~;.., ~>H53R J I J./I t 3 ;et08~ ~S .. :8tb55 1. !IP-biH"! ::>:RI.3l't'5 t,U;:' lI l3 .;:~ ,,~e0 :791ql i:!) 1'.0 ~\c:; :< ~61(lS •. At'! 1.5~/H3 • ...,t ~. , ; 8t'81H t;&~52.~ ";FJ63~5 J ; 6(114, 3 ~ ~ t ~e~~ .789 98 1:7~lr-e 2."J896 ',"fl4 t! ;WlIt8(1 ·7,!iblS 1,88.'-' >:8389b ~,8.413 ,tlU'8A '84IJ6G1l tJ .. e6~$ l:51i63 I, :U"O 3 ,01.'9 .. ·8l.uJ~ i. , 593M' :S;~33I1Q 1,4"413 ,PJ\I8Q1 :q;>IHI? ,,~qt6" :\.~~3119 ~tS!'llf13 ,P,M8f11

1: '~l;Id&] I 7 7·"'··~ ':'33Q Q 1,MHtl3 ,~1"'80 , .' .. :~H42'> \.872SS ':3~3"Q 1.7!\'f4t:~ .~t08Pl :eS452 1;<f7 i f€," 3:33349 l ~ 8~'''lt 3 • 9HHI~ , :8Fb8t ~,t-6'f,;t tl::>:?5f111 1,3~qt3 rAt~8'· , . .. 7 <UH'5 1,74~6"- t4;;a158.~ 1,~~~13 ,~t08111 '8~.49 J .. e656- 4.'2583 1,51 4 t3 ,1188ft :71283 t:9J8a. h:~25"1 1 ••• 4t3 .lliHUI

297

Table F.13 Data, Type 4B, No Grates

C HW TW D -D- S e BD . 0

jbI1.:S ,;3834 e 3~'~"'11 .; ..... ~

,.IIJ • • 33'66 1,Z~t8~ 1 ... !12." ." .... ,'8'JI ;47tJ77 ttl~34e u:~'7.e .,,, .... ,".111 .b8811l 1. 'I 1,,-.a It:'67,fIII ",".'." ,"131 :SQ52~ i >4.':;" 8 :l:t91I1jiq ,,: : "~iI"'H .""P13" :33901 i.:2!7~'H l: II Q'}B2 ~ ,"""~"~~ :1'lif.13t' ::;9251"

" .. ):Vi714 ~"'~3A~ !.2'6~lr' "',1'\..,0"Hj

:;.»373 IJ I: 'nH8~ :S:6753Q ". ~l""HHII t 0FH,1AfI

:647'57 i: ~(n 6:~ '!:9,369 fA· " '1'1"4;;;; :r6"'''~~ • 'I!' ,",

:2634,1 " -" 'Il 'I '.l:1'513Q · 1.,..1& \, ", \"'Hhll~ .lIh4W6~

.. 271~49 1,'~156tl II ~??58] .t: ,~"fhH:J ~o(HH1A'" # 11 b llS CJ 1#2~>ft" J,'Hllq~ H ,<'i~~"';;'" ,J',tNH" .. -,q9bb •• /q 15M) 3.Q;t1?9 ".tlAlil'e~~ • "8(118!' '71Rb1 i .. t.l t 6'~ 3;Q"'?9 ,1171.153 ;~('!ij~" :'2';4 l 1

, !,'itlt,J l.,Q'.729 ,97.,53 IthHjA~1

,71Kt-1 1 .. til 1 thl "LQ.'729 ,57{41)3 .~""A0 .7t8~, i:~1"p) 3:')(l7?9 .67053 ~"''')~A\'l -. ,:Q'729 :17"'53 .7t8bl t 41t6'" , JiJA08.1 'It. , r..,

:1536;J " "~'"'"8" '-;:5£1596 \'1 ; ""~It"~ • !"":)blt' J.,'" !,' ,?.~.,,, A, J99MI 3; 7Mf~4 iIt},~.,tHh4 ~ "J@6'~' .lf06e t J .q~b"UI 3.967.' ., ..... .8063' ;113)'1 I,Stt36fl l:I':'id8922 A, ....... ;'.0)11 'I' ,23863 ~,5~36ft 4,~258J ., .... "" ,1I86JI1I .2'SMn :. ~~5;-,l 3.07539 "',"'''''' ,1iII863f1 ;;~17~'1

.. 3:111\7111 !: 4'5?'~~~ ~."'''''''~~ ,"061"

~217q1 t • ':. R:I ~ r' 4:1'7J"01 :3'~~""'l ,~~b3~ t . ~ ."

.. " 3 ~ I~" : : S~ 7 it ~ ":;:;'583 :; • ,1 $I ShH1 .lIIHb3t' : ?t'H 5

' .. :\ >1~tl7 7 \ l ; "VI iii " !t. :~nb10 ! .. 7 :"~ F; '\

>·3i.l~~' , > ... fI. 7?J '!: ?,':)8 3 • Slt973 ;~~6~0 : <~lIlh'" ):r}R.1'~ £1: 7'56 "S :blt<H3 .i1I11t)]fII

:7,\"11 t:bfI 7htA. II: 2;>58:5 ;74973 : .,ftH,.30

:lllSt:I' j : 3<10'1',1 1( 2>.51B ,84913 ~.}Jb3\IJ :223*>' t: 596':';'" 1\: 2,583 .9 4973 ,IcH~61'" :2$9{5 1:?~11P.06 ~:IIr;/n7 ;5 49 73 .0~b3" "ztt9i5

.- .. 3; ItSl&7 , : ,H~b3Q1 1 • (>l: II Aft I fJ/IIH3 ::.'!t 9 IS ... 2 ";'1 eO', ~ • Il C; II 11 t74973 ;il?'63V , I

:-.: 1I '5 i~ 77 :l~~4j5 j • ?,"~'! R~'" .81.1<Hl • ..J'I&30 "2~9j5 "I .. 2 \j / ll) .d . ...: IJ I) II 7 7 ~q1l973 ; "1116 3~ :5;'156

II .

