Effects of Inlet Geometry on Hydraulic Performance of Box Culverts
Errata for Effects of Inlet Geometry on Hydraulic Performance of Box Culverts Publication No. (FHWAHRT06138)
Dear Customer:
A number of technical corrections were made to this report after the report was originally published on the Web site. The following table shows the modifications that were made to this electronic report.
Page Number 
Correction 
Page 42 
Table 1 replaced 
Page 47 and 48 
Table 2 replaced 
Page 59 
Table 3 replaced 
Page 62 
Table 4 replaced 
Page 73 
Table 7 replaced 
Page 73 
Table 8 replaced 
Page 74 
Table 9 replaced 
Page 74 
Table 10 replaced 
Page 85 
Table 11 replaced 
Page 86 
Table 12 replaced 
Page 120 and 121 
Table 17 replaced 
Page 122 and 123 
Table 18 replaced 
FOREWORD
This report describes a laboratory study of culvert hydraulics done at the TurnerFairbank Highway research Center (TFHRC) hydraulics lab in partnership with the South Dakota DOT (SDDOT). The study focused on rectangularshaped culverts with a number of inlet geometry conditions representing inlets that are currently available for highway culverts. Design coefficients are recommended for several inlet configurations that are not specifically covered in the Federal Highway Administration Hydraulic Design Series No. 5 (HDS5). This report will be of interest to hydraulic engineers involved in culvert design and to researchers involved in developing improved culvert design guidelines. It is being published as a Web document only.
Gary L. Henderson Director, Office of Infrastructure Research and Development
This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation.
The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document.
Quality Assurance Statement
The Federal Highway Administration (FHWA) provides highquality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.
1. Report No. FHWAHRT06138  2. Government Accession No. N/A  3. Recipient’s Catalog No. N/A 
4. Title and Subtitle Effects of Inlet Geometry on Hydraulic Performance of Box Culverts  5. Report Date December 2006 
6. Performing Organization Code N/A 
7. Author(s) J. Sterling Jones, Kornel Kerenyi, and Stuart Stein  8. Performing Organization Report No. N/A 
9. Performing Organization Name and Address GKY and Associates, Inc. 5411E. Backlick Road Springfield, VA 22151 
10. Work Unit No. (TRAIS) N/A 
11. Contract or Grant No. DTFH6104C00037 
13. Type of Report and Period Covered Final Lab Report 1102 to 1104 
12. Sponsoring Agency Name and Address Office of Infrastructure R&D  South Dakota DOT  Federal Highway Administration  Office of Research  6300 Georgetown Pike  700 East Broadway Avenue  McLean, VA 22101  Pierre, SD 57501   14. Sponsoring Agency’s Code SD Project SD200204 FHWA Task Order 3 
15. Supplementary Notes Contracting Officer's Technical Representative: J. Sterling Jones, HRDI07. South Dakota Technical Panel: Mark Clausen, Noel Clocksin, Kevin Goeden, Cory Haeder, Terry Jorgensen, Paul Oien, Daris Ormesher, Rich Phillips, Steve Wagner Brad Newlin designed models and developed preliminary analysis algorithms. Holger Dauster and Amon Tarakemeh provided invaluable assistance with instrumentation, data collection, and analysis. Donna and Dave Pearson provided senior editing and EDP services. 
