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Publication Number: FHWA-RD-06-138
Date: October 2006

Effects of Inlet Geometry on Hydraulic Performance of Box Culverts

APPENDIX C. SUMMARY OF REGRESSION COEFFICIENTS

Tables 17, 18, and 19 of this appendix summarize the regression coefficients derived from all of the experiments conducted during this study. Table 17 lists the inlet control design coefficients—K, M, c, and Y—that apply to the HDS-5 form 2 unsubmerged and submerged flow equations in figures 14 and 15 in chapter 3.

Table 18 lists the inlet control fifth-order polynomial constants—a, b, c, d, e, and f—that are used by computer programmers to bridge the transition from unsubmerged to submerged flow by coding the two equations as a continuous function. The full fifth-order polynomial used in culvert design is given in figure 132.

Figure 132. Equation. Fifth-order polynomial.

View Alternate Text

Ku is the units conversion constant and equals 1.811 for SI units and 1.0 for customary English units.

Table 19 lists the outlet control loss coefficients Ke and Ko used to compute culvert entrance and culvert outlet losses. The coefficients are commonly expressed as functions of the barrel velocity head, as indicated in the equations in figures 19 and 20 in chapter 3.

The downstream channel velocity for this study was taken as the average velocity in the tailbox using the full width of the tailbox multiplied by the average tailwater depth as the flow area.

Table 17. Inlet control design coefficients, all experiments.