3:Q931'1 f • ?S5M. q: ~~"ir;ti I :;-,'~r~H·

;lJ7~1 ,.;37 .. 8. 3t~734S4 ", lth1883 ,""''''£80 :258t7 !,'5118A" 4.se124 Ift···fllI ."".81 ~ltlU,q 1.57aU0 ":."l5a " • ".'Ute : .... 81

298

Table F.14 Data, Type 4B, Pipe Grates

C HW Q TW

S e -D- BD1.5 D 0

:'5111.5 1: l~l128 l~q1l741 ~.~0 .. ~\4 ;"0.30 :Sb." ~;]~7d8 ~;"339q ~92'H'" , ~HH 3'" ;J~9" l.'-?188 '\.'H27' ;~, QJ9~'H" ,110130

;,.," i;3S9ae q;01H96 1'1,9HtHH.1 ,tHU30

•• 81'. 1.1'1988 """& ,~!' •• ,iltt1a "' .

4~2611" ~59J!& 1 ..... 868 ,".113 ,"IS& , ;6-1181 ~,4b7~6 4f2"1~ "" .... ,.t'IJI :.51,.L4 ~,''ltt6A ',.'1!4 1

'!!)] ,'tII!!1I!I

;~-;Z~5 1, Ii i'(:,;&8 4,1~HI5I1 ",,, ..... ,'ltSI .. 39"" " 2~~.bI~ ,~~ £1<)982 ~ ,~'vHUH~ ,~1.411il

;131il 1,219~8 ~j.q<lqR2 ,8:1333 ,"'iti13~

.183'8 !.l21i'~h~ 'h 'Q714 ~,~tMU0 ,fJ('1irl8~

:2tt.,] 1, }]iiIH ~~o75J9 ";.0"80" ,~'~~8'~

;6116] 1,3,1o\Q6.j l~913Rq ,,; ll!tH10 ,0!1t08~

~32]4! J,';~16,. IJ:157JlI '" , I:i ("H' lD , i6':~~A(;'

.321"1 ~,,)71J6-) 1.l:2'58~ ..,: .. HHH~'" • '''fA" R 1(1 ;7Q2'2 1 '" ;~fH· 1.l:~?5A' ,97"53 ;<,ijJR0 , , .

,1)18'2 1, 'lt~qH,· 3:7 l11ttl ,R8 721t.f ,~~0~~

.59~'6 t '\.Q ••. ~.~ ,:74114 ,R2;.t53 ,0W0RfJ1 I - .'. 3:741t'. :'5925\1 ~, 3lI2e .. ~ d.0~"'091 , d'tHJR.1

: tl?'84" '.4<'1.'6~ (1:''115 /1 ; 9?'~53 , k":Hlt8~ :7,,1,182 i; ,177 #)14 '(1915 /1 .REl387 .n0~1\'"

;74254 1,"77 6 ~~ Ll:l<l154 ;78387 ~~qtA8ti .47618 1 ?QA8;~ 3 ~'UH 9t1 il, (',;"''''H~ , ;J~..,tH' .-, .821T3 1.4.~ 41\F' 3.<'12729 ~~.;,1~~liIJt) • ~1~\oHh~

:521Z7 !; tl 3?P. " 3:9771'9 :S71i1J53 :w4~S480

~821'17 '., ~r~?~H~ 3:9i'729 ;~705:S ;"0t18~ ~8~1'T l 4J'A'1 3:927;>9 .77A53 .00080 .: ' ... -;1\2598 ~, ~q4)H 3 ~ '1?729 ~8'053 ;'hHHh~ 1,801 ;,'''1(,:1 3.92729 ,~7IlJS3 , ~AI!Hh~

:7~544 1 4)lb~ 3:92729 , 97(~53 ,0A~8r -, 3:9'l7?9 ·7180. ~,'HJh,f ,57~53 ,~ClhHH1

:I . ~>/:n?9 ,,71861 1,I4·tho .67"'53 • MJCHIV,

:~!~:! !, li t1b.· 3:92729 ;77~1I)3 ~ r!l0~8~; .I , 21/~ ~ v: ~:'iI!C;~b ~,t'k\~11~0 ,"~h3'"

#2659, 1,17~t'.~ 3: 76,~qIJ ~. J"'iln"@ ,I8D!163Vl ~:967r;7

. .. 255lH 1,4712,t 11,~9"1if" ,0~b~'"

;26591 !,5t72 n tl: I!S9?2 ~~. ~~00i1, • -'0&3" ,23 863 ',~C;36" ":;!i'5A~ ~;0"0f1'4 ;1i9~H)~~ .. 2,Q3& !,552i.H 1l:??58l ,5334'11 d8b3~

4;22583 ' . waa261 !,554'~ .b6bl1wt ,"Bb30 :']863 1,'55361 ",22583 ;,4'73 ,al.S' .2J8b3 1,5~3" "'~2~581 .8~91] ,".65' :21863 t. S536. 4:22581 :qaQ71 ..1618

299

Table F.IS Data, Type 4B, Bar Grates

C HW Q TW S

e -D-BD1•S D 0

i 27S"

-II

3', "337 " . !,ICJ 1'" ., , •• g.) , "'W8t)

