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.  b. 
c.  d. 
1 inch = 2.54 cm 
Figure 38. Diagrams. Effective flow depth at vena contracta for rounded bevel edges.
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 20.32cm (8inch) rounded bevel edge produces the optimal geometric configuration.
Figure 39. Graph. Effective flow depth versus headwater/tailwater difference.
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.
  
a. HDS5 Inlet, Chart 8, Scale 3 0°flared wingwalls (WW), square edged at crown, no WW bevel, no corner fillets  b. FCS0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, no corner fillets  c. PCA 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, no corner fillets 
  
d. FCS30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  e. FCS0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch and 12inch corner fillets  f. PCA 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, 6inch and 12inch corner fillets 
Head Loss Experiments for Bevel Effects
Precast (PC) models, fabricated with the optimum bevel on the top plate and 10.16cm (4inch) 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 HDS5 inlet that has 0degreeflared wingwalls and no bevels on either the top plate or the wingwalls and with a model of an FC 30degreeflared 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 0degree wingwall flare but with the straight top plate bevel and square edge wingwall edges. That comparison suggests that the 10.16cm (4inch) 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 30degreeflared 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 30.48cm (12inch) corner fillets and FC culverts are constructed with 15.24cm (6inch) corner fillets, but those sizes were varied in this study to make clear comparisons.
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.
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 clipon 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 "FChybrid" in figure 44. The other was the PC top plate with the FC wingwalls and is labeled "PChybrid" 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 10.16cm(4inch) radius bevel on wingwalls.
Figure 45. Graph. Inlet control, precast hybrid inlet with no bevel on wingwalls.
Effect of Corner Fillets
Corner fillets are fabrication expedients intended to minimize highstress 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 0cm (0inch), 15.24cm (6inch), or 30.48cm (12inch) 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 30.48cm (12inch) fillets when compared with the 15.24cm (6inch) fillets and no fillets.
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.
The likely combinations are probably 30.48cm (12inch) fillets with PC culverts and 15.24cm (6inch) fillets with FC culverts. Figure 48 compares the PC model with 30.48cm (12inch) corner fillets to the FC models with 15.24cm (6inch) fillets.
Figure 48. Graph. Inlet control, precast with 30.48cm (12inch) fillets and field cast with 15.24cm (6inch) fillets.
The entranceloss coefficients, K_{e}, 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, K_{e}, 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 FCS30 model with 30degreeflared wingwalls, it was 0.26. Coefficients from different sources for the HDS5 model are listed for comparison. The HDS5 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.
Model  Span:Rise  Slope (percent)  Fillets (inches)  K_{e}  K Form 1 Eq.  M Form 1 Eq.  K Form 2 Eq.  M Form 2 Eq.  C  Y 
FCS0 
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 
PCA 
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 
PCA 
2:1 
3 
6 
0.35 


0.60 
0.56 
0.0329 
0.79 
PCA 
2:1 
3 
12 
0.40 


0.60 
0.55 
0.0316 
0.81 
FCS30 
1:1 
0.7 
6 
0.26 






HDS5
chart 8
scale 3 


0 
0.70 
0.061 
0.75 


0.0423 
0.82 
HDS5
from Graziano (2001)(3) 
1:1 
3 
0 
0.68 
0.009 
1.54 
0.48 
0.73 
0.0435 
0.62 
HDS5
from this study 
1:1 
3 
0 

0.0481 
0.76 
0.55 
0.64 
0.0469 
0.55 
0.7 
0 
0.79 






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 spantorise 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
  
a. FCS30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  b. FCS0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  c. PCA 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, 12inch corner fillets 
  
d. FCD30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  e. FCD0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  f. PCB 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, 12inch corner fillets 
  
g. FCT30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  h. FCT0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  i. PCC 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, 12inch corner fillets 
  
j. FCQ30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  k. FCQ0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, 6inch corner fillets  l. PCD 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, 12inch corner fillets 
  
m. FCD30E 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, extended center walls, 6inch corner fillets  n. FCD0E 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, extended center walls, 6inch corner fillets  o. PCBE 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, extended center walls, 12inch corner fillets 
  
p. FCT30E 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, extended center walls, 6inch corner fillets  q. FCT0E 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, extended center walls, 6inch corner fillets  r. PCCE 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, extended center walls, 12inch corner fillets 
  
