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

Effects of Inlet Geometry on Hydraulic Performance of Box Culverts

CHAPTER 6. EXPERIMENTAL RESULTS

EFFECTS OF BEVELS AND CORNER FILLETS

Miniflume Test Results for Bevel Effects

The small demonstration miniflume was used with PIV to determine the best shape for the top edge from several alternate shapes that were suggested. The goal of the PIV miniflume experiments was to accurately measure the flow field at the vena contracta. Post processing of PIV results provides streamlines that can be visually interpreted to show the shape that produces the maximum effective flow depth at the vena contracta. This shape is likely to have the least headloss when incorporated into the inlet geometry. The effective flow depth at the vena contracta for various bevel edge conditions are shown in figures 37 and 38.

Figure 37. Diagrams. Effective flow depth at vena contracta for nonrounded bevel edges.

a.

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b.

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c.

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d.

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1 inch = 2.54 cm

Figure 38. Diagrams. Effective flow depth at vena contracta for rounded bevel edges.

a.b.
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c.

 
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1 inch = 2.54 cm

For each experiment, headwater and tailwater depths were measured. The difference of these depths versus the vena contracta measurement is plotted on figure 39. The results show that the 20.32-cm- (8-inch-) rounded bevel edge produces the optimal geometric configuration.

Figure 39. Graph. Effective flow depth versus headwater/tailwater difference.

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1 inch = 2.54 cm
1 mm = 0.039 inch

The PIV miniflume tests demonstrated which shape is best, but the question then becomes how much gain does this shape produce in the hydraulic performance? To answer that question, tests were conducted on the effects of bevels and of corner fillets. Sketches and descriptions of the models tested are set forth in figure 40. The results are discussed in the remainder of this section, and selected information is presented in table 1 at the end of the section.

Figure 40. Sketches. Models tested for effects of bevels and corner fillets.

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a. HDS-5 Inlet, Chart 8, Scale 3
0°-flared wingwalls (WW),
square edged at crown,
no WW bevel,
no corner fillets
b. FC-S-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
no corner fillets
c. PC-A
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
no corner fillets
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d. FC-S-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
e. FC-S-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch and 12-inch corner fillets
f. PC-A
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
6-inch and 12-inch corner fillets
1 inch = 2.54 cm

Head Loss Experiments for Bevel Effects

Precast (PC) models, fabricated with the optimum bevel on the top plate and 10.16-cm- (4-inch-) radius rounded bevels on the wingwall edges, and field cast (FC) models, fabricated with the SDDOT standard straight bevel on the top plate and no bevels on the wingwall edges, were tested in the culvert test facility. Additional tests were made with a model of the closest HDS-5 inlet that has 0-degree-flared wingwalls and no bevels on either the top plate or the wingwalls and with a model of an FC 30-degree-flared wingwall culvert. For unsubmerged flow when the top plate is not exposed to the flow, figures 41 and 42 show that the performance curve for the PC model with the optimum top plate bevel and rounded wingwall edges is almost identical to the performance curve for the comparable FC model with 0-degree wingwall flare but with the straight top plate bevel and square edge wingwall edges. That comparison suggests that the 10.16-cm- (4-inch-) radius bevel on the wingwall edges does not contribute much gain. The gain shows up in the submerged condition with approximately 10 percent headwater reduction at the highest discharge intensities. Figure 43 shows that the optimum bevel model is almost as efficient as the 30-degree-flared wingwall at the higher discharge intensities.

The performance curves shown in figures 41 and 42 compare inlets and barrels with the same corner fillets to isolate the effects of the bevels. In South Dakota, the PC culverts are fabricated with 30.48-cm (12-inch) corner fillets and FC culverts are constructed with 15.24-cm (6-inch) corner fillets, but those sizes were varied in this study to make clear comparisons.

Figure 41. Graph. Inlet control performance curves, FC-S-0 versus PC-A, zero corner fillets.

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Figure 42. Graph. Inlet control performance curves, FC-S-0 versus PC-A, 15.24-cm (6-inch) fillets.

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Figure 43. Graph. Inlet control, precast with 15.24-cm (6-inch fillets) and field cast with 15.24-cm (6-inch) fillets.

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Effect of Wingwall Top Edge Bevel

Tests were conducted to isolate the effects of the bevels on the edges of the wingwalls. Earlier comparisons suggested that the wingwall bevels had very little effect, but those comparisons were based on the unsubmerged flow only.

Since the models were precisely fabricated with clip-on components, it was relatively easy to mix and match components to isolate the wingwall bevels. Two special models were tested. One was the FC model top plate with the PC model wingwalls and is labeled "FC-hybrid" in figure 44. The other was the PC top plate with the FC wingwalls and is labeled "PC-hybrid" in figure 45. In both cases, the performance curves for the hybrid models plotted almost identically over the curves for the models with the other wingwalls for both unsubmerged and submerged flow. The slight deviation in figure 45 is on the wrong side to suggest that there is any advantage to rounding the wingwall edges.

Figure 44. Graph. Inlet control, field cast hybrid inlet with 10.16-cm-(4-inch-) radius bevel on wingwalls.

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Figure 45. Graph. Inlet control, precast hybrid inlet with no bevel on wingwalls.

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Effect of Corner Fillets

Corner fillets are fabrication expedients intended to minimize high-stress areas in the corners for rectangular culvert shapes. The PC industry tends to use slightly larger corner fillets than might be used for FC construction. Obviously, the corner fillets reduce flow area slightly, but the issue is what effect they might have on hydraulic performance beyond that reduction in flow area. Varying the corner fillets was one of the most aggravating challenges in the experimental design for this study. Ideally, the experimental coefficients would have been the same for the different fillets provided the correct net area was used in the computations. Then the same corner fillets could have been used for all of the tests and the culvert models would have been much simpler to fabricate.