,24'J7 !,3956' 3"'.'. R,'.""'} .0(111~~"

"e5!' !,'17bat 4,'.12' .. , ... "" ; lrl-'08Vl

.315t1 1.'1"fll-.'-- 4''; t 91'4 ~,0.fI .. trl t~HH'8~

;25343 ~;316(U ":67539 "',03g~0 ,wH'b3'" .2"6'~ !,4511f~VI ~;8R7t4 " ,ftfU193 ,8~63A

;'9"3 t,tl8"8" 41'1,,·1' I,""" ,'"'''' ,.51113 ~, "3~fu' 4,"583 ,sa'73 ,"'). .571'. 1,"396. 4,11183 ,"'73 ,"'" i"ll' 1,·39b~ 4,225"3 ,' •• ,3 ,"6)' .~72'8 I," 3. eN, ('\ a.;»25'H 111\4973 ," .. 6" :S736l I 11396;~ 1i:~25A3 ,qi1 9 73 • ~\'6'~1 -,

»15 iI17 ; il01,3'" :?1 964 t 2'1f,,' ,sn973 >0, 3:n5471 ;71 964 1,2t76~ ,6b973 ,Yi0&3H

:2"~'1 J 212t,'ol 3:Il~U77 ,.,«971 , lt~b3"~ e ,

3;454 77 ,2lH~J 1,2 ~ ~'.h" ,8"913 !'''0b]i",

:4t2]~1 t .• 2.t2.r:, ~.t\1)1I77 .<11.1973 ."~63~

·2~12' ';6J6b8.1 ~:;>Ajlj8c) ;Slt913 ~ff.M630 '2~U"5 '. f>«tJ~H Q:26IiJSC) ,63'3'>41 1"~63P :2",885 I bt>'b~," II ~ 2 A«~8 9 t7~913 ,iH'6]0 ~,

• :2"1:' J2 1,6'J"'~h 4.'f\~8c) .8IblH} .0 .. 63C1 ;24183 il :2IhtSC)

. ~jJ"'b3'" l,b,H,f''' ,9 4913

,.57 bP.8 1.43 4 6\\ ";2?5 R :3 1II,0!""~" !,~9,6~P

..;21944 1,2176" J1. 4 S(f17 8,t1"00~J , ~f£!63A

:24"JI 1 .. &.b8~ "~2R'''9 ".1.'''. • ... bJe

300

APPENDIX G

Data From Pipe Culver Experiments

1.0

10 (\J

"-0 ~

II

0.101- ~ ) 10 Cl

w "-0 0 w ~

0.01' I1II 1I11 I1I1I IIII III1

0.0001 0.001 0.01 0.1 1.0 10.0

Z/D2.~=~ /02·~= Q/9.91

Figure G.l Curve for Determining Critical Depth (d c ) in Pipe Culvert

Table G.l Data for Pipe Culvert, Outlet Control, No Grates

C HW -,jh; TW e -D- -D- S

0

;."'9 1;3!'5'~ 1~5d~"J ","'." .lhhi(,7

,5'7'U t, 16 112' l.U!12 .,t4""'ltI ~"~"(,7 ,7.,5& J.~q5~9 2~HU~ ",fI"'" • ;)'.,61 1

'''43 , ~().q,,:, 1:"'.248 I!."'''''''' ; (UJ36'

• 8''15'' 1, 7t lAIltr. l:t ll"o,l .. ;, ...... • !eU!'''' :73560 I 7~d I!' l:J'5"'Sq '~tW~.ldd ~<H'Ho7 ., '

;~V,j87 ~, 65118~ ~~'1!161' ;.:t, e~~Y\~l~ .~:Ullb7

• q 12~" ',"'544\'~ '.'5~59q 'I.i1 \IJt'I;' '~ ~ri.llti67 :9\718 iI. "11~A7" ~:ur;9U8 ilt~~11'1~8J1f .;'(h~"7

I • 'f 11 q 14 ';''1,'' r.' 3 ~ /'11',1)1 '" , .' n". ~~I<l' ~~'\~b1 :qqb8~ '. 71 "A~, ' .. (H,'!'l~ ~4," 9!~"'() ,";"1117

! •• Aq5) ;J .. ~416·' !.I:l12::!! ;1 ..... \~;I.'1 • .JJJt,,7 1# 't1 *' 12 1;!'~5t,; 'I::nni! ~;";'H.;a · ~"'I~" 7 !I

<494'~' :P,\f, 7 1.itJ711 ',7'"1 IH1;" rJ .~",~;.H~ :~2743 \,111,>1"-' 3~17B\q '. # ilt.-··,,:~~" ~ .''1' ~"{> 7 , ".} f'

#(\]3"3 :.714'"'" ::',.17$119 .31533 .";.41167 :A(>7S'5 I" "6ft. '; 3~11P'lq :3A2Md ~.It:Jt1h'

"

:~::::'t i I!I 1.7 VI!:., 3:17~lq :£148&7 ~ t-lth'~ 7 ;1C?418 l'7""R,' 3:.7819 ;~32!!1" , ";~?67 .. .