16. Abstract Each year, the South Dakota Department of Transportation (SDDOT) designs and builds many castinplace (CIP), or field cast, and precast box culvert structures that allow drainage to pass under roadways. The CIP boxes typically have 30degreeflared wingwalls, and the precast have straight wingwalls with 10.16centimeter (cm) (4inch) bevels on the inside edges of the wingwalls and top slab. Previous research conducted on a limited number of single barrel box culverts indicated that further research was necessary to determine (1) the effects of multiple barrel structures, (2) loss coefficients of unsubmerged outlets, and (3) the effects of 30.48cm (12inch) corner fillets versus 15.24cm (6inch) corner fillets. In order to optimize the design of both types of box culverts, it was also necessary to determine the effects of spantorise ratios, skewed end conditions, and optimum edge conditions on typical box culvert installations 
17. Key Words Culvert, inlet, headwall, wingwall  18. Distribution Statement No restrictions. This document is available to the public through the National Technical Information Service; Springfield, VA 22161 
19. Security Classification (of this report) Unclassified  20. Security Classification (of this page) Unclassified  21. No. of Pages 158  22. Price 
Form DOT F 1700.7 (872)  Reproduction of completed page authorized (art. 5/94) 
TABLE OF CONTENTS
1. INTRODUCTION
PROBLEM STATEMENT
OBJECTIVES
PROCEDURES AND FACILITIES
2. LITERATURE REVIEW
3. THEORY AND DESIGN CALCULATIONS FOR INLET AND OUTLET CONTROL
INLET CONTROL HYDRAULICS OF CULVERTS
OUTLET CONTROL HYDRAULICS OF CULVERTS
4. DATA ACQUISITION AND DATA ANALYSIS PROCEDURES
DATA ACQUISITION FOR CULVERT SETUP
DATA MANAGEMENT
DATA ANALYSIS FOR INLET CONTROL TESTS
DATA ANALYSIS FOR OUTLET CONTROL TESTS
5. EXPERIMENTAL PROCEDURES
MINIFLUME EXPERIMENTS
CULVERT SETUP EXPERIMENTS
6. EXPERIMENTAL RESULTS
EFFECTS OF BEVELS AND CORNER FILLETS
EFFECTS OF MULTIPLE BARRELS
EFFECTS OF SPANTORISE RATIO
EFFECTS OF HEADWALL SKEW
OUTLET CONTROL ENTRANCE LOSS COEFFICIENTS Ke FOR LOW FLOWS (UNSUBMERGED CONDITIONS)
OUTLET CONTROL EXIT LOSS COEFFICIENTS Ko
FIFTHORDER POLYNOMIALS
7. CONCLUSIONS AND RECOMMENDATIONS
FINDINGS AND CONCLUSIONS
RECOMMENDATIONS
APPENDIX A. EXPANDED TEST MATRIX
APPENDIX B. INLET CONTROL COMPARISON CHARTS
APPENDIX C. SUMMARY OF REGRESSION COEFFICIENTS
APPENDIX D. EXAMPLE PROBLEM
REFERENCES
LIST OF FIGURES
Figure 1. Photo. Culvert headbox under construction
Figure 2. Diagram. Arrangement of the ceramic class pressure sensors
Figure 3. Sketch. Precast flared end section tested by Graziano and by McEnroe
Figure 4. Equation. HW/D, prefabricated metal end section, unsubmerged condition
Figure 5. Equation. HW/D, prefabricated metal end section, transition zone
Figure 6. Equation. HW/D, prefabricated metal end section, submerged condition
Figure 7. Equation. HW/D, precast concrete end section, unsubmerged condition
Figure 8. Equation. HW/D, precast concrete end section, transition zone
Figure 9. Equation. HW/D, precast concrete end section, submerged condition
Figure 10. Equation. Figure 8 in HDS5 format.
Figure 11. Sketch. Relationship of entrance loss coefficient to Reynolds number
Figure 12. Diagram. Typical inlet control flow condition
Figure 13. Equation. Unsubmerged form 1, inlet control
Figure 14. Equation. Unsubmerged form 2, inlet control
Figure 15. Equation. Submerged form, inlet control
Figure 16. Diagram. Outlet control for full flow condition
Figure 17. Equation. Headdischarge relationship, outlet control
Figure 18. Equation. Total energy losses
Figure 19. Equation. Entrance loss
Figure 20. Equation. Exit loss
Figure 21. Diagram. Data management flow chart
Figure 22. Equation. Regression analysis, chisquared
Figure 23. Equation. Fifthorder polynomial for HW/D
Figure 24. Equation. Entrance loss coefficient
Figure 25. Diagram. Technique to determine HLe
Figure 26. Graph. Typical behavior of Ke versus discharge intensity
Figure 27. Diagram and Photo. Miniflume and PIV setup
Figure 28. Photos. Bevel models and PIV camera at culvert entrance
Figure 29. Diagram. Integration of velocity flow field in stream functions to study culvert flow contraction
Figure 30. Diagrams. Tested bevel edge conditions and effective flow depth criterion
Figure 31. Diagram. Culvert setupside view