Even though the net area was used in computations, the entrance loss coefficients for outlet control did vary with the size of the corner fillets. The performance curves for inlet control show no difference using 0-cm (0-inch), 15.24-cm (6-inch), or 30.48-cm (12-inch) corner fillets. Figures 46 and 47 for FC and PC models, respectively, indicate that, for inlet control, there was no headwater increase with fillet size for any given discharge intensity. The entrance loss coefficients for outlet control increased significantly for the 30.48-cm (12-inch) fillets when compared with the 15.24-cm (6-inch) fillets and no fillets.

Figure 46. Graph. Inlet control effects of corner fillets for the field cast model.

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Figure 47. Graph. Inlet control effects of corner fillets for the precast model.

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The likely combinations are probably 30.48-cm (12-inch) fillets with PC culverts and 15.24-cm (6-inch) fillets with FC culverts. Figure 48 compares the PC model with 30.48-cm (12-inch) corner fillets to the FC models with 15.24-cm (6-inch) fillets.

Figure 48. Graph. Inlet control, precast with 30.48-cm (12-inch) fillets and field cast with 15.24-cm (6-inch) fillets.

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The entrance-loss coefficients, Ke, for outlet control, and the regression coefficients for the inlet control results plotted in figures 41 through 48 are summarized in table 1. The outlet control coefficient, Ke, for the PC model with the optimum bevels varied from 0.23 to 0.33; for the FCS- 0 model, it varied from 0.46 to 0.64; and for the FC-S-30 model with 30-degree-flared wingwalls, it was 0.26. Coefficients from different sources for the HDS-5 model are listed for comparison. The HDS-5 model presumably had square edges on the top plate as well as on the wingwalls.

Table 1. Effects of bevels and corner fillets—summary of inlet and outlet control coefficients.
ModelSpan:RiseSlope (percent)Fillets (inches)KeK Form 1 Eq.M Form 1 Eq.K Form 2 Eq.M Form 2 Eq.C Y

FC-S-0

1:1

   0.7

  0

0.46

 

 

 

 

 

 

   0.7

  6

0.50

 

 

 

 

 

 

   0.7

12

0.62

 

 

 

 

 

 

3

  0

0.45

 

 

0.55

0.64

0.0453

0.54

3

  6

0.47

 

 

0.57

0.62

0.0448

0.56

3

12

0.64

 

 

0.58

0.61

0.0447

0.54

PC-A

1:1

   0.7

  0

0.27

 

 

 

 

 

 

   0.7

  6

0.25

 

 

 

 

 

 

   0.7

12

0.33

 

 

 

 

 

 

3

  0

0.25

 

 

0.56

0.63

0.0371

0.67

3

  6

0.23

 

 

0.57

0.62

0.0371

0.67

3

12

0.30

 

 

0.57

0.61

0.0361

0.68

PC-A

2:1

3

  6

0.35

 

 

0.60

0.56

0.0329

0.79

PC-A

2:1

3

12

0.40

 

 

0.60

0.55

0.0316

0.81

FC-S-30

1:1

   0.7

  6

0.26

 

 

 

 

 

 

HDS-5
chart 8
scale 3

 

 

  0

0.70

0.061

0.75

 

 

0.0423

0.82

HDS-5
from Graziano (2001)(3)

1:1

3

  0

0.68

0.009

1.54

0.48

0.73

0.0435

0.62

HDS-5
from this study

1:1

3

  0

 

0.0481

0.76

0.55

0.64

0.0469

0.55

   0.7

  0

0.79

 

 

 

 

 

 

1 inch = 2.54 cm.

Notes: For empty cells, data were not available or not applicable. Eq. is equation. Form 1 and form 2 equations are identified in chapter 3.

EFFECTS OF MULTIPLE BARRELS

Three questions need to be addressed with regard to multiple barrel culverts:

  • Is it reasonable to assume that single barrel coefficients are applicable for multiple barrel culverts?
  • Does the advantage of flared wingwalls diminish as the number of barrels or overall span-to-rise ratio increases? Is it less important to have flared wingwalls as the number of barrels increases?
  • Is there a hydraulic advantage to extending the center walls of a multiple barrel culvert onto the approach apron?

Sketches of all the models tested in this series are illustrated in figure 49.

Figure 49. Sketches. Models tested for effects of multiple barrels

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a. FC-S-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
b. FC-S-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
c. PC-A
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
12-inch corner fillets
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d. FC-D-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
e. FC-D-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
f. PC-B
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
12-inch corner fillets
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g. FC-T-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
h. FC-T-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
i. PC-C
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
12-inch corner fillets
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j. FC-Q-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
k. FC-Q-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
6-inch corner fillets
l. PC-D
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
12-inch corner fillets
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m. FC-D-30-E
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
extended center walls,
6-inch corner fillets
n. FC-D-0-E
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
extended center walls,
6-inch corner fillets
o. PC-B-E
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
extended center walls,
12-inch corner fillets
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p. FC-T-30-E
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
extended center walls,
6-inch corner fillets
q. FC-T-0-E
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
extended center walls,
6-inch corner fillets
r. PC-C-E
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
extended center walls,
12-inch corner fillets
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s. FC-Q-30-E
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
extended center walls,
6-inch corner fillets
t. FC-Q-0-E
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
extended center walls,
6-inch corner fillets
u. PC-D-E
0°-flared wingwalls,
8-inch-radius top bevel,
4-inch-radius WW bevel,
extended center walls,
12-inch corner fillets
1 inch = 2.54 cm

Multiple Barrels Versus Single Barrel

Figures 50 and 51 show that there is almost no difference in the performance of multiple barrels and a single barrel culvert for unsubmerged inlet control. For submerged inlet control, figures 50 and 51 show a slight hydraulic advantage for the multiple barrel field cast models when compared to the single barrel model. Figure 52 indicates a fairly substantial hydraulic advantage for the multiple barrel precast models when compared to the single barrel model for submerged inlet control. Several of the precast models were retested to verify the multiple barrel results.