3:11131 0 .1:'21 t3 !,P.F4.' ,bU~~ ,."'h~l:t 7 - ~" 4StI ~, l'B:>'; ':118IQ , 74<tt/)'T • ;~a.,~ 7 :aZ1C?i J • 71ffo'.iJ 3:11 1'\19 .: 82q .",- :~:,'l"'I,' ~8~21? 1.; Hili!4 ~ 3:11R\q ,'11533 : .:h~ 'ill 7 ;837;115 !, ~ h" 'J ' • >~17lltq r 91'1~;:! ~ ':'167 • 8?91H t. ;q.? ~ .. 17l\tQ 1.,q32~1IJ • i.lliH\#) 7 :fI'H 11 ~;.'''hA .. J:PIHQ l~n2H :«JU67 :A38CJU ',&l31;,) l:t1f'19 1,21.1867 >.,;467 :S6Ub 1",Q'-lfH l:l7R{!J 1.3'tRb1 : '!. \~,i '> 7 :~t<~'l :-.27,:~,! .. 3:17!'<JQ t ~ 41t 1\6 7 ~"'",i~67

!~ii=: ';'''5b, ':171\19 ':51513 :/lIP"'b7 i' , 'I ~ 6 .~ " 3:I7AIGl I; 6C)\i6 7 :r;;;\(\;;1

:fll Q7S ',Il".'.~. ' ~:t7~l1q 1.61533 ;i"I'l"';;" - LHt87'~ I 7?~6' I: 154f,j:,} ,.,' 'H':-"'~' • ',:, ~'71\ ~ .,' ,,','

::'Q45b : ~~~~~; t ::51 6~~C; t'I,hHHH.~ ~0:HM # 36654 1 >.I184? ., ,;.\"'~~J • \.l:17 A(lI :19898 .3'66'; 1:6~t;qb tl, tI~'J;'hj ~1II~'tU'l ., • !l II 85j:1 ,,9':i.?.bl 1.19315 r" WHH1~ ,AfI'''0 :4tt7~? t 'HH,tl!< 1:<Jt4aq fI , IH'·,' ~ 0 .~1/I7~0

:~"f>17 I ,..tjAll<\ 2:wlb.Jb~ ,~ 'H'~0" ~\hf7R~ , t !~7533 :1oZ5, 1.,~~19()11 2~tl/.)j!~~ ,,3n"'~

#1:111795 1".\51~.1 2" 1lo ,j6.\ ,. '571533 ,(lI.,7l\., 'lI4528 ~, 1&5flll.~ ~:~b"biM ,,67'533 ,fJti\7A~ #

.'~f·#,i"6111 .1I44'? I ",<pi ,77~33 ,"HJ76d ., . ·~.qq'l 1,1'.\'" :?:" '>.H.I~ ,"7'533 .0d780 .f3"I'I~l ',1771. 1 l:~otlo" ,91533 ~~n8~ , , :"~~b(' " .,ns, I! ?t\?~.i t .tH5B ,e~H8\t

;(,5115 1, J'Iqt> , ;' >6~H)1" t; US33 t ~\t'78"

.6l8.8 h·ns~c. ?:1l6~";/I J ,27S'B .. 0a180 :62'.' I '71'J'~ 2~\;'MJbll! \.37533 : ()97 A" :"5,)658

., 2:~l374 1;'17533 :~"7t\0 !:~f,f)lIJ

; '59198 ,.16I\'I!t'o/I :;J~a~374 1,57533 ; 91nA~ .~44''5 I " 664f A .~ ;..t.',l~nll t.67533 .tft1AId

304

Table G.l Data for Pipe Culvert, Outlet Control, No Grates

C HW --.SL TW • e -n- _ D2• 5 -n- s .19,Q6 'I; .1 J 1111 ,-,

0

;A834ft " • 1 1258 1 t 17SH ,~'17Aq ?,lIli4d 2:11258 .~"79' ',tQJ61:! 2; J72S J

J "R7ISH ,"~78" ;4A1?S ~ t 9~'S~h.1 , ')\07'11' ! t 1376. ';.3.937 tlI,fI ....... J "Ui e ~,I cU~ .... 2¥45683 ' """'" ,6-2 •• ~ ,251'2' ,",'t81., ,""'" 1.583J5 ",'if",,, • 'SQ 14) 1;252"" 2:583)5 ' lJ~780 : jq 1113 r ,25i' q :>; S~,n5 ',1"'8 ,8,U. : "'Q9~IJ ! ;25ZII' ;" _';I\H5

,1llSH , ·,oa181'1 .57S'n • "1-'1811

:f>l191 I, ;25~Ml 1~'51l33'i ,67513 ~.01A0 : td 34Cl !, 21~I.U '1.'56335 ,77533 .~f)78'" :M8 11 t,.519'-\3. .'>:S6335 ,87533 • ~\07 8~' : HZ]*» 1,:n44<1 2:'~n5 ,enS]) ;"il7&it :tt56S<:l !,II~'h'- ':S"'B5 1, ~7513 t-.,.7SY'I ;q24 7? i.~!IIlHld ?:5~H5 1,17'13 ,eA7A~ ~~"Q~ !~l)n6~ ;t~5enS 1,27513 .tI'7~t'

: 765bl 1,1S8'''~ ~:5'51S? t.37S'B ~~rn7R" :A?7~b ,! t 8 ~h"J c' " ;):J'~!52 l~q7'5'B ,'''ct7~l :7711~1 I J q-;qt,l"I .>:5-;152 t.S7S·n tlil"7~t'I : 772~5 "t "1"/' t 1", ~:'5"1C;2 1;675,33 .. "jII7~H!\ :7«;671 7.1~"'! '_S">'C)2 t.77513 ~1j~78kl ~7b5'1 '·2b· .. ·} ,,:1')-;1'52 1~1-\7Sn ~1itt17'HI ,_ a. .