Figure 32. Diagram. Culvert setuptop view
Figure 33. Photo. Culvert setupoverview
Figure 34. Photo. Culvert model barrels
Figure 35. Photo. Twodimensional robot to measure velocity distribution in tailbox
Figure 36. Photo. Groove connectors to assemble models
Figure 37. Diagrams. Effective flow depth at vena contracta for nonrounded bevel edges
Figure 38. Diagrams. Effective flow depth at vena contracta for rounded bevel edges
Figure 39. Graph. Effective flow depth versus headwater/tailwater difference
Figure 40. Sketches. Models tested for effects of bevels and corner fillets
Figure 41. Graph. Inlet control performance curves, FCS0 versus PCA, zero corner fillets
Figure 42. Graph. Inlet control performance curves, FCS0 versus PCA, 15.24cm (6inch) fillets
Figure 43. Graph. Inlet control, precast with 15.24cm (6inch fillets) and field cast with 15.24cm (6inch) fillets
Figure 44. Graph. Inlet control, field cast hybrid inlet with 10.16cm (4inch) radius bevel on wingwalls
Figure 45. Graph. Inlet control, precast hybrid inlet with no bevel on wingwalls
Figure 46. Graph. Inlet control effects of corner fillets for the field cast model
Figure 47. Graph. Inlet control effects of corner fillets for the precast model
Figure 48. Graph. Inlet control, precast with 30.48cm (12inch) fillets and field cast with 15.24cm (6inch) fillets
Figure 49. Sketches. Models tested for the effects of multiple barrels
Figure 50. Graph. Inlet control comparison, field cast 0degreeflared wingwall models
Figure 51. Graph. Inlet control comparison, field cast 30degreeflared wingwall models
Figure 52. Graph. Inlet control comparison, precast models
Figure 53. Graph. Inlet control comparison, singlebarrel models
Figure 54. Graph. Inlet control comparison, doublebarrel models
Figure 55. Graph. Inlet control comparison, triplebarrel models
Figure 56. Graph. Inlet control comparison, quadruplebarrel models
Figure 57. Graph. Inlet control comparison, extended or nonextended center walls, field cast model
Figure 58. Inlet control comparison, extended or nonextended center walls, precast model
Figure 59. Sketches. Models tested for effects of spantorise ratio
Figure 60. Graph. Inlet control comparison, FCS0 spantorise ratios
Figure 61. Graph. Inlet control comparison, PCA spantorise ratios
Figure 62. Graph. Inlet control comparison, FCS30 spantorise ratios
Figure 63. Graph. Inlet control comparison, 1:1 spantorise ratio
Figure 64. Graph. Inlet control comparison, 2:1 spantorise ratio
Figure 65. Graph. Inlet control comparison, 3:1 spantorise ratio
Figure 66. Graph. Inlet control comparison, 4:1 spantorise ratio
Figure 67. Sketch. Definition sketch for skew tests
Figure 68. Sketches. Models tested for effects of headwall skew
Figure 69. Diagrams. Plan view of skewed headwall models tested
Figure 70. Inlet control comparison, skew angles
Figure 71. Graph. Entrance loss coefficient versus the Reynolds number, HDS5 8/3
Figure 72. Graph. Standard deviation of Ke versus the Reynolds number
Figure 73. Diagram. Culvert contraction
Figure 74. Equation. Expansion loss equation
Figure 75. Equation. Exit loss, with coefficient of 1
Figure 76. Equation. Downstream velocity
Figure 77. Equation. Exit loss, with coefficient Ko
Figure 78. Diagram. Flow expansion in the tailbox for high tailwater
Figure 79. Diagram. Flow expansion in the tailbox for low tailwater
Figure 80. Diagram. Vertical flow expansion in the tailbox and projected EGL
Figure 81. Graph. Transition area, unsubmerged and submerged inlet flow conditions
Figure 82. Equation. Transition area, unsubmerged and submerged inlet flow conditions
Figure 83. Graph. PC and FC single barrel models (sketches 1, 7, 11 in figure 93)
Figure 84. Graph. PC and FC multiple barrel models (sketches 1, 2, 7, 8, 11, 12 in figure 93)
Figure 85. Graph. Combined corner fillet data, FCS0 and PCA models (sketches 7, 10, 11, 14 in figure 93)
Figure 86. Graph. Combined multiple barrel data, FC0 models (sketches 7, 8 in figure 93)
Figure 87. Graph. Combined multiple barrel data, FC30 models (sketches 1, 2 in figure 93)
Figure 88. Graph. Combined multiple barrel data, PC models (sketches 11, 12 in figure 93)
Figure 89. Graph. Combined spantorise data, FCS0 models (sketches 7, 9 in figure 93)
Figure 90. Graph. Combined spantorise data, FCS30 models (sketches 1, 3 in figure 93)