Figure 50. Graph. Inlet control comparison, field cast 0-degree-flared wingwall models.

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Figure 51. Graph. Inlet control comparison, field cast 30-degree-flared wingwall models.

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Figure 52. Graph. Inlet control comparison, precast models.

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The coefficients derived for the multiple barrel tests (figures 50 to 58) are summarized in table 2. The outlet control results in table 2 were somewhat inconsistent. The Ke values for the field cast models with 0-degree wingwalls were almost identical for the single-barrel, double-barrel, triplebarrel, and quad-barrel models and averaged 0.52. These results support the practice of using the single barrel coefficients for multiple barrel analyses. For the 30-degree-flared wingwall models, the Ke values averaged 0.32 for the multiple barrel models when compared to Ke = 0.26 for the single barrel model. While not a big difference, it was counter to the inlet control indication in that the multiple barrels looked slightly worse than the single barrel for outlet control. For the precast models, the average Ke for the multiple barrel models was 0.54, and the Ke for the single barrel model was 0.33.

Although there are slight differences in single barrel and multiple barrel performance that were worthy of documentation, it is reasonable to combine the double-barrel, triple-barrel, and quadbarrel results.

Table 2. Summary of inlet and outlet control coefficients for models tested for effects of multiple barrels.
ModelSlope (percent)Fillets (inches)KeK Form 2 Eq.M Form 2 Eq.cY

FC-S-0

3

6

 

0.57

0.62

0.0448

0.56

   0.7

6

0.50

 

 

 

 

FC-S-30

3

6

 

0.47

0.68

0.0394

0.53

   0.7

6

0.26

 

 

 

 

FC-D-0

3

6

 

0.55

0.61

0.0391

0.66

   0.7

6

0.52

 

 

 

 

FC-D-0-E

3

6

 

0.55

0.60

0.0394

0.65

   0.7

6

0.53

 

 

 

 

FC-D-30

3

6

 

0.46

0.66

0.0366

0.61

   0.7

6

0.34

 

 

 

 

FC-D-30-E

3

6

 

0.46

0.67

0.0381

0.59

   0.7

6

0.31

 

 

 

 

FC-T-0

3

6

 

0.58

0.58

0.0377

0.69

   0.7

6

0.54

 

 

 

 

FC-T-0-E

3

6

 

0.60

0.57

0.0405

0.67

   0.7

6

0.58

 

 

 

 

FC-T-30

3

6

 

0.48

0.67

0.0379

0.60

   0.7

6

0.31

 

 

 

 

FC-T-30-E

3

6

 

0.51

0.64

0.0405

0.60

   0.7

6

0.32

 

 

 

 

FC-Q-0

3

  6

 

0.55

0.61

0.0377

0.71

   0.7

  6

0.52

 

 

 

 

FC-Q-0-E

3

  6

 

0.58

0.59

0.0418

0.64

   0.7

  6

0.50

 

 

 

 

FC-Q-30

3

  6

 

0.47

0.71

0.0372

0.64

   0.7

  6

0.32

 

 

 

 

FC-Q-30-E

3

  6

 

0.50

0.65

0.0398

0.60

   0.7

  6

0.34

 

 

 

 

PC-A

3

12

 

0.57

0.61

0.0361

0.68

   0.7

12

0.33

 

 

 

 

PC-B

3

12

 

0.54

0.60

0.0253

0.90

   0.7

12

0.49

 

 

 

 

PC-B-E

3

12

 

0.57

0.58

0.0315

0.81

   0.7

12

0.56

 

 

 

 

PC-C

3

12

 

0.57

0.57

0.0219

0.98

   0.7

12

0.54

 

 

 

 

PC-C-E

3

12

 

0.59

0.58

0.0263

0.91

   0.7

12

0.51

 

 

 

 

PC-D

3

12

 

0.55

0.61

0.0250

0.92

   0.7

12

0.59

 

 

 

 

PC-D-E

3

12

 

0.60

0.54

0.0296

0.85

   0.7

12

0.58

 

 

 

 

1 inch = 2.54 cm

Notes: For empty cells, data are not available or not applicable. Eq. is equation. The form 2 equation is identified in chapter 3.

Effect of Wingwall-Flare Angle

As the number of barrels increases, a smaller percentage of flow is influenced by the wingwalls, with less advantage to having flared wingwalls. To visualize the effect, observe the space (Δ) between the 30-degree- and the 0-degree-flared wingwall performance curves in figures 53–56. Although the gap never closes, the curves become closer as the number of barrels increases. Interestingly, the PC multiple barrel models with the optimum curved top plates outperformed the 30-degree-flared wingwall multiple barrel models at headwater to culvert depth ratios greater than 1.5. It is reasonable to expect that the optimum top plate bevel will have a more pronounced effect on performance at the high headwater depths as the number of barrels and total span increase.

Figure 53. Graph. Inlet control comparison, single-barrel models.

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Figure 54. Graph. Inlet control comparison, double-barrel models.

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Figure 55. Graph. Inlet control comparison, triple-barrel models.

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Figure 56. Graph. Inlet control comparison, quadruple-barrel models.

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Effect of Center Wall Extension

There is no hydraulic advantage or disadvantage to extending center walls for multiple barrel culverts. Figure 57 is typical of all results for the field cast model in that, for the inlet control tests, the performance for the extended center walls matched the performance for the nonextended center walls. Field cast inlets show nearly the same performance with or without center wall extensions. Figure 58 shows a similar comparison for the precast models with and without extended center walls. The data point for the highest discharge intensity for the PC-B model was omitted from the trend line in figure 58 because it was considered an outlier point.

For outlet control, the Ke values tabulated in table 2 are almost identical in every case for the extended center walls and the corresponding nonextended center walls, including the case of precast models.

Figure 57. Graph. Inlet control comparison, extended or nonextended center walls, field cast model.