• 1:.7778 I 3 ~ 7 t,' ;>~71I(H VO, ~~q~i1 • '1t71\V! :('\1'759 1:Jq~~3 ?:AP3Qt 1':'. r iH'('\~ : -;:n 8 .. ~ :'9\685 I • 'j /) (;,.., ;> >nS31 ~:.'Qlt'loi .111"7 ... " :qqUl i: 5;n~!~ 3>'931 II :;: ,Ii~lft":·~ >~780 • 91J69~ ! ; '5l. IV " ,.f'3 III ~ fJ1'5B ~""\ 7 1\(/1 ~q4l9'.)' T .

t.~.??' : ,_,03,1\ .57513 .;' lA 71~ 1/1 :qq4~4 ~:SRi)4<' 3;13C;57 ~ ~,l~.~l'\t.I .~~7I.HI : 994Q.Il t ~ ';/1,6 /1.., 3.tJ5c)7 .. 1.I715'B : M~7~a :9~lqf» I • :> Q .t ?~I ': ;3'5'H ;57S'B >.418 .. :qQ1.i51.i !:('~V" ~:nS"7 .6'7S'B : Wl!7 1'\" :9~2l5 i; .,?'56' :J: nS'57 ~ 775H · t~~17R~ , ;Qg,;>71 .1 .... 1,52. :r.: n5c;7 ,1\7533 .Y.I~7A'J .qQUo ~t711'~":' < 13557 .n~H :~917AfJ :9°"'67 J ,8: p: .. ~:13S57 1~\i'7SB :"n~~

I~ :'I,JY15f1 ~,<I;,!;>., 1: 135'17 Itl7S'B >jP18~ :qq&,r , 'lql,}iH !:r~I)'57 1,27533 ~.HH~H:l

1 :.:<49'HI ,!,' ~5i»~ ~:13':i'51 1.HS'n :~'&7A'" 1 ::iJ'178 2': t Q;~~,~ 1: nl)57 1: 11 7S'B : I'n~1Il ,.:.IIU13 ';2~<lR •• ,;: .135')7 1~S7r,3S :""78~ 1: e:ct'H' i '. 3q 1 n '~n~t; 1 !.6'7533 :~1.'78~ ~989Z1 ,. !16}R:' ~~t35'i7 t ~ 71513 ;1I!~1f'i:t ~q477" ,.""''''6" !'. nS'51 1.1'\1533 • ~t71HJ .... ~ -: 91815 1: 673;>' ~:~12M r\. ~\*'iH'''' :t.4f!'7~~ ·Q8211' i:7}Q&,.; 3:'854 3

, ~~ft7~0 l' • r"~th".i!

'Q8261 ,:811'1oJ '\ ~5.13~q ~~Qt0~"*, .o07f\e 1:1 25J' 1~912"fI J,78t415 ",,,.tl.'" ;.".,8111 '.'3268 " .. ~bt' 1.870'19 ',-*.8." ,"I'7SI 1;1'J~5 ',t'!b~ 3~J77 13 ',e"."" .. '1181 , t1.11~'9 ',3tl3'h. 4.11223 ',' ••• 8 ; '81" 1~174JI 1,ij'.'Ht 4:313111 A, 'tt tlh' " .1.,88 l:t!Z71 I. ~',$I\~'~ il ~1I ~731~ 0,l:Ia.UI'l :"~7A~1 1: 1138' 2:b,"lP-8;.c. ~:501c)9 J • ~el!H!J ~ :"'''780

305

Table G.2

C e

:S2506 :MJ511 : 7'U'. :",qeq :1\3Q-b :"6"67 :8~1.9 :9H14 ;9&68e

I.i:nee I. 1535 ;;1~ ,>'7 ! .• ·.~~b2 ,;!>~03

• 8 0 783 :A1./181 :f\()7t13 :9;>9l4> -4!"'4C ~ 9'~8"8 : q'~J~17 '''Il\7~3 :A1U7 : <flJ33 :q""A5~ :9~'223 ;P'l\b66 • 8 /''1Q5 :~'H64 :97,83"" >63.9 • ... r:.;;>7? t .'. -.. ::"9J'J : ':t~?V - I, 108 ~ ',,"'201 - 7126Cf ':7t2bC!l :~q.t3" ~7"::63~ :" ~'I :1 5 :6481"1 :Sq~'5 :6'98'8 :7l!S4l "719155 :7~q88 .7J.1'7.6 :b761j5 ·B~26? :7U~lq :75lll Q

Data for Pipe Culvert, Outlet Control, Pipe Grates

HW -D-

1:.H?tI~ ! : u '''~;,~ ... 1 j . lllj.l ! ,0M"J~ f.7f.15l_ i;sltle .. '.,SAl"'. I. 9q~,.;· ,:.'" & 2 t ':27.'18;> ,j>: 3 }fill· ." - III' /I, ., " tr, " . :a.f.,,?: .. ~; 7 !tt)~~·' 1.77-:' ;j

: : 7 7 il .. !: 71J:· ~; 1 H." I! 77S(·:' 1 • '7 "" 6 11 ,. 1: !jl'~~. i: 811 'Ill 1:e71. p,

1-'1';;64 • . , • '~n~~,' ~. . ,~ ?: I ',' 9 /• "

':J~b:~~ i>: Y,:,>;' .. ):'1 t,? 11·

? ~ SH,,¥ : ? Ii 5" . : 79,;13 :~~pil. :.A'ill''.' :'17tf"

1 < ",':>; '\? '< - !J . 1. I 1 II,.; i:lli6d i: 1 J 1 {,.,

i:'171">] i;nSb'" ~,!7l8" '.:24'~?' ~,~17",J ~,41tj8.,

1.':.>116I..J i:,."Rlhi i: 1 P'h~~: i:8?3e* ';'1"'2~ i', ... :t<f~" 1. I VI a 'I

~ D2 • 5

? 5t:' <Ie3 2:(,2312 '~711445 3: t44 248 ]~ 152'. J;J§'59 :S.~'lUIi

':'5?SQ? ,:f>sc}ltB ':f\If'tfi~ ~:<lf)"'l~ '\: ! 1l2J <:H',\?2 !J - '19411" :f .