Figure 91. Graph. Combined spantorise data, PC models (sketches 10, 13 in figure 93)
Figure 92. Graph. Skewed and nonskewed headwalls, FCT30 models (sketches 4, 5 in figure 93)
Figure 93. Thumbnail sketches of inlets recommended for implementation
Figure 94. Graph. Inlet control, FCS0 and PCA, no corner fillets
Figure 95. Graph. Inlet control, FCS0 and PCA, 15.24cm (6inch) corner fillets
Figure 96. Graph. Inlet control, FCS0 and PCA, 30.48cm (12inch) corner fillets
Figure 97. Graph. Inlet control, FCS30, FCS0, and PCA
Figure 98. Graph. Inlet control, PCA, 15.24 and 30.48cm (6 and 12inch) corner fillets
Figure 99. Graph. Inlet control, field cast hybrid inlet with 10.16cm (4inch) radius bevel on wingwalls
Figure 100. Graph. Inlet control, precast hybrid inlet with no bevel on wingwalls
Figure 101. Graph. Inlet control, FCS0, FCD0, FCT0, and FCQ0
Figure 102. Graph. Inlet control, FCS0, FCD0E, FCT0E, and FCQ0E
Figure 103. Graph. Inlet control, FCS30, FCD30, FCT30, and FCQ30
Figure 104. Graph. Inlet control, FCS30, FCD30E, FCT30E, and FCQ30E
Figure 105. Graph. Inlet control, FCS0 and FCS30
Figure 106. Graph. Inlet control, FCD0 and FCD30
Figure 107. Graph. Inlet control, FCT0 and FCT30
Figure 108. Graph. Inlet control, FCQ0 and FCQ30
Figure 109. Graph. Inlet control, FCD0 and FCD0E
Figure 110. Graph. Inlet control, FCT0 and FCT0E
Figure 111. Graph. Inlet control, FCQ0 and FCQ0E
Figure 112. Graph. Inlet control, FCD30 and FCD30E
Figure 113. Graph. Inlet control, FCT30 and FCT30E
Figure 114. Graph. Inlet control, FCQ30 and FCQ30E
Figure 115. Graph. Inlet control, PCA, PCB, PCC, and PCD
Figure 116. Graph. Inlet control, PCA, PCBE, PCCE, and PCDE
Figure 117. Graph. Inlet control, PCB and PCBE
Figure 118. Graph. Inlet control, PCC and PCCE
Figure 119. Graph. Inlet control, FCS30, FCS0, and PCA
Figure 120. Graph. Inlet control, FCD30, FCD0, and PCB
Figure 121. Graph. Inlet control, FCT30, FCT0, and PCC
Figure 122. Graph. Inlet control, FCQ30, FCQ0, and PCD
Figure 123. Graph. Inlet control, FCS0, various spantorise ratios
Figure 124. Graph. Inlet control, FCS30, various spantorise ratios
Figure 125. Graph. Inlet control, PCA, various spantorise ratios
Figure 126. Graph. Inlet control, FCS0, FCS30, and PCA, 1:1 spantorise ratio
Figure 127. Graph. Inlet control, FCS0, FCS30, and PCA, 2:1 spantorise ratio
Figure 128. Graph. Inlet control, FCS0, FCS30, and PCA, 3:1 spantorise ratio
Figure 129. Graph. Inlet control, FCS0, FCS30, and PCA, 4:1 spantorise ratio
Figure 130. Graph. Inlet control, FCT30 at various headwall skews
Figure 131. Graph. Inlet control, FCS30, 0 and 30degree skew
Figure 132. Equation. Fifthorder polynomial
Figure 133. Graph. Discharge, tailwater variation
Figure 134. Graph. Downstream cross section
Figure 135. Graph. Cross section area versus tailwater elevation
Figure 136. Equation. Downstream flow area for tailwater elevation
Figure 137. Equation. Flow area under headwater elevation
Figure 138. Equation. Downstream channel velocity for Q25
Figure 139. Equation. Downstream channel velocity for Q100
Figure 140. Equation. Critical depth, below top corner fillets
Figure 141. Equation. Critical depth, partially submerged top corner fillets
Figure 142. Equation. Normal culvert depth
Figure 143. Equations. Flow area and hydraulic radius, depth below top corner fillet
Figure 144. Equations. Flow area and hydraulic radius, top fillets partially submerged
Figure 145. Equation. Initial depth
Figure 146. Equation. For Ko equals 1.0
Figure 147. Diagram. Definition sketch for exit loss
Figure 148. Equation. Initial depth, ignoring tailwater velocity head
Figure 149. Equations. For d less than (Da)
Figure 150. Equations. For d less than D but greater than (Da)
Figure 151. Equations. For d equal to D (the last iteration)
Figure 152. Equation. Friction slope
Figure 153. Equation. Step length
Figure 154. Equation. EGL at upstream culvert end (the entrance)
Figure 155. Sketches. Entrance loss coefficients (Ke) of culverts in example problem
Figure 156. Equation. Entrance loss
Figure 157. Equation. Headwater energy grade line
Figure 158. Equation. Headwater hydraulic grade line
Figure 159. Diagram. FCD30 model, Q100 elevations
Figure 160. Diagram. FCD0 model, Q100 elevations
Figure 161. Diagram. PCB model, 30.48cm (12inch) corner fillets, Q100 elevations