s. FCQ30E 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, extended center walls, 6inch corner fillets  t. FCQ0E 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, extended center walls, 6inch corner fillets  u. PCDE 0°flared wingwalls, 8inchradius top bevel, 4inchradius WW bevel, extended center walls, 12inch corner fillets 
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 0degreeflared wingwall models.
Figure 51. Graph. Inlet control comparison, field cast 30degreeflared wingwall models.
Figure 52. Graph. Inlet control comparison, precast models.
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 K_{e} values for the field cast models with 0degree wingwalls were almost identical for the singlebarrel, doublebarrel, triplebarrel, and quadbarrel models and averaged 0.52. These results support the practice of using the single barrel coefficients for multiple barrel analyses. For the 30degreeflared wingwall models, the K_{e} values averaged 0.32 for the multiple barrel models when compared to K_{e} = 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 K_{e} for the multiple barrel models was 0.54, and the K_{e} 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 doublebarrel, triplebarrel, and quadbarrel results.
Table 2. Summary of inlet and outlet control coefficients for models tested for effects of multiple barrels.
Model  Slope (percent)  Fillets (inches)  K_{e}  K Form 2 Eq.  M Form 2 Eq.  c  Y 
FCS0 
3 
6 

0.57 
0.62 
0.0448 
0.56 
0.7 
6 
0.50 




FCS30 
3 
6 

0.47 
0.68 
0.0394 
0.53 
0.7 
6 
0.26 




FCD0 
3 
6 

0.55 
0.61 
0.0391 
0.66 
0.7 
6 
0.52 




FCD0E 
3 
6 

0.55 
0.60 
0.0394 
0.65 
0.7 
6 
0.53 




FCD30 
3 
6 

0.46 
0.66 
0.0366 
0.61 
0.7 
6 
0.34 




FCD30E 
3 
6 

0.46 
0.67 
0.0381 
0.59 
0.7 
6 
0.31 




FCT0 
3 
6 

0.58 
0.58 
0.0377 
0.69 
0.7 
6 
0.54 




FCT0E 
3 
6 

0.60 
0.57 
0.0405 
0.67 
0.7 
6 
0.58 




FCT30 
3 
6 

0.48 
0.67 
0.0379 
0.60 
0.7 
6 
0.31 




FCT30E 
3 
6 

0.51 
0.64 
0.0405 
0.60 
0.7 
6 
0.32 




FCQ0 
3 
6 

0.55 
0.61 
0.0377 
0.71 
0.7 
6 
0.52 




FCQ0E 
3 
6 

0.58 
0.59 
0.0418 
0.64 
0.7 
6 
0.50 




FCQ30 
3 
6 

0.47 
0.71 
0.0372 
0.64 
0.7 
6 
0.32 




FCQ30E 
3 
6 

0.50 
0.65 
0.0398 
0.60 
0.7 
6 
0.34 




PCA 
3 
12 

0.57 
0.61 
0.0361 
0.68 
0.7 
12 
0.33 




PCB 
3 
12 

0.54 
0.60 
0.0253 
0.90 
0.7 
12 
0.49 




PCBE 
3 
12 

0.57 
0.58 
0.0315 
0.81 
0.7 
12 
0.56 




PCC 
3 
12 

0.57 
0.57 
0.0219 
0.98 
0.7 
12 
0.54 




PCCE 
3 
12 

0.59 
0.58 
0.0263 
0.91 
0.7 
12 
0.51 




PCD 
3 
12 

0.55 
0.61 
0.0250 
0.92 
0.7 
12 
0.59 




PCDE 
3 
12 

0.60 
0.54 
0.0296 
0.85 
0.7 
12 
0.58 




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 WingwallFlare 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 30degree and the 0degreeflared 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 30degreeflared 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, 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.
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 PCB model was omitted from the trend line in figure 58 because it was considered an outlier point.
For outlet control, the K_{e} 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.
Figure 58. Graph. Inlet control comparison, extended or nonextended center walls, precast model.
EFFECTS OF SPANTORISE RATIO
Models tested concerning the spantorise ratio are illustrated in figure 59.
Multiple SpantoRise Versus Basic 1:1 SpantoRise
For inlet control in field cast models with 0degree wingwalls (FCS0), figure 60 shows that a very slight loss in performance might occur as the spantorise 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 spantorise ratio increases for the field cast models with 30degreeflared wingwalls (FCS30). This decrease in performance can be attributed in part to the diminishing effects of the wingwall flare angle with increasing spantorise, 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 spantorise ratio.
  