~.,7~lq

3:17819 !>: \ 7H I q ,.:17rQQ ~:t1f\lq 3:17~iq ~:178tQ ':Ufl,q J~171\1q }:t71\tq J:i7t\lq "'-.17A.\Q ~:t7"t9 3:0819 ~: qiq q -:.:!7 fQ Q

, : I 'i -~ ~ v: ':3Ib:1'i l: '1 HILI?

'. '.6 .15Q6 ~ '.1<)315 I : '1 t ,! if 9 l:'ll58 2:1125A ~~1.1?Se. ;J:(\,?,)~ ):It?S~ :?:ill58 ': nflS I ":'7;t51 ,< t 725 I ~: 112'5 t 2:17251 '-: HZ5 t ,,: 17 Z5t :>:"2151 2: 17251 ?:1721}1

306

TW D

1',:1 ,h'~ <' II! •• ~; .. ~~ l

tM~~" .... ","hil •• 1f,"""111 ", ..... " '~, A"QI"~ ,\ ."iI!~ ,'~ , : .>J ~,."'I d : ~·I u: H -1 ill ., •. '! "'A "",. ~ f I '.'; •• It!

J!, , ... ~ .. 0. :~ •• H: IJ ;J "

"': "li"';'~1 ~, 1oJ""4-1'-t'

• 1115'33 >'''533 ;S1I8b7 ,61533 .7 /1807 :~\J 533 ~/jqA"7 .Qo5H

I ;~:32."r, 1.H8 /}7 I: ;>"'2 .F· I :3srn '~dq~(J7 1:6153'3 i: n2'lh~ ~ ~ "\HhH~ .. ' ~!:, IJ .• ~ , _ n

". '.1~"~~ .~; ''',JQ:''''~ ~, .!,:lI',..~~

,"' , .. ;, 'Hh) "l. ,,"'IA~ if

:'17533 ;«;7s:n ,n7SH ! 7751 \ ,A1533 ,Q7513

1,'1'17'533 .,17513 1,211531 1.37533 t:U75'B ,:r;7I5B t;61533 t ,17533 t,~1513

s o

• .. ~)(':'" 7 :"'0:"67 ~"""67 ,.,8861 ,1I.e61 , I1JtU~61 .I"M"61 : ;~~I ~'61 : "'Y}~b 7 : ""Hilt> 7 : ',.4\W67

: \'~I"" 7 ~ i~3~" 7 ~ "}.!A61 • ."~'~)~ 1 : '.4:,;",7 :~li!~~67 ~~~1'>~7 ~.i':t~'61 • """:~b1 :~t:67 : Hh~1,7 .\~iH)~'7

: "H'~b 7 : '~H16'7 ~ "~ ,III: I, 7 : "r'I"b '7 >i:.\.'tl1 .".1'<;61 >, •. ~" '7 : ',~.'7A'" : ','~7R0 : iHH 8:6 · ',- .:118" , . '" f..

, ",'! 7 A "~

.~~713r.

~ !"'1I7~Hi .~i:n~iI'

• ti~17lHl : ,M78il1 :e!47AH ~~"780 ":\~\713" ,{"',j)7A~

.II07R'" ;!607A0 .1"'713 111 : 't7!'17 Art

:"1HA'" ;~r.1MJ .0~7~11J

:f.·,1nH'

Table G.2 Data for Pipe Culvert, Outlet Control, Pipe Grates

C HW _Q- TW S

e -D-n2 • 5

-D- o

:t321t 1., ) t ()"" 1;1'7251 ... , ""IUlft ," .. 7111 " ;~~485 1,1158011 ";3"~J7 ","flGUn • .'''78' • bb?]1 ~r21Y'fI '.1115683 ~,""''II'' ,~"78iJ :b81H1~ I,n"e~ ~:5eB5 ~.lfI'~1!! ~ IU178" : 7 '.l J lll~ ~ ,:~ 16"~' ::O:S'51'52 ~ ~ ,! 'Jh': J: " ~ ~~78~' :'1 6 62 I .,N~~:~ ;<!5~1C;2 .:t7'5~3 • ",i-I7 Iht ;7~LlJ7 ~;,nIH~: "~C;C;1152 ;'S7'S'n '''~7R~

?:'551'52 ' . ,7 11 3'S3 ~,276f1.' .o1'5'B , 'JII7 8" .1 'I: 7' , . ,"'I"~",,, :<~r;15~ :77'3:B • .n7 8~A :7 1q 6? I; 31 ~/).~ ?:S."r;? :e.7SB :'0!I7A~ :7~~"8 • , J1'. J~ .. I ~~511i11j2 ~q7l5n ."07Rfd ;18b87 ,.4f:,')Q" 2.I5~t'52 ',81513 : lit 1878 il .S4f2'l1 1:55~.>· ?:S'5t'S? 1.\7533 :~"78" : 777"7 i :~~48"A }~'551S2 I; 27533 ;~0781l1 "7{>.69'\ ~.71J,.>.r;··: ?:SS!CS2 1.37533 , i,iCll7MI : P1A6 t:"t,?11 ?:-;'5l'S? 1: tH533 ,~H"11\ ~

: IH5~~ , :-1') I", ?:~ljlr;2 t~'515B .~1~7'HJ

:SI3Ji1 ': :.1 (.5;.,.: ;!I:55J52 1.67533 ~ ,~ ... 7 f\t'! :'9513 i>' . 7 II·· ):SC;t52 f:77S3~ : 'LH8~ ,. . .