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Figure 58. Graph. Inlet control comparison, extended or nonextended center walls, precast model.

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EFFECTS OF SPAN-TO-RISE RATIO

Models tested concerning the span-to-rise ratio are illustrated in figure 59.

Multiple Span-to-Rise Versus Basic 1:1 Span-to-Rise

For inlet control in field cast models with 0-degree wingwalls (FC-S-0), figure 60 shows that a very slight loss in performance might occur as the span-to-rise ratio increases for unsubmerged flow but almost no effect for submerged flow. Figure 61 shows similar results for the precast models. Figure 62 shows a discernable decrease in performance in the submerged flow zone as the span-to-rise ratio increases for the field cast models with 30-degree-flared wingwalls (FC-S-30). This decrease in performance can be attributed in part to the diminishing effects of the wingwall flare angle with increasing span-to-rise, as discussed shortly. Table 3 at the end of this section also contains data on inlet control.

Figure 59. Sketches. Models tested for effects of span-to-rise ratio.

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a. FC-S-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 1:1,
no corner fillets
e. FC-S-0
0-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 1:1,
no corner fillets
i. PC-A
0°-flared wingwalls,
8-inch-straight top bevel,
4-inch-radius WW bevel,
span-to-rise 1:1,
no corner fillets
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b. FC-S-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 2:1,
no corner fillets
f. FC-S-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 2:1,
no corner fillets
j. PC-A
0°-flared wingwalls,
8-inch-straight top bevel,
4-inch-radius WW bevel,
span-to-rise 2:1,
no corner fillets
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c. FC-S-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 3:1,
no corner fillets
g. FC-S-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 3:1,
no corner fillets
k. PC-A
0°-flared wingwalls,
8-inch-straight top bevel,
4-inch-radius WW bevel,
span-to-rise 3:1,
no corner fillets
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d. FC-S-30
30°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 4:1,
no corner fillets
h. FC-S-0
0°-flared wingwalls,
4-inch-straight top bevel,
no WW bevel,
span-to-rise 4:1,
no corner fillets
l. PC-A
0°-flared wingwalls,
8-inch-straight top bevel,
4-inch-radius WW bevel,
span-to-rise 4:1,
no corner fillets
1 inch = 2.54 cm

Figure 60. Graph. Inlet control comparison, FC-S-0 span-to-rise ratios.

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Figure 61. Graph. Inlet control comparison, PC-A span-to-rise ratios.

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Figure 62. Graph. Inlet control comparison, FC-S-30 span-to-rise ratios.

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For outlet control, the entrance loss coefficient Ke for the FC-S-0 models varied from 0.32 for the 3:1 span-to-rise ratio to 0.46 for the 1:1 ratio (table 3 at the end of this section), but there was no clear trend, and the variation can be attributed to experimental scatter. Similarly, for the PC-A models, the entrance loss coefficient Ke varied from 0.26 for the 4:1 span-to-rise ratio to 0.34 for the 2:1 ratio; again, there was no clear trend. There was a slight trend in the entrance loss coefficients for the FC-S-30 models in that Ke was 0.27 for the 1:1 and 2:1 span-to-rise ratios and was 0.19 and 0.18 for the 3:1 and 4:1 ratios, respectively. The trend was just the opposite from the effect observed for the inlet control tests. One may draw from the outlet control results the reasonable conclusions that the variations represent experimental scatter and that the basic 1:1 model entrance loss coefficients can be applied for various span-to-rise ratios.

Wingwall Flare and the Span-to-Rise Ratio

Figures 63–66 show that the wingwall flare angle has a diminishing effect as the span-to-rise ratio increases, which is analogous to the multiple barrel phenomenon. This observation can be visualized by inspecting the spacing, labeled as (Δ) in these figures, between the 0-degree-flared wingwall curves and the 30-degree-flared wingwall curves. As the span-to-rise and headwater depth ratios increase, the effect of the top plate bevel increases and the effect of the wingwall flare angle decreases, which explains why the PC models slightly outperformed the 30-degreeflared wingwall models for a few situations. This was similar to, but less pronounced than in, the case of the multiple barrel comparison.

The outlet control entrance loss coefficients listed in table 3 for the FC-S-30 models did not, however, support the assumption that the wingwall flare angle has a diminishing effect as the span-to-rise ratio increases. The outlet control loss coefficient Ke was 0.27 for the basic 1:1 span-to-rise ratio, but decreased to 0.18 for the 4:1 ratio.

Figure 63. Graph. Inlet control comparison, 1:1 span-to-rise ratio.

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Figure 64. Graph. Inlet control comparison, 2:1 span-to-rise ratio.

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Figure 65. Graph. Inlet control comparison, 3:1 span-to-rise ratio.

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Figure 66. Graph. Inlet control comparison, 4:1 span-to-rise ratio.

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Table 3. Summary of inlet and outlet control coefficients for models tested for effects of span-to-rise ratio.
ModelSpan:RiseSlope (percent)Fillets (inches)KeK Form 2 Eq.M Form 2 Eq.cY

FC-S-0

1:1

3

0

 

0.55

0.64

0.0453

0.54

   0.7

0

0.46

 

 

 

 

2:1

3

0

 

0.60

0.56

0.0404

0.68

   0.7

0

0.40

 

 

 

 

3:1

3

0

 

0.61

0.58

0.0413

0.67

   0.7

0

0.32

 

 

 

 

4:1

3

0

 

0.62

0.57

0.0421

0.65

   0.7

0

0.40

 

 

 

 

FC-S-30

1:1

3

0

 

0.44

0.74

0.0403

0.48

   0.7

0

0.27

 

 

 

 

2:1

3

0

 

0.47

0.66

0.0397

0.56

   0.7

0

0.22

 

 

 

 

3:1

3

0

 

0.48

0.66

0.0414

0.54

   0.7

0

0.19

 

 

 

 

4:1

3

0

 

0.50

0.63

0.0410

0.59

   0.7

0

0.18

 

 

 

 

PC-A

1:1

3

0

 

0.56

0.62

0.0371

0.66

   0.7

0

0.27

 

 

 

 

2:1

3

0

 

0.60

0.56

0.0329

0.79

   0.7

0

0.34

 

 

 

 

3:1

3

0

 

0.60

0.58

0.0331

0.79

   0.7

0

0.29

 

 

 

 

4:1

3

0

 

0.62

0.57

0.0340

0.79

   0.7

0

0.26

 

 

 

 

1 inch = 2.54 cm

Notes: For empty cells, data are not available or not applicable. Eq. is equation. The form 2 equation is identified in chapter 3.