InletModelSlope (percent)Fillet (inches)BarrelsSpan: RiseSkew (degrees)KMcY

Bevels and fillets experiments

1.1

FC-S-0

3.0

  0

1

1:1

0

0.55

0.64

0.0453

0.54

1.2

FC-S-0

3.0

  6

1

1:1

0

0.57

0.62

0.0448

0.56

1.3

FC-S-0

3.0

12

1

1:1

0

0.58

0.61

0.0447

0.54

1.4

PC-A

3.0

  0

1

1:1

0

0.56

0.63

0.0371

0.67

1.5

PC-A

3.0

  6

1

1:1

0

0.57

0.62

0.0371

0.67

1.6

PC-A

3.0

12

1

1:1

0

0.57

0.61

0.0361

0.68

1.7

PC-A

3.0

  6

1

2:1

0

0.60

0.56

0.0329

0.79

1.8

PC-A

3.0

12

1

2:1

0

0.60

0.55

0.0316

0.81

1.9

PC-A hybrid

3.0

  0

1

1:1

0

0.63

0.58

0.0331

0.80

1.10

FC-S-0 hybrid

3.0

  0

1

1:1

0

0.62

0.59

0.0445

0.66

Multiple barrel experiments

2.1

FC-S-0

3.0

  6

1

1:1

0

0.57

0.62

0.0448

0.56

2.2

FC-S-30

3.0

  6

1

1:1

0

0.47

0.69

0.0394

0.53

2.3

FC-D-0

3.0

  6

2

1:1

0

0.55

0.61

0.0391

0.66

2.4

FC-D-0-E

3.0

  6

2

1:1

0

0.55

0.61

0.0394

0.65

2.5

FC-D-30

3.0

  6

2

1:1

0

0.47

0.66

0.0366

0.61

2.6

FC-D-30-E

3.0

  6

2

1:1

0

0.46

0.67

0.0381

0.59

2.7

FC-T-0

3.0

  6

3

1:1

0

0.58

0.58

0.0377

0.69

2.8

FC-T-0-E

3.0

  6

3

1:1

0

0.60

0.57

0.0405

0.67

2.9

FC-T-30

3.0

  6

3

1:1

0

0.48

0.67

0.0379

0.60

2.10

FC-T-30-E

3.0

  6

3

1:1

0

0.51

0.64

0.0405

0.60

2.11

FC-Q-0

3.0

  6

4

1:1

0

0.55

0.61

0.0377

0.71

2.12

FC-Q-0-E

3.0

  6

4

1:1

0

0.58

0.59

0.0418

0.64

2.13

FC-Q-30

3.0

  6

4

1:1

0

0.47

0.71

0.0372

0.64

2.14

FC-Q-30-E

3.0

  6

4

1:1

0

0.50

0.65

0.0398

0.60

2.15

PC-A

3.0

12

1

1:1

0

0.57

0.61

0.0361

0.68

2.16

PC-B

3.0

12

2

1:1

0

0.54

0.61

0.0253

0.91

2.17

PC-B-E

3.0

12

2

1:1

0

0.57

0.58

0.0315

0.81

2.18

PC-C

3.0

12

3

1:1

0

0.57

0.57

0.0219

0.98

2.19

PC-C-E

3.0

12

3

1:1

0

0.59

0.58

0.0263

0.91

2.20

PC-D

3.0

12

4

1:1

0

0.55

0.61

0.0250

0.92

2.21

PC-D-E

3.0

12

4

1:1

0

0.60

0.54

0.0296

0.85

Span-to-rise experiments

3.1

FC-S-0

3.0

0

1

1:1

0

0.55

0.64

0.0453

0.54

3.2

FC-S-0

3.0

0

1

2:1

0

0.61

0.56

0.0404

0.68

3.3

FC-S-0

3.0

0

1

3:1

0

0.61

0.58

0.0413

0.67

3.4

FC-S-0

3.0

0

1

4:1

0

0.62

0.57

0.0421

0.65

3.5

FC-S-30

3.0

0

1

1:1

0

0.44

0.74

0.0403

0.48

3.6

FC-S-30

3.0

0

1

2:1

0

0.47

0.66

0.0397

0.56

3.7

FC-S-30

3.0

0

1

3:1

0

0.48

0.66

0.0414

0.54

3.8

FC-S-30

3.0

0

1

4:1

0

0.50

0.63

0.0410

0.59

3.9

PC-A

3.0

0

1

1:1

0

0.56

0.63

0.0371

0.67

3.10

PC-A

3.0

0

1

2:1

0

0.60

0.56

0.0329

0.79

3.11

PC-A

3.0

0

1

3:1

0

0.60

0.58

0.0331

0.79

3.12

PC-A

3.0

0

1

4:1

0

0.62

0.57

0.0340

0.79

Skewed headwall experiments

4.01

FC-T-0

3.0

6

3

1:1

0

0.58

0.58

0.0377

0.69

4.02

FC-T-30

3.0

6

3

1:1

0

0.48

0.67

0.0369

0.62

4.03

FC-T-30

3.0

0

3

1:1

15

0.66

0.51

0.0289

0.95

4.04

FC-T-30

3.0

0

3

1:1

30

0.70

0.48

0.0312

0.94

4.05

FC-T-30

3.0

0

3

1:1

45

0.69

0.50

0.0224

1.10

4.06

FC-S-30

3.0

0

1

3:1

30

0.68

0.46

0.0306

0.89

1 inch = 2.54 cm

Table 18. Inlet control fifth-order polynomial coefficients, all experiments.