:7/lj~j) ;> • ~'~ ,~ t.. :~ ?~~,)t,)? t;fHSB :;"\:I7~0I : 7':;4~b t : J':; ,', .. ~ .>:7tt IH ~; .~~, ".4'. {i. : iHI7 IHt :~17 b<l i : .'1,",; I ? ~ .? ~"Hnq I ,J. •. 1 '.F'''' i~ >d78't .. , .'

:9 11 !::-b ' .,. f! f~ , (\ ,~ ~>75H ~~ • ~: ,~~ of' .., : )!" 7" ~ .,. . :Q9S13 , • ~ .... ,) t· .~:1181C) ~ir. ~ Jj , .• ~ ~ ~<HHRP :9QC;n 1 . ? ..... ' ;> \ '~;7Rlq ~1I15H :io!i.:t)1AiI • q9513

, ~:t7t;lQ :0~78iJ 1.h'S .,," .57533

1: ~~ .. ?4t3 i . '> 3 I 6; 3;171119 ~675~3 ~:..1fH~f! , 1.t51 7 : • t., ~.~ ~ ,.' 3.t7""IQ • 7 7533 .,.c~'7~0

: Qt'.917 '"0'1,,11' Y,~i7fo1tq ,H7c)'B ; ~.7 8" '. , :99917 , . 1" ~ ,,~. 3:11819 .97C,13 .:''''7~PI

t:.'6"~ i:e"h~ 3:'7$\)9 1:\!;7513 :'JCH8@ ! .• ' I 932 · -Q<:;! AI'" ~>7~lQ 1.11533 :'~~HP · . i ',,,'1 i 5 , : v ~, 7 I,' 3:,71'119 1:nS33 : :.~" 7 "fl .. 1: ··I:·/I/J 7 ;;·1~;·.P } "":17 R!Q 1~37533 :";;;7 IH'l !

:96bt Q ',?,,3?,· 3~t7~\fq 1,47'533 ~t"H8~ :91\337 7,:'<)9"( 3:17dt9 1 1 '57533 • ~'i7~~ :9A37~ ". :,.<:'~? 3:171'19 :.67533 ~ "('.7 8'~ :Q65~i ~ • ~ P. (, p., 3:171-qq ,:775:33 : f.~~7a~ :QS943

' .. ' . ,:.1fl19 I >7S'B ~K~7~~ , .57 B fI ,1

:8~H? ~ : () 3 'j II .: 3:272(,11 'J: p4l<HI~It, : "H!I7lh1 t: ,;2679 1 • 7iU I. '. 3:38S11~ O! ~ L~!l'~q'~ : "'t!78I7J

'p, ~ ~:5q3bq ~ (se7~(o1J : 9A II! t •.. ,;>~, ~.1'CiI""'~ t:(.,~827 ,:'1'5I:.t1' \: h£nS ,~;it.I~'4kl~i :~Hj78'" l"ib2" '.:I\o:·.~ !: 876 '1 q :~ •• ~"ij.,C : idl';7ae ~ ?-tq'"S; 3~977:n ~; >!I~iII~'" ~d~7~i'I t.ll'S1

t:152~1 ~~ V"~~ <n.n' " , ~, 'tHl ? ~_ .W)P780 . l;pq", " !('19tJt < 3133 11 t., .'~~"'tl ~f""7A0 . . t 15SQ(J ,):5-;~6" 1.1;13='131.1 .,"'lIIee ,''''15-I " • ~ 7Il LUI 1.1 .. 15611114:1 " • ., flell" .1.,80 l.lqt33

307

Table G.3 Data For Pipe Culvert, Inlet Control, No Grates

C HW r;h TW

S e -D- o

:;?7Utb . 7~ ' ..... J.3352tt ~, 0thHjrt ,l'15.,1f18 , .,. ,. :296i6 .1A.bS., 1 :'12571 9,"~.'1il .~5f1A0 :J •• 7, ;'1563 ,:5J8]' -, .. ", ~f5"" :1')1' ,84be l l :',.6 •• -, ..... , ,lit! .... :2'ltl' ,e7)28 1;764941 .. ,., .... ,'I);l!"" ;28.'. ,QfJ52111 p ft11 J. I,'''''' ,'!.'" , .~~'.4 ,q2'6~ ! ';"194 II f 9, "111'0 .~!~ ... :27296 t li~5'6' ?" ~1'9~;...\ 9' "~"'S'" ~(f5(\018 . , -, .. ,",J ') 4 'It

;267/J~ 1,lfl2.lh: ?:6Jt3~ ~ I rj';h!~f t (,l;15;..;~"

.. 319'1 , ';)7'" ?:7,.,"A ".i'i(W"~ .5>'5'9"" ; jAlI)q

.- , ';B7S64 ~;~"!1tlJ~ ~i!-;\'I3' 1,<?52lH;

, 'Hl8.S t,3'{j8f~ ?r'"92t llJ ~, ',4f(~"".(! • t5S.t rJ0 .. 48285 l.,lAMA~ 3.13557 ':fl. N .... H·t- : 1(15~'4/'I" :St'J5e 1. 41 41,,:' !f.:?o4@1 ~:tJf}~J~ : ~C;~~:JA "'.:' H.;>4 l;St~HP 3::57071 ~: PI'J!~fH~ :a5J~" , ..It.)