EFFECTS OF HEADWALL SKEW

Skewed headwalls as illustrated in figure 67 were tested for skew angles of 0, 15, 30, and 45 degrees. Although it is not uncommon to see culvert installations with the approach flow actually skewed to the culvert alignment, this condition is considered bad practice and was not included in the test matrix.

Figure 67. Sketch. Definition sketch for skew tests.

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The field cast triple-barrel 30-degree-flared wingwalls model (FC-T-30) and the field cast singlebarrel 30-degree-flared wingwalls model with a 3:1 span-to-rise ratio (FC-S-30 (3:1)) illustrated in figure 684 were used for these tests.

Figure 68. Sketches. Models tested for effects of headwall skew.

View Alternate Text
View Alternate Text
View Alternate Text
View Alternate Text
a. FC-T-30
30°-flared wingwalls,
4-inch-straight top
bevel, no wingwall
bevel, 0° skew,
no corner fillets
b. FC-T-30
30°-flared wingwalls,
4-inch-straight top bevel,
no wingwall bevel,
15° skew,
no corner fillets
c. FC-T-30
30°-flared wingwalls,
4-inch-straight top
bevel, no wingwall
bevel, 30° skew,
no corner fillets
d. FC-T-30
30°-flared wingwalls,
4-inch-straight top
bevel, no wingwall
bevel, 45° skew,
no corner fillets
View Alternate Text
View Alternate Text
e. FC-S-30
30°-flared wingwalls, 4-inch-straight top bevel,
no wingwall bevel,
3:1 span-to-rise,
0° skew,
no corner fillets
f. FC-S-30
30°-flared wingwalls, 4-inch-straight top bevel,
no wingwall bevel,
3:1 span-to-rise,
30° skew,
no corner fillets

Figure 69 is the plan view of the skewed inlets tested.

Figure 69. Diagrams. Plan view of skewed headwall models tested.

View Alternate Text
View Alternate Text
a. FC-T-30, 0-degree skewb. FC-T-30, 15-degree skew
View Alternate Text
View Alternate Text
c. FC-T-30, 30-degree skewd. FC-T-30, 45-degree skew

For inlet control, figure 70 shows that the performance curves for the three skewed headwalls (at 15, 30, and 45 degrees) do cluster but are separated from the performance curve for the 0-degree headwall. Consequently, it is reasonable to combine the 15-degree, 30-degree, and 45-degree skew curves for inlet control. The performance curve for the HDS-5, chart 12, scale 3, inlet, which was noted in that publication to be a good approximation for skews from 15 degrees to 45 degrees, is plotted in this figure for comparison, but it does not compare favorably with the skewed headwall models tested in this study. HDS-5 does not specify if that inlet represents a skewed headwall or a skewed flow alignment.

The outlet control entrance loss coefficient Ke could be averaged at 0.36 for 0-degree and 15- degree skew angles, but increased to 0.46 for 30-degree and 45-degree skew angles. Table 4 summarizes the inlet and outlet control coefficients.

Figure 70. Graph. Inlet control comparison, skew angles.

View Alternate Text

Table 4. Summary of inlet and outlet control coefficients for models tested for effects of headwall skew.
ModelSpan:Rise Skew Slope (percent) Fillets (inches) Ke K Form 2 Eq. M Form 2 Eq. c Y

FC-S-30

3:1

3

0

 

0.48

0.66

0.0414

0.54

   0.7

0

0.19

 

 

 

 

30°

3

0

 

0.68

0.46

0.0306

0.89

   0.7

0

0.39

 

 

 

 

FC-T-30

3:1

3

0

 

0.48

0.67

0.0369

0.62

   0.7

0

0.35

 

 

 

 

15°

3

0

 

0.66

0.50

0.0289

0.95

   0.7

0

0.36

 

 

 

 

30°

3

0

 

0.70

0.48

0.0312

0.94

   0.7

0

0.44

 

 

 

 

45°

3

0

 

0.69

0.50

0.0224

1.10

   0.7

0

0.46

 

 

 

 

1 inch = 2.54 cm

Notes: For empty cells, data are not available or not applicable. Eq. is equation. The form 2 equation is identified in chapter 3.

OUTLET CONTROL ENTRANCE LOSS COEFFICIENTS Ke FOR LOW FLOWS (UNSUBMERGED CONDITIONS)

In culvert design, outlet control is typically associated with full or nearly full barrel flow. Outlet control can occur, however, for partly full flow if the culvert barrel slope is flat enough. This condition is often encountered when environmental considerations, such as allowing the passage of fish, mandate a flatter slope. Outlet control loss coefficients are usually tabulated as constants for inlet types. Whereas some experimental scatter is expected, the scatter in the loss coefficients for unsubmerged flow in this study was so extreme that researchers decided to separate the unsubmerged data from the submerged data for the outlet control experiments. The unsubmerged loss coefficients are not considered reliable for implementation, but the results and attempted analyses are useful for future research.