a. FCS30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 1:1, no corner fillets  e. FCS0 0flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 1:1, no corner fillets  i. PCA 0°flared wingwalls, 8inchstraight top bevel, 4inchradius WW bevel, spantorise 1:1, no corner fillets 
  
b. FCS30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 2:1, no corner fillets  f. FCS0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 2:1, no corner fillets  j. PCA 0°flared wingwalls, 8inchstraight top bevel, 4inchradius WW bevel, spantorise 2:1, no corner fillets 
  
c. FCS30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 3:1, no corner fillets  g. FCS0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 3:1, no corner fillets  k. PCA 0°flared wingwalls, 8inchstraight top bevel, 4inchradius WW bevel, spantorise 3:1, no corner fillets 
  
d. FCS30 30°flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 4:1, no corner fillets  h. FCS0 0°flared wingwalls, 4inchstraight top bevel, no WW bevel, spantorise 4:1, no corner fillets  l. PCA 0°flared wingwalls, 8inchstraight top bevel, 4inchradius WW bevel, spantorise 4:1, no corner fillets 
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.
For outlet control, the entrance loss coefficient K_{e} for the FCS0 models varied from 0.32 for the 3:1 spantorise 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 PCA models, the entrance loss coefficient K_{e} varied from 0.26 for the 4:1 spantorise 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 FCS30 models in that K_{e} was 0.27 for the 1:1 and 2:1 spantorise 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 spantorise ratios.
Wingwall Flare and the SpantoRise Ratio
Figures 63–66 show that the wingwall flare angle has a diminishing effect as the spantorise 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 0degreeflared wingwall curves and the 30degreeflared wingwall curves. As the spantorise 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 30degreeflared 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 FCS30 models did not, however, support the assumption that the wingwall flare angle has a diminishing effect as the spantorise ratio increases. The outlet control loss coefficient K_{e} was 0.27 for the basic 1:1 spantorise ratio, but decreased to 0.18 for the 4:1 ratio.
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.
Table 3. Summary of inlet and outlet control coefficients for models tested for effects of spantorise ratio.
Model  Span:Rise  Slope (percent)  Fillets (inches)  K_{e}  K Form 2 Eq.  M Form 2 Eq.  c  Y 
FCS0 
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 




FCS30 
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 




PCA 
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 




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.
The field cast triplebarrel 30degreeflared wingwalls model (FCT30) and the field cast singlebarrel 30degreeflared wingwalls model with a 3:1 spantorise ratio (FCS30 (3:1)) illustrated in figure 684 were used for these tests.
Figure 68. Sketches. Models tested for effects of headwall skew.
   
a. FCT30 30°flared wingwalls, 4inchstraight top bevel, no wingwall bevel, 0° skew, no corner fillets  b. FCT30 30°flared wingwalls, 4inchstraight top bevel, no wingwall bevel, 15° skew, no corner fillets  c. FCT30 30°flared wingwalls, 4inchstraight top bevel, no wingwall bevel, 30° skew, no corner fillets  d. FCT30 30°flared wingwalls, 4inchstraight top bevel, no wingwall bevel, 45° skew, no corner fillets 
 
e. FCS30 30°flared wingwalls, 4inchstraight top bevel, no wingwall bevel, 3:1 spantorise, 0° skew, no corner fillets  f. FCS30 30°flared wingwalls, 4inchstraight top bevel, no wingwall bevel, 3:1 spantorise, 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.
 
a. FCT30, 0degree skew  b. FCT30, 15degree skew 
 
c. FCT30, 30degree skew  d. FCT30, 45degree 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 0degree headwall. Consequently, it is reasonable to combine the 15degree, 30degree, and 45degree skew curves for inlet control. The performance curve for the HDS5, 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. HDS5 does not specify if that inlet represents a skewed headwall or a skewed flow alignment.
The outlet control entrance loss coefficient K_{e} could be averaged at 0.36 for 0degree and 15 degree skew angles, but increased to 0.46 for 30degree and 45degree skew angles. Table 4 summarizes the inlet and outlet control coefficients.
Figure 70. Graph. Inlet control comparison, skew angles.
Table 4. Summary of inlet and outlet control coefficients for models tested for effects of headwall skew.
Model  Span:Rise  Skew 
Slope (percent) 
Fillets (inches)  K_{e}  K Form 2 Eq.  M Form 2 Eq.  c  Y 
FCS30 
3:1 
0° 
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 