~ ...... ttl'5 t ')'53b,~ 3:'51715 0:if4~~0 ;~5Nh) ., ': (l'S";'i:\ !~: "B~~,jc; .,)Q210 :.~H'5b.\ • ~5i1?'0

;61606 ~: '51.\ 2~(' ~:71.1~4~~ 9;~~"t!ii ;-J5~~" • ,,)C).,.,c) I; 6?'Hpt '!,: '''569'J ~."oCIJA"'~ • ~5~H'" :61343 !: 61·32J J:95893 'I: QItH'::Jt1 ;e5-'1J9 :63857 I .. h lb/P' J >~58q3 il,;".~~"'~'~ • 05 '1 !.tGII :72190 1:'1AI6; 11:275Sb ft • f.::t" '!' 'J.' : r)S¥! 910

;3~1~" j:tk''''~ tl:S:-JS9 tl;kI(P":;' :~SH~A .. • 'UStH. a: LHF1'= q:63 A91 k":~a~"'~!!1 ~"'5M~" : 113688 • : 9 'I k~:" (l: 1'5S69 A. ~"..,Q§;' • ti50~'~ .. t~~3t9 1:' "" 'I" lJ:7~5'i<~ II" :,~ A" III 7. : .. j5~{"~ :Z'Iq'b .1: ;I)"~f'.,' LI:q7l?~ :i! >, tiP ~:3 :~C;I!9'~ ;3JU49 '"1311)" 5~.j7t7q " ~ e~irl:~i~ ; ~5 ~"'f" I .2b948 'rl'1f6e~ '5;.' "l.J1 -,"'.'" ,'58'. ;.18~5 1,1172' 5;29312 oj, '''1'' .. 1 ,""'" .Ab9J8 1.5Q12' 5':.'13659 I.""'" .--'58.0

. .

308

..

.. .

Table G.4 Data For Pipe Culvert, Inlet Control, Pipe Grates

C e

:l1q6' :3 16113 ;38J'l'1 .'5".61\ :39!8.:l :3~2tS:. :~n?''3 ;32376 .3196e :31." : IH 5~l :"53061 '" "~'49Q2 , .49780 :C;7 Q66 ;6-:.:6'H .. (,45cr:A

:6f'2'~ :!';,SR~I :i. t}7611 : 1SUJ3 :.)7 24 i : 'H'StSb : J4';<;3'3 ;31167 : lIJ61U Jq.1.

! 3.,15 It ; .; 1&8t' 1.~t541

HW -D-

·11f\~·" :: ..... ,7'88P ,8>q,~

,80,a, ,!~.aOJ

It)"). ,'" , 7. , .

_,9/"' ... J.,''712:: 1,1280~ ) J I 9 "HJ ~' • ~ f. "c~. .&f'~·~"··

'.331£U j;J7fh"'~ 1.1='36 J

t;]P.76~ t ,4!l~;> :' t .I) •• ;:;>~ I . ~f, &/~ ~ -, : I. o? .... ;' ,I ~. 1)·Htl! .~ , 1 • .., fJ !, II; ~ '" 8 ... ·· i\ '. ... r. W_i '., ).

• : ~, (~lJ .' \;q'i2'~i ) • ,"r,~CJ - ,,,!

;:J; .. ~q2tJ ' .. 1l81.1' ';''I;II;~~ ',3#)1'''' ? t, ,I <;;h'

Q n2 •5

1:3152" I~Q2577 1.5381q 1 :64&'" t;7649. I". t\ 7J ,~ 1 • ~911 I~ I ?: IHI9Ifh~ ~:b313Il ?: 7?,HtA ;>:n7564 ?:1 0 2li' 3:1:a-S'57 3:"I,l.Iel :':37671 ':S,7JiI) ~:b5'i,iI)J 3: 749ll¥1 ,: 9S~q'\ !.': "iSRq~ Q:'755b t.I:!>w'l389 1':h3RCJI II: 75569 Q:185)tiU 1I;~1l2e 5 .. 8717Q 5:1~2.t 5:~9]" e;:I.t"o'59

309

TW -D-

~';. gl"'." ~!"''''M . ,'''.'' ., ..... " ',,,.e.,, ~, t'¢'lA~)

~,~f4t11~1

~.""~"0 ,; 190~'9:~ '" 4AC!' ~' •• '.11 , . ~

Vt.0Y1A!,f':1

VI: 0,UH'~~ ill ~ K"'''~:,4 ~.Jtf""~ ,~ ~ iii'''\ ~"8" iii I ~~"":1~i lit • "., i" t'\ ,lh3

"': iH·"(.if~ ..,; : "}If .H';;~

• ~.,,;*p~~

fh: H'I~)W" ,<)I' ,;Ia., ... ',A. IV f "" •• .,., 'J H~W,'- ';

~ it. ~"I"':.·,· "," .,tIiI.'~ '.~ ' .. • , ~, .., ~t..- ~ •

." ..... P' '1·· .. • ... .,11 ... " .. /11 Ilt,Wf!tlJjillt ~ .il'.Il I'"

s o

.SiI.i :.! .•. ,.,~.tI .. ,IIJIJ"'" , ,,115"" , ,4Sl-'IltY'

• 1:i!StJ 111"1 ;@~A8~ ,t1~JII99" • ;."5k10~ : '~W;\~\A1l ;r45A0A , 05~1"\!t • ~5"'01?\ ;"'5~"!II f.,SC10t'1 , Q!5~H'A .0"HH~H~ • ",·se~.,,, : {'I5(;!1-'!~ : 1iJ5~'H' : f~-;"'''~ : J5IH'J1'I :,!H'!~t' ; (\5~VI"

,illS"." ,"I)'." ,e'S"p0 ,estJt"r! • ~'lt'lt1!ltl

hydraulic performance of culverts with safety grates · the texas highway department and messrs....

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