Table 5 summarizes the average entrance loss coefficients for unsubmerged flow conditions. Not all the data points could be used to derive the average coefficients because some of the values were so far out of range that they were discounted during the data reduction phase of the study. The worst values seemed to occur at the lowest flows, and the problem was attributed to the resolution limits of the pressure sensors. The accuracy of the current pressure transducer used is ± 5 mm (0.196 inch). At the very low flows, the actual head losses measured were less than the resolution of the pressure sensor. These measurements, which were mostly "noise" in the sensors, were divided by a velocity head, which was near zero, to compute the entrance loss coefficients, which were often an order of magnitude larger than expected. In general, the average entrance loss coefficients for unsubmerged conditions tended to be higher than the coefficients for submerged conditions. It was difficult, however, to determine if this tendency was real or just a result of the selection process on which values to include in the average.

Effects of Reynolds Number on Ke

One hypothesis considered as a possible explanation for the large scatter in the entrance loss coefficient at low flows was that Ke depended on the Reynolds number. If that hypothesis were true, there should be a correlation between Ke and the Reynolds number regardless of whether the culvert were submerged.

The Reynolds number hypothesis was tested using full barrel flow with the HDS-5, chart 8, scale 3, inlet because it was easier to control Reynolds numbers for full barrel flow than for free surface flow. Data was acquired with the Reynolds number held constant while the headwater depth ratio (HW/D) was varied. This process was repeated for a range of Reynolds numbers up to the maximum Reynolds number that could be accomplished with the experimental apparatus.

The Reynolds number is defined as a characteristic velocity times a characteristic length divided by the kinematic viscosity. The hydraulic radius times four was used as the characteristic diameter. Only submerged conditions were tested, so the characteristic length was the barrel diameter, D. The average flow velocity was calculated by dividing the discharge by the area of the barrel. The entrance loss coefficients for the HDS-5, chart 8, scale 3, inlet for Reynolds numbers ranging from 65000 to 260000 are presented in figure 71.

Table 5. Summary of outlet control entrance loss coefficients, Ke, for low flows.
Model Slope (percent) Fillets (inches) Number of Barrels Span:Rise Skew Unsubmerged Ke*

FC-S-0

0.7

  0

1

1:1

  0.73

FC-S-0

0.7

  6

1

1:1

  0.90

FC-S-0

0.7

12

1

1:1

0.9

PC-A

0.7

  0

1

1:1

  0.67

PC-A

0.7

  6

1

1:1

  0.63

PC-A

0.7

12

1

1:1

  0.56

FC-S-30

0.7

  0

1

1:1

  0.39

FC-S-30

0.7

  6

1

1:1

  0.71

FC-S-0

0.7

  6

1

1:1

0.9

FC-S-30

0.7

  6

1

1:1

  0.71

FC-D-0

0.7

  6

2

1:1

  0.71

FC-D-0-E

0.7

  6

2

1:1

  0.32

FC-D-30

0.7

 6

2

1:1

  0.74

FC-D-30-E

0.7

  6

2

1:1

  0.42

FC-T-0

0.7

  6

3

1:1

0.6

FC-T-0-E

0.7

  6

3

1:1

0.8

FC-T-30

0.7

  6

3

1:1

  0.48

FC-T-30-E

0.7

  6

3

1:1

  0.41

FC-Q-0

0.7

  6

4

1:1

  0.83

FC-Q-0-E

3.0

  6

4

1:1

  0.87

FC-Q-30

0.7

  6

4

1:1

  0.38

FC-Q-30-E

0.7

  6

4

1:1

  0.38

PC-A

0.7

12

1

1:1

  0.56

PC-B

0.7

12

2

1:1

  0.96

PC-B-E

0.7

12

2

1:1

  0.75

PC-C

0.7

12

3

1:1

  0.94

PC-C-E

0.7

12

3

1:1

  0.96

PC-D

0.7

12

4

1:1

  0.91

PC-D-E

0.7

12

4

1:1

  0.93

FC-S-0

0.7

  0

1

1:1

  0.73

FC-S-0

0.7

  0

1

2:1

  0.48

FC-S-0

0.7

  0

1

3:1

  0.66

FC-S-0

0.7

  0

1

4:1

  0.62

FC-S-30

0.7

  0

1

1:1

  0.17

FC-S-30

0.7

  0

1

2:1

  0.39

FC-S-30

0.7

  0

1

3:1

  0.48

FC-S-30

0.7

  0

1

4:1

  0.53

PC-A

0.7

  0

1

1:1

  0.67

PC-A

0.7

  0

1

2:1

  0.42

* These values are not to be used because of the resolution limits of the pressure transducers. 1 inch = 2.54 cm

Figure 71. Graph. Entrance loss coefficient versus the Reynolds number, HDS-5 8/3.

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The computed entrance loss coefficients scattered between 0.6 and 0.95 for low Reynolds numbers, and the scatter generally decreased with increasing Reynolds numbers, but there was no correlation between Ke and the Reynolds number. Figure 72 shows that the standard deviation of the Ke data gradually decreased with an increasing Reynolds number. This figure is included to demonstrate statistically that, although there is a wide spread in Ke around the 162,000 Reynolds number, the scatter in Ke values decreased as the Reynolds number increased.

Figure 72. Graph. Standard deviation of Ke versus the Reynolds number.

View Alternate Text

Based on difficulties measuring low flow depths accurately, the FHWA Hydraulics Laboratory is developing an optical pressure measurement (OPM) system, which is expected to have a much higher resolution (± 0.1 mm) (±0.039 inch). The OPM system will use an array of standpipes mounted along a culvert barrel. Each standpipe has contact image sensors attached, which will measure the water column using imaging techniques. This new sensor was not available for this study but will be used in future research after it has been tested and calibrated.

Another potential concept for determining entrance loss coefficients for low flows is to relate them to a contraction coefficient. The form loss, or head loss HLe or contraction loss HLc, because of contraction is primarily caused by the reexpansion of the flow following contraction and can therefore be calculated approximately by using areas A and Ac, illustrated in figure 73, and the expansion loss equation (figure 74).

Figure 73. Diagram. Culvert contraction.