FCT30 
3:1 
0° 
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 




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 K_{e} 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 K_{e}
One hypothesis considered as a possible explanation for the large scatter in the entrance loss coefficient at low flows was that K_{e} depended on the Reynolds number. If that hypothesis were true, there should be a correlation between K_{e} and the Reynolds number regardless of whether the culvert were submerged.
The Reynolds number hypothesis was tested using full barrel flow with the HDS5, 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 HDS5, 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, K_{e}, for low flows.
Model 
Slope (percent) 
Fillets (inches) 
Number of Barrels  Span:Rise  Skew  Unsubmerged K_{e}^{*} 
FCS0 
0.7 
0 
1 
1:1 
0° 
0.73 
FCS0 
0.7 
6 
1 
1:1 
0° 
0.90 
FCS0 
0.7 
12 
1 
1:1 
0° 
0.9 
PCA 
0.7 
0 
1 
1:1 
0° 
0.67 
PCA 
0.7 
6 
1 
1:1 
0° 
0.63 
PCA 
0.7 
12 
1 
1:1 
0° 
0.56 
FCS30 
0.7 
0 
1 
1:1 
0° 
0.39 
FCS30 
0.7 
6 
1 
1:1 
0° 
0.71 
FCS0 
0.7 
6 
1 
1:1 
0° 
0.9 
FCS30 
0.7 
6 
1 
1:1 
0° 
0.71 
FCD0 
0.7 
6 
2 
1:1 
0° 
0.71 
FCD0E 
0.7 
6 
2 
1:1 
0° 
0.32 
FCD30 
0.7 
6 
2 
1:1 
0° 
0.74 
FCD30E 
0.7 
6 
2 
1:1 
0° 
0.42 
FCT0 
0.7 
6 
3 
1:1 
0° 
0.6 
FCT0E 
0.7 
6 
3 
1:1 
0° 
0.8 
FCT30 
0.7 
6 
3 
1:1 
0° 
0.48 
FCT30E 
0.7 
6 
3 
1:1 
0° 
0.41 
FCQ0 
0.7 
6 
4 
1:1 
0° 
0.83 
FCQ0E 
3.0 
6 
4 
1:1 
0° 
0.87 
FCQ30 
0.7 
6 
4 
1:1 
0° 
0.38 
FCQ30E 
0.7 
6 
4 
1:1 
0° 
0.38 
PCA 
0.7 
12 
1 
1:1 
0° 
0.56 
PCB 
0.7 
12 
2 
1:1 
0° 
0.96 
PCBE 
0.7 
12 
2 
1:1 
0° 
0.75 
PCC 
0.7 
12 
3 
1:1 
0° 
0.94 
PCCE 
0.7 
12 
3 
1:1 
0° 
0.96 
PCD 
0.7 
12 
4 
1:1 
0° 
0.91 
PCDE 
0.7 
12 
4 
1:1 
0° 
0.93 
FCS0 
0.7 
0 
1 
1:1 
0° 
0.73 
FCS0 
0.7 
0 
1 
2:1 
0° 
0.48 
FCS0 
0.7 
0 
1 
3:1 
0° 
0.66 
FCS0 
0.7 
0 
1 
4:1 
0° 
0.62 
FCS30 
0.7 
0 
1 
1:1 
0° 
0.17 
FCS30 
0.7 
0 
1 
2:1 
0° 
0.39 
FCS30 
0.7 
0 
1 
3:1 
0° 
0.48 
FCS30 
0.7 
0 
1 
4:1 
0° 
0.53 
PCA 
0.7 
0 
1 
1:1 
0° 
0.67 
PCA 
0.7 
0 
1 
2:1 
0° 
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, HDS5 8/3.
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 K_{e} and the Reynolds number. Figure 72 shows that the standard deviation of the K_{e} data gradually decreased with an increasing Reynolds number. This figure is included to demonstrate statistically that, although there is a wide spread in K_{e} around the 162,000 Reynolds number, the scatter in K_{e} values decreased as the Reynolds number increased.
Figure 72. Graph. Standard deviation of K_{e} versus the Reynolds number.
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 H_{Le} or contraction loss H_{Lc}, 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 A_{c}, illustrated in figure 73, and the expansion loss equation (figure 74).
Figure 73. Diagram. Culvert contraction.
By considering the flow expansion from the contracted section, area A_{c}, 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.
The contraction coefficient C_{c} is equal to A_{c} / A, and depends on the area ratio A / A_{a}, 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 K_{o}
The exit loss is a function of the change in velocity at the outlet of the culvert barrel. Figure 75 contains the equation, from HDS5, for the exit loss for a sudden expansion, as at an end wall.
Figure 75. Equation. Exit loss, with coefficient of 1.
The channel velocity downstream of the culvert is V_{d}. The mean flow is V. HDS5 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 fullflow 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.
Where:  
 