InletModelSlope (percent)Fillet (inches)BarrelsSpan: RiseSkew (degrees)abcdef

Bevels and fillets experiments

1.1

FC-S-0

3.0

  0

1

1:1

0

0.211536

0.224341

0.208370

−0.12199

0.024676

−0.00161

1.2

FC-S-0

3.0

  6

1

1:1

0

0.224471

0.247312

0.186514

−0.11350

0.023189

−0.00151

1.3

FC-S-0

3.0

12

1

1:1

0

0.245464

0.218175

0.210202

−0.12126

0.024063

−0.00153

1.4

PC-A

3.0

  0

1

1:1

0

0.194217

0.310678

0.109365

−0.07741

0.016183

−0.00106

1.5

PC-A

3.0

  6

1

1:1

0

0.203074

0.313529

0.107677

−0.07685

0.016046

−0.00104

1.6

PC-A

3.0

12

1

1:1

0

0.210576

0.314554

0.101951

−0.07265

0.014939

−0.00095

1.7

PC-A

3.0

  6

1

2:1

0

0.186778

0.482282

−0.07044

−0.00309

0.003186

−0.00026

1.8

PC-A

3.0

12

1

2:1

0

0.189232

0.496842

0.090840

0.005876

0.001525

−0.00015

1.9

PC-A hybrid

3.0

  0

1

1:1

0

0.240477

0.307282

0.167334

−0.11478

0.024511

−0.00168

1.10

FC-S-0 hybrid

3.0

  0

1

1:1

0

0.324959

0.032735

0.428664

−0.22300

0.044585

−0.00300

Multiple barrel experiments

2.1

FC-S-0

3.0

  6

1

1:1

0

0.224471

0.247312

0.186514

−0.11350

0.023189

−0.00151

2.2

FC-S-30

3.0

  6

1

1:1

0

0.148953

0.250437

0.129334

−0.08043

0.016465

−0.00106

2.3

FC-D-0

3.0

  6

2

1:1

0

0.154694

0.436581

−0.03432

−0.01750

0.006033

−0.00044

2.4

FC-D-0-E

3.0

  6

2

1:1

0

0.168455

0.406534

−0.00092

−0.03180

0.008541

−0.00060

2.5

FC-D-30

3.0

  6

2

1:1

0

0.101044

0.419241

−0.05507

−0.00269

0.002885

−0.00023

2.6

FC-D-30-E

3.0

  6

2

1:1

0

0.103678

0.402060

−0.03596

−0.01110

0.004465

−0.00033

2.7

FC-T-0

3.0

  6

3

1:1

0

0.185570

0.425924

−0.01513

−0.02737

0.007816

−0.00055

2.8

FC-T-0-E

3.0

  6

3

1:1

0

0.220522

0.370427

0.057110

−0.06003

0.013803

−0.00093

2.9

FC-T-30

3.0

  6

3

1:1

0

0.132482

0.340923

0.042681

−0.04425

0.010089

−0.00067

2.10

FC-T-30-E

3.0

  6

3

1:1

0

0.146450

0.369886

0.018327

−0.03716

0.009256

−0.00064

2.11

FC-Q-0

3.0

  6

4

1:1

0

0.154223

0.448350

−0.04069

−0.01406

0.005238

−0.00039

2.12

FC-Q-0-E

3.0

  6

4

1:1

0

0.202572

0.369396

0.056302

−0.05916

0.013704

−0.00093

2.13

FC-Q-30

3.0

  6

4

1:1

0

0.108394

0.355482

0.027300

−0.03433

0.007929

−0.00052

2.14

FC-Q-30-E

3.0

  6

4

1:1

0

0.144926

0.350135

0.041407

−0.04611

0.010763

−0.00073

 

Table 18. Inlet control fifth-order polynomial coefficients, all experiments. — Continued