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By considering the flow expansion from the contracted section, area Ac, to the normal section, area A, the head loss or contraction loss is given by the equation in figure 74.

Figure 74. Equation. Expansion loss equation.

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The contraction coefficient Cc is equal to Ac / A, and depends on the area ratio A / Aa, the nature of the contraction or inlet geometry, and slightly on the Reynolds number. To quantify the contracted area, detailed velocity profiles can be measured in the contraction zone using either PIV or laser doppler anemometry (LDA). Based on the measured velocity vector fields, streamlines can be integrated to compute the contracted area.

Neither of the latter two concepts has yet been tried because they were beyond the scope of this study, but they have promise.

OUTLET CONTROL EXIT LOSS COEFFICIENTS Ko

The exit loss is a function of the change in velocity at the outlet of the culvert barrel. Figure 75 contains the equation, from HDS-5, for the exit loss for a sudden expansion, as at an end wall.

Figure 75. Equation. Exit loss, with coefficient of 1.

View Alternate Text

The channel velocity downstream of the culvert is Vd. The mean flow is V. HDS-5 states that the coefficient 1 may overestimate exit loss and a multiplier less then one can be used. If the downstream velocity is neglected, the exit loss is assumed to be the full-flow velocity head in the barrel.

Outlet loss data was analyzed by averaging the pressure tap measurements for the five pressure taps located downstream of the culvert outlet, as illustrated in figures 78, 79, and 80, to determine the average HGL in the tailbox. The downstream velocity was computed from the equation in figure 76. The area of flow was assumed to be the full width of the tailbox multiplied by the average tailwater depth at the five pressure taps.

Figure 76. Equation. Downstream velocity.

View Alternate Text
Where: 
  
Qis discharge.
WTBis the full width of the tailbox.
TWis the average tailwater depth at the five pressure taps.

The velocity head Vd2/2g was added to the HGL elevation to establish an average downstream EGL elevation, which was subtracted from the EGL at the end of the culvert to determine the head loss at the outlet, HLo. The exit loss coefficient, Ko, was then computed from the equation in figure 77.

Figure 77. Equation. Exit loss, with coefficient Ko.

View Alternate Text

The difficulty with this procedure is that the downstream velocity, and therefore the computed coefficient, is a function of the laboratory dimensions of the tailbox. The downstream velocity was artificially low because the assumed flow area included a significant dead zone on each side of the culvert. That explains why some of the Ko values in table 6 are actually greater than 1.0.

In an effort to develop a more rational procedure for simulating downstream computation from a laboratory experimental setup, the velocity distributions in the tailbox were measured for a several experiments. The goal was to analyze how velocity profiles expand when moving further downstream and how the downstream velocity affects the exit loss. It would be reasonable to use the effective velocities in the expansion zone, illustrated in figures 78, 79, and 80, at each of the pressure taps to determine EGL. EGL could then be projected to the plane of the culvert outlet to determine the exit head loss, HLo, as illustrated in figure 80. The effective velocities vary with the distance downstream of the culvert; the challenge is in deciding what velocity to use in the equation in figure 77 to compute Ko. An arbitrary, but reasonable, selection could be the velocity at three culvert widths downstream of the outlet.

Although this alternative procedure was not used in this study to compute the exit loss coefficients, the measurements in the expansion zone provide good insight about flow downstream of culvert outlets.

Figure 78. Diagram. Flow expansion in the tailbox for high tailwater.

View Alternate Text

Figure 79. Diagram. Flow expansion in the tailbox for low tailwater.

View Alternate Text
1cm/s = 0.033 ft/s

Figure 80. Diagram. Vertical flow expansion in the tailbox and projected EGL.

View Alternate Text
Note: Vertical to horizontal scale is exaggerated by approximately 2:1.

The energy exit loss coefficients Ko are summarized in table 6 for different culvert barrel configurations. Each Ko value listed in table 6 is an average of several inlet geometries that had the same barrel configuration because, in the opinion of the researchers, the exit loss should not be significantly influenced by the inlet geometry.

Table 6. Summary of outlet loss coefficients.
Culvert barrel configurationKo unsubmerged*Ko submerged
a.View Alternate Text0.73 1.12
b.View Alternate Text1.00 1.11
c.View Alternate Text0.89 0.96
d.View Alternate Text0.94 1.08
e.View Alternate Text1.07 1.19
f.View Alternate Text1.04 1.03
g.View Alternate Text0.66 0.97
h.View Alternate Text1.28 1.35
i.View Alternate Text0.85 1.11
j.View Alternate TextSkew 0.86 0.99
k.View Alternate TextSkew 1.10 1.26
* These values are not to be used because of the resolution limits of the pressure transducers.

FIFTH-ORDER POLYNOMIALS

In the area between submerged and unsubmerged flow conditions, a transition area exists for which neither the submerged nor the unsubmerged forms of the equations provide accurate headwater predictions. An example of this transition area can be seen in figure 81. Fifth-order polynomial equations were developed that predict headwater in this region of uncertainty and over the entire range of measured HW/D ratios.

Figure 81. Graph. Transition area, unsubmerged and submerged inlet flow conditions.

View Alternate Text

For culvert discharges within the range of the regression analysis, the polynomial equation gives a direct solution for inlet headwater, regardless of whether the inlet is submerged:

Figure 82. Equation. Transition area, unsubmerged and submerged inlet flow conditions.

View Alternate Text
Where: 
  
a to fare polynomial regression design coefficients.

The polynomial regression coefficients are presented in tables 7 to 10. Application of the polynomial equations presents numerical difficulties and errors at low and high values of HW/D. At low values, the HW/D prediction approaches the intercept coefficient, a, instead of zero, as it should. At high values of HW/D, greater than about 2.3, the equations have a maximum. Therefore, the useful operating range of the polynomial equations is approximately 0.4 < HW/D < 2.3.