Q  is discharge. 
W_{TB}  is the full width of the tailbox. 
TW  is the average tailwater depth at the five pressure taps. 
The velocity head V_{d}^{2}/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, H_{Lo}. The exit loss coefficient, K_{o}, was then computed from the equation in figure 77.
Figure 77. Equation. Exit loss, with coefficient K_{o}.
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 K_{o} 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, H_{Lo}, 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 K_{o}. 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.
Figure 79. Diagram. Flow expansion in the tailbox for low tailwater.
Figure 80. Diagram. Vertical flow expansion in the tailbox and projected EGL.
Note: Vertical to horizontal scale is exaggerated by approximately 2:1. 
The energy exit loss coefficients K_{o} are summarized in table 6 for different culvert barrel configurations. Each K_{o} 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 configuration  K_{o} unsubmerged^{*}  K_{o} submerged 
a.  0.73  1.12 
b.  1.00  1.11 
c.  0.89  0.96 
d.  0.94  1.08 
e.  1.07  1.19 
f.  1.04  1.03 
g.  0.66  0.97 
h.  1.28  1.35 
i.  0.85  1.11 
j.  Skew  0.86  0.99 
k.  Skew  1.10  1.26 
* These values are not to be used because of the resolution limits of the pressure transducers. 
FIFTHORDER 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. Fifthorder 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.
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.
Where:  
 
a to f  are 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:Rise  a  b  c  d  e  f 
FCS0 
0 
1:1 
0.211536 
0.224341 
0.208370 
−0.121994 
0.024676 
−0.001609 
FCS0 
6 
1:1 
0.224471 
0.247312 
0.186514 
−0.113509 
0.023189 
−0.001514 
FCS0 
12 
1:1 
0.245464 
0.218175 
0.210202 
−0.121260 
0.024063 
−0.001536 
PCA 
0 
1:1 
0.194217 
0.310678 
0.109365 
−0.077409 
0.016183 
−0.001059 
PCA 
6 
1:1 
0.203074 
0.313529 
0.107677 
−0.076856 
0.016046 
−0.001046 
PCA 
12 
1:1 
0.210576 
0.314554 
0.101951 
−0.072650 
0.014939 
−0.000956 
PCA 
6 
2:1 
0.186778 
0.482282 
−0.070441 
−0.003094 
0.003186 
−0.000258 
PCA 
12 
2:1 
0.189232 
0.496842 
−0.090840 
0.005876 
0.001525 
−0.000152 
Table 8. Polynomial regression coefficients, models tested for spantorise ratio.
Model 
Fillet (inches) 
Span:Rise  a  b  c  d  e  f 
FCS0 
0 
1:1 
0.211536 
0.224341 
0.208370 
−0.121994 
0.024676 
−0.001609 
FCS0 
0 
2:1 
0.207152 
0.432143 
−0.011800 
−0.032349 
0.009224 
−0.000668 
FCS0 
0 
3:1 
0.227185 
0.361402 
0.077047 
−0.069984 
0.015731 
−0.001063 
FCS0 
0 
4:1 
0.246621 
0.315820 
0.126140 
−0.091438 
0.019626 
−0.001311 
FCS30 
0 
1:1 
0.163450 
0.127103 
0.256193 
−0.131631 
0.025211 
−0.001601 
FCS30 
0 
2:1 
0.114704 
0.376884 
−0.007409 
−0.024267 
0.006977 
−0.000502 
FCS30 
0 
3:1 
0.141479 
0.321334 
0.064086 
−0.056126 
0.012732 
−0.000862 
FCS30 
0 
4:1 
0.230000