InletModelSlope (percent)Fillet (inches)BarrelsSpan: RiseSkew (degrees)abcdef

2.15

PC-A

3.0

12

1

1:1

   0

0.210576

0.314554

0.101951

−0.07265

0.014939

−0.00095

2.16

PC-B

3.0

12

2

1:1

   0

0.099284

0.607914

−0.22159

0.066777

−0.00985

0.000567

2.17

PC-B-E

3.0

12

2

1:1

   0

0.149381

0.540449

−0.14226

0.029009

−0.00258

0.000099

2.18

PC-C

3.0

12

3

1:1

   0

0.147326

0.545578

−0.14618

0.032208

−0.00349

0.000151

2.19

PC-C-E

3.0

12

3

1:1

   0

0.153250

0.555777

−0.15207

0.035094

−0.00419

0.000219

2.20

PC-D

3.0

12

4

1:1

   0

0.107009

0.600450

−0.20745

0.060926

−0.00892

0.000516

2.21

PC-D-E

3.0

12

4

1:1

   0

0.158898

0.585920

−0.19181

0.048483

−0.00586

0.000294

Span-to-rise experiments

3.1

FC-S-0

3.0

  0

1

1:1

   0

0.211536

0.224341

0.208370

−0.12199

0.024676

−0.00161

3.2

FC-S-0

3.0

  0

1

2:1

   0

0.207152

0.432143

−0.01180

−0.03235

0.009224

−0.00067

3.3

FC-S-0

3.0

  0

1

3:1

   0

0.227185

0.361402

0.077047

−0.06998

0.015731

−0.00106

3.4

FC-S-0

3.0

  0

1

4:1

   0

0.246621

0.315820

0.126140

−0.09144

0.019626

−0.00131

3.5

FC-S-30

3.0

  0

1

1:1

   0

0.163450

0.127103

0.256193

−0.13163

0.025211

−0.00160

3.6

FC-S-30

3.0

  0

1

2:1

   0

0.114704

0.376884

−0.00741

−0.02427

0.006977

−0.00050

3.7

FC-S-30

3.0

  0

1

3:1

   0

0.141479

0.321334

0.064086

−0.05613

0.012732

−0.00086

3.8

FC-S-30

3.0

  0

1

4:1

   0

0.23000

0.117000

0.241000

−0.12600

0.025000

−0.00164

3.9

PC-A

3.0

  0

1

1:1

   0

0.194217

0.310678

0.109365

−0.07741

0.016183

−0.00106

3.10

PC-A

3.0

  0

1

2:1

   0

0.154724

0.592825

−0.19007

0.048610

−0.00636

0.000370

3.11

PC-A

3.0

  0

1

3:1

   0

0.200747

0.424467

0.000339

−0.03291

0.008306

−0.00057

3.12

PC-A

3.0

  0

1

4:1

   0

0.220017

0.404031

0.029449

−0.04658

0.010869

−0.00073

Skewed headwall experiments

4.01

FC-T-0

3.0

 6

3

1:1

   0

0.183389

0.409080

0.005613

−0.03583

0.009284

−0.00065

4.02

FC-T-30

3.0

 6

3

1:1

   0

0.128409

0.355047

0.026694

−0.03750

0.008897

−0.00060

4.03

FC-T-30

3.0

  0

3

1:1

15

0.182031

0.686256

−0.27704

0.082113

−0.01167

0.000654

4.04

FC-T-30

3.0

  0

3

1:1

30

0.225978

0.658427

−0.24032

0.063449

−0.00797

0.000409

4.05

FC-T-30

3.0

  0

3

1:1

45

0.187459

0.743672

−0.32364

0.103601

−0.01612

0.000958

4.06

FC-S-30

3.0

  0

1

3:1

30

0.213123

0.685460

−0.29816

0.088583

−0.01224

0.000663

1 inch = 2.54 cm

Table 19. Outlet control design coefficients, all experiments

InletModelSlope (percent)Fillet (inches)BarrelsSpan: RiseSkew (degrees)Outlet loss Ko unsubmergedOutlet loss KosubmergedEntrance loss KeunsubmergedEntrance loss Kesubmerged
Bevels and fillets experiments
1.1FC-S-03.0011:10NA1.22NA0.45
1.2FC-S-03.0611:10NA1.25NA0.47
1.3FC-S-03.01211:10NA1.17NA0.64
1.4PC-A3.0011:10NA1.22NA0.25
1.5PC-A3.0611:10NA1.18NA0.23
1.6PC-A3.01211:10NA1.19NA0.30
1.7PC-A3.0612:10NA1.25NA0.35
1.8PC-A3.01212:10NA0.98NA0.40
1.1FC-S-00.7011:101.031.170.730.46
1.2FC-S-00.7611:100.871.120.900.50
1.3FC-S-00.71211:101.101.130.900.62
1.4PC-A0.7011:101.071.190.670.27
1.5PC-A0.7611:101.281.300.630.25
1.6PC-A0.71211:101.101.140.560.33
Multiple barrel experiments
2.1FC-S-00.7611:100.871.120.900.50
2.2FC-S-300.7611:101.071.160.710.26
2.3FC-D-00.7621:100.841.070.710.52
2.4FC-D-0-E0.7621:100.861.090.320.53
2.5FC-D-300.7621:100.761.030.740.34
2.6FC-D-30-E0.7621:100.901.090.420.31
2.7FC-T-00.7631:101.000.910.600.54
2.8FC-T-0-E0.7631:100.900.930.800.58
2.9FC-T-300.7631:101.001.050.480.31
2.10FC-T-30-E0.7631:101.091.260.410.32
2.11FC-Q-00.7641:101.231.090.830.52
2.12FC-Q-0-E0.7641:101.081.160.870.50
2.13FC-Q-300.7641:100.861.080.380.32
2.14FC-Q-30-E0.7641:100.891.050.380.34
2.15PC-A0.71211:101.101.140.560.33
2.16PC-B0.71221:100.791.000.960.49
2.17PC-B-E0.71221:100.961.080.750.56
2.18PC-C0.71231:101.011.250.940.54
2.19PC-C-E0.71231:101.211.140.960.51
2.20PC-D0.71241:101.050.980.910.59
2.21PC-D-E0.71241:101.071.050.930.58
Span-to-rise experiments
3.1FC-S-00.7011:101.031.170.730.46
3.2FC-S-00.7012:100.871.020.480.40
3.3FC-S-00.7013:101.201.450.660.32
3.4FC-S-00.7014:101.071.160.620.40
3.5FC-S-300.7011:100.751.120.390.27
3.6FC-S-300.7012:100.971.070.390.22
3.7FC-S-300.7013:101.491.270.480.19
3.8FC-S-300.7014:100.871.140.530.18
3.9PC-A0.7011:101.071.190.670.27
3.10PC-A0.7012:100.921.090.420.34
3.11PC-A0.7013:101.761.520.800.29
3.12PC-A0.7014:100.951.150.690.26
Skewed headwall experiments
4.1FC-T-00.7011:101.311.320.840.39
4.2FC-T-300.7011:100.860.980.470.35
4.3FC-T-300.7011:1150.881.130.860.47
4.4FC-T-300.7011:1300.941.000.430.36
4.5FC-T-300.7011:1450.950.970.850.44
4.6FC-S-300.7011:1300.841.030.900.46
1 inch = 2.54 cm

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). The hydraulics and hydrology research program at the TFHRC Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
FHWA
United States Department of Transportation - Federal Highway Administration