Table 7. Polynomial regression coefficients, models tested for bevels and corner fillets.
Model Fillet (inches) Span:Riseabcdef

FC-S-0

  0

1:1

0.211536

0.224341

0.208370

−0.121994

0.024676

−0.001609

FC-S-0

  6

1:1

0.224471

0.247312

0.186514

−0.113509

0.023189

−0.001514

FC-S-0

12

1:1

0.245464

0.218175

0.210202

−0.121260

0.024063

−0.001536

PC-A

  0

1:1

0.194217

0.310678

0.109365

−0.077409

0.016183

−0.001059

PC-A

  6

1:1

0.203074

0.313529

0.107677

−0.076856

0.016046

−0.001046

PC-A

12

1:1

0.210576

0.314554

0.101951

−0.072650

0.014939

−0.000956

PC-A

  6

2:1

0.186778

0.482282

−0.070441

−0.003094

0.003186

−0.000258

PC-A

12

2:1

0.189232

0.496842

−0.090840

0.005876

0.001525

−0.000152

1 inch = 2.54 cm

Table 8. Polynomial regression coefficients, models tested for span-to-rise ratio.
Model Fillet (inches) Span:Riseabcdef

FC-S-0

0

1:1

0.211536

0.224341

0.208370

−0.121994

0.024676

−0.001609

FC-S-0

0

2:1

0.207152

0.432143

−0.011800

−0.032349

0.009224

−0.000668

FC-S-0

0

3:1

0.227185

0.361402

0.077047

−0.069984

0.015731

−0.001063

FC-S-0

0

4:1

0.246621

0.315820

0.126140

−0.091438

0.019626

−0.001311

FC-S-30

0

1:1

0.163450

0.127103

0.256193

−0.131631

0.025211

−0.001601

FC-S-30

0

2:1

0.114704

0.376884

−0.007409

−0.024267

0.006977

−0.000502

FC-S-30

0

3:1

0.141479

0.321334

0.064086

−0.056126

0.012732

−0.000862

FC-S-30

0

4:1

0.230000

0.117000

0.241000

−0.126000

0.025000

−0.001640

PC-A

0

1:1

0.194217

0.310678

0.109365

−0.077409

0.016183

−0.001059

PC-A

0

2:1

0.154724

0.592825

−0.190065

0.048610

−0.006357

0.000370

PC-A

0

3:1

0.200747

0.424467

0.000339

−0.032906

0.008306

−0.000569

PC-A

0

4:1

0.220017

0.404031

0.029449

−0.046577

0.010869

−0.000734

1 inch = 2.54 cm

Table 9. Polynomial regression coefficients, models tested for multiple barrels.
Model Fillet (inches) No. of Barrels a b c d e f

FC-S-0

  6

1

0.224471

0.247312

0.186514

−0.113509

0.023189

−0.001514

FC-S-30

  6

1

0.148953

0.250437

0.129334

−0.080435

0.016465

−0.001069

FC-D-0

  6

2

0.154694

0.436581

−0.034324

−0.017500

0.006033

−0.000449

FC-D-0-E

  6

2

0.168455

0.406534

−0.000921

−0.031807

0.008541

−0.000602

FC-D-30

  6

2

0.101044

0.419241

−0.055078

−0.002691

0.002885

−0.000237

FC-D-30-E

  6

2

0.103678

0.402060

−0.035969

−0.011102

0.004465

−0.000338

FC-T-0

  6

3

0.185570

0.425924

−0.015139

−0.027376

0.007816

−0.000559

FC-T-0-E

  6

3

0.220522

0.370427

0.057110

−0.060032

0.013803

−0.000936

FC-T-30

  6

3

0.132482

0.340923

0.042681

−0.044257

0.010089

−0.000674

FC-T-30-E

  6

3

0.146450

0.369886

0.018327

−0.037160

0.009256

−0.000639

FC-Q-0

  6

4

0.154223

0.448350

−0.040698

−0.014061

0.005238

−0.000392

FC-Q-0-E

  6

4

0.202572

0.369396

0.056302

−0.059162

0.013704

−0.000934

FC-Q-30

  6

4

0.108394

0.355482

0.027300

−0.034330

0.007929

−0.000526

FC-Q-30-E

  6

4

0.144926

0.350135

0.041407

−0.046111

0.010763

−0.000730

PC-A

12

1

0.210576

0.314554

0.101951

−0.072650

0.014939

−0.000956

PC-B

12

2

0.099284

0.607914

−0.221590

0.066777

−0.009847

0.000567

PC-B-E

12

2

0.149381

0.540449

−0.142259

0.029009

−0.002577

0.000099

PC-C

12

3

0.147326

0.545578

−0.146179

0.032208

−0.003485

0.000151

PC-C-E

12

3

0.153250

0.555777

−0.152070

0.035094

−0.004187

0.000219

PC-D

12

4

0.107009

0.600450

−0.207455

0.060926

−0.008924

0.000516

PC-D-E

12

4

0.158898

0.585920

−0.191810

0.048483

−0.005859

0.000294

1 inch = 2.54 cm

 

Table 10. Polynomial regression coefficients, models tested for skewed headwall.
Model Fillet (inches) Skew Angle (degrees) a b c d e f

FC-S-30

0

30

0.213123

0.685460

−0.298162

0.088583

−0.012236

0.000663

FC-T-30

0

  0

0.128409

0.355047

0.026694

−0.037498

0.008897

−0.000603

FC-T-0

0

  0

0.183389

0.409080

0.005613

−0.035825

0.009284

−0.000650

FC-T-30

0

15

0.182031

0.686256

−0.277043

0.082113

−0.011673

0.000654

FC-T-30

0

30

0.225978

0.658427

−0.240324

0.063449

−0.007969

0.000409

FC-T-30

0

45

0.187459

0.743672

−0.323642

0.103601

−0.016120

0.000958

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.
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United States Department of Transportation - Federal Highway Administration