0.117000 
0.241000 
−0.126000 
0.025000 
−0.001640 
PCA 
0 
1:1 
0.194217 
0.310678 
0.109365 
−0.077409 
0.016183 
−0.001059 
PCA 
0 
2:1 
0.154724 
0.592825 
−0.190065 
0.048610 
−0.006357 
0.000370 
PCA 
0 
3:1 
0.200747 
0.424467 
0.000339 
−0.032906 
0.008306 
−0.000569 
PCA 
0 
4:1 
0.220017 
0.404031 
0.029449 
−0.046577 
0.010869 
−0.000734 
Table 9. Polynomial regression coefficients, models tested for multiple barrels.
Model 
Fillet (inches) 
No. of Barrels  a  b  c  d  e  f 
FCS0 
6 
1 
0.224471 
0.247312 
0.186514 
−0.113509 
0.023189 
−0.001514 
FCS30 
6 
1 
0.148953 
0.250437 
0.129334 
−0.080435 
0.016465 
−0.001069 
FCD0 
6 
2 
0.154694 
0.436581 
−0.034324 
−0.017500 
0.006033 
−0.000449 
FCD0E 
6 
2 
0.168455 
0.406534 
−0.000921 
−0.031807 
0.008541 
−0.000602 
FCD30 
6 
2 
0.101044 
0.419241 
−0.055078 
−0.002691 
0.002885 
−0.000237 
FCD30E 
6 
2 
0.103678 
0.402060 
−0.035969 
−0.011102 
0.004465 
−0.000338 
FCT0 
6 
3 
0.185570 
0.425924 
−0.015139 
−0.027376 
0.007816 
−0.000559 
FCT0E 
6 
3 
0.220522 
0.370427 
0.057110 
−0.060032 
0.013803 
−0.000936 
FCT30 
6 
3 
0.132482 
0.340923 
0.042681 
−0.044257 
0.010089 
−0.000674 
FCT30E 
6 
3 
0.146450 
0.369886 
0.018327 
−0.037160 
0.009256 
−0.000639 
FCQ0 
6 
4 
0.154223 
0.448350 
−0.040698 
−0.014061 
0.005238 
−0.000392 
FCQ0E 
6 
4 
0.202572 
0.369396 
0.056302 
−0.059162 
0.013704 
−0.000934 
FCQ30 
6 
4 
0.108394 
0.355482 
0.027300 
−0.034330 
0.007929 
−0.000526 
FCQ30E 
6 
4 
0.144926 
0.350135 
0.041407 
−0.046111 
0.010763 
−0.000730 
PCA 
12 
1 
0.210576 
0.314554 
0.101951 
−0.072650 
0.014939 
−0.000956 
PCB 
12 
2 
0.099284 
0.607914 
−0.221590 
0.066777 
−0.009847 
0.000567 
PCBE 
12 
2 
0.149381 
0.540449 
−0.142259 
0.029009 
−0.002577 
0.000099 
PCC 
12 
3 
0.147326 
0.545578 
−0.146179 
0.032208 
−0.003485 
0.000151 
PCCE 
12 
3 
0.153250 
0.555777 
−0.152070 
0.035094 
−0.004187 
0.000219 
PCD 
12 
4 
0.107009 
0.600450 
−0.207455 
0.060926 
−0.008924 
0.000516 
PCDE 
12 
4 
0.158898 
0.585920 
−0.191810 
0.048483 
−0.005859 
0.000294 
Table 10. Polynomial regression coefficients, models tested for skewed headwall.
Model 
Fillet (inches) 
Skew Angle (degrees)  a  b  c  d  e  f 
FCS30 
0 
30 
0.213123 
0.685460 
−0.298162 
0.088583 
−0.012236 
0.000663 
FCT30 
0 
0 
0.128409 
0.355047 
0.026694 
−0.037498 
0.008897 
−0.000603 
FCT0 
0 
0 
0.183389 
0.409080 
0.005613 
−0.035825 
0.009284 
−0.000650 
FCT30 
0 
15 
0.182031 
0.686256 
−0.277043 
0.082113 
−0.011673 
0.000654 
FCT30 
0 
30 
0.225978 
0.658427 
−0.240324 
0.063449 
−0.007969 
0.000409 
FCT30 
0 
45 
0.187459 
0.743672 
−0.323642 
0.103601 
−0.016120 
0.000958 
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