Figure 162. Diagram. PCB model, no corner fillets, Q100 elevations
Figure 163. Equations. Brink depth at culvert outlet
Figure 164. Equation. Headwater EGL
Figure 165. Diagram. Net area used for backwater computations
LIST OF TABLES
Table 1. Effects of bevels and corner filletssummary of inlet and outlet control coefficients
Table 2. Summary of inlet and outlet control coefficients for models tested for effects of multiple barrels
Table 3. Summary of inlet and outlet control coefficients for models tested for effects of spantorise ratio
Table 4. Summary of inlet and outlet control coefficients for models tested for effects of headwall skew
Table 5. Summary of outlet control entrance loss coefficients, K_{e}, for low flows
Table 6. Summary of outlet loss coefficients
Table 7. Polynomial regression coefficients, models tested for bevels and corner fillets
Table 8. Polynomial regression coefficients, models tested for spantorise ratio
Table 9. Polynomial regression coefficients, models tested for multiple barrels
Table 10. Polynomial regression coefficients, models tested for skewed headwall
Table 11. Design coefficients suggested for future editions of HDS5
Table 12. Fifthorder polynomial coefficients
Table 13. Tests to analyze the effects of bevels for wingwalls and top edges
Table 14. Tests to analyze the effects of multiple barrels
Table 15. Tests to analyze the effects of the spantorise ratio
Table 16. Tests to analyze the effects of skew
Table 17. Inlet control design coefficients, all experiments
Table 18. Inlet control fifthorder polynomial coefficients, all experiments
Table 19. Outlet control design coefficients, all experiments
Table 20. Example problem, downstream cross section ground point coordinates
Table 21. Example problem, tailwater rating information
Table 22. Example problem, step 3 solutions
Table 23. Example problem, step 4 solutions
Table 24. Example problem, step 5 solutions
Table 25. Example problem, step backwater and entrance loss results for Q_{25}
Table 26. Example problem, step backwater and entrance loss results for Q_{100}
LIST OF ACRONYMS AND ABBREVIATIONS
2D  twodimensional 
ccd  charge coupled device 
CIP  castinplace 
DOT  Department of transportation 
EGL  energy grade line 
FC  field cast 
FHWA  Federal Highway Administration 
HDS  Hydraulic Design Series 
HECRAS  Hydrologic Engineering Center River Analysis System 
HGL  hydraulic grade line 
HW/D  headwater depth (ratio) 
LDA  laser doppler anemometry 
NCHRP  National Cooperative Highway Research Program 
OPM  optical pressure measurement 
PC  precast 
PIV  particle image velocimetry 
PVC  polyvinyl chloride 
SI 
International System of Units (the Metric System) 
SDDOT  South Dakota Department of Transportation 
TFHRC  TurnerFairbank Highway Research Center 
VI  virtual instruments 
WW  wingwall 
LIST OF SYMBOLS
(A comprehensive list can be found in Hydraulic Design of Highway Culverts (HDS5)(1)) 
A  full crosssectional area of culvert barrel 
c  coefficient for submerged inlet control equation 
D  interior height of the culvert barrel 
EGL  energy grade line (sometimes E.G.L.) 
h  height of hydraulic grade line above centerline of orifice 
H_{c}  specific head at critical depth (d_{c} + V_{c}^{2}/2g) 
H_{e}  entrance head loss 
H_{f}  friction head loss in culvert barrel 
H_{L}  total energy loss 
H_{Le}, H_{Lc}  inlet loss (also the inlet head loss or the contraction loss) 
H_{Lf}, H_{f}  friction loss 
H_{Lo}  exit loss 
H_{o}  exit head loss 
HGL  hydraulic grade line (sometimes H.G.L.) 
HW  headwater; depth from inlet invert to upstream total energy grade line 
HW_{i}  headwater depth above inlet control section invert 
HW_{o}  headwater depth above culvert outlet invert 
HW/D  headwater depth ratio 
g  acceleration due to gravity 
K  coefficient for unsubmerged inlet control equation 
K_{e}  coefficient for outlet control entrance loss 
K_{o}  exit loss coefficient usually assumed to be 1.0 for design purposes 
K_{u}  1.811 for SI; 1.0 for the English system 
M  exponent in unsubmerged inlet control equation 
Q  discharge 
S  culvert barrel slope 
TW  tailwater; depth of water measured from culvert outlet invert 
V  mean velocity of flow 
V_{d} 
downstream velocity 
V_{u} 
approach (upstream) velocity 
y  depth of flow 
Y  additive term in submerged inlet control equation 
Contents  Next
