9
PART 3 Hydrology, Hydraulics, and Water Quality
PART 3
Hydrology, Hydraulics, and Water Quality
In response to recent and ongoing adaptation of culvert designs to envi-ronmentally sensitive installations, inlet loss coefficients and inlet controlflow performance data are presented that are specific to environmen-tally sensitive culvert geometries. A common practice for such culvertdesigns is to bury the culvert inverts and create a simulated streambedthrough the culvert. Common cross-sectional geometries of such cul-verts typically include circular, elliptical, or pipe arch. These buried- ordepressed-invert culverts create inlet geometries for which inlet lossinformation and inlet control flow performance curves have not beendeveloped. Regardless of the method used to design environmentally sen-sitive culverts, the ability of the culvert to pass the design flood must bedetermined. In an effort to provide such information, an elliptical smooth-wall culvert with an invert burial depth of 50% was tested under vari-ous conditions (e.g., various end treatments, inlet and outlet control,submerged and unsubmerged inlet conditions, and ponded and chan-nelized approach flow conditions) to determine the inlet loss coeffi-cient and flow performance curve characteristics. The test resultsshow that the inlet loss coefficient is relatively independent of bothReynolds number and the ratio of the distance from the inlet invertto the upstream total energy grade line to the culvert diameter (HW/D)and that the inlet loss coefficients for the elliptical culvert with 50% bur-ial depth are approximately equal to the published coefficients for tra-ditional culvert inlets. The inlet control data adapt well to the Form 1and Form 2 unsubmerged and the submerged equations recommendedby FHWA.
There are various techniques for designing fish-friendly culverts.Some rely primarily on traditional hydraulic engineering calcula-tions, whereas others focus more on streambed simulation techniques.Three methods used in Washington State for designing culverts forfish passage include the no-slope, hydraulic, and stream simulationmethods (1). As research on fish and culvert interaction developsfurther, modifications to the current design procedures for fish pas-sage culverts will likely be implemented. In addition to the issuesof fish or debris passage issues associated with environmentallysensitive culvert installations, the hydraulic performance of theculvert is also important. Regardless of the design method used,environmentally sensitive culverts must be able to pass the designflood.
A current study at the Utah Water Research Laboratory (UWRL),at Utah State University, funded by NCHRP Project 15-24 isresearching, among other issues, inlet loss coefficients and inlet con-
trol flow performance for various common environmentally sensi-tive culvert designs. A significant literature review produced littleor no hydraulic performance information specific to common envi-ronmentally sensitive culvert designs for calculating flow capacity.Consequently, a primary focus of this study includes testing envi-ronmentally sensitive culvert designs in the laboratory to quantifytheir hydraulic characteristics. The results of this study should pro-vide design engineers with useful information for determining theflow capacity of environmentally sensitive culvert installations,regardless of the design method used.
A current design technique for fish passage culverts uses commer-cially available culvert shapes, such as circular, elliptical, box, or pipearch, with the culvert invert buried below the streambed elevation.These culverts are referred to as buried- or depressed-invert culverts.The culvert invert is buried so that a quasi-natural streambed can beconstructed through the culvert. The depth of invert burial can vary.The geometry of the buried-invert culvert provides a wider flow chan-nel through the culvert at lower discharges, which reduces flow veloc-ities and encourages fish passage. Examples of fish passage culvertsare shown in Figure 1.
The hydraulic characteristics of a 50% buried-invert, elliptical cul-vert are discussed. The buried-invert, elliptical culvert was testedunder outlet control with a square-edged inlet with headwall. Thesame culvert was tested under inlet control with a square-edged inletwith headwall, a projecting inlet, and a 45-degree beveled inlet withheadwall. Both inlet and outlet control tests featured various condi-tions including submerged inlet, unsubmerged inlet, ponded andchannelized approach conditions, and the end treatments previouslymentioned. The independent variables in the data collection wereReynolds number (based on the average flow conditions in the cul-vert) and the ratio of the distance from the inlet invert to the upstreamtotal energy grade line to the culvert diameter (HW/D).
OUTLET CONTROL HYDRAULICS OF CULVERTS
Outlet flow control in culverts refers to a wide range of flow condi-tions in which the flow rate is determined by the balance of drivinghead and head loss throughout the culvert. Outlet control producessubcritical flow in the culvert. If the culvert is installed on a mildslope, outlet control can occur for both submerged or unsubmergedinlet conditions and submerged or unsubmerged outlet conditions.The outlet control head–discharge relationship, in which head refersto the total energy upstream of the culvert, relative to some datum(typically the inlet invert), is determined by using conservation ofenergy:
Y ZV
gY Z
V
gHU U
UD D
DL+ + = + + +
2 2
2 21( )
Hydraulic Characteristics of Buried-InvertElliptical Culverts
Blake P. Tullis, S. Collin Robinson, and Jacob C. Young
Utah Water Research Laboratory, Utah State University, 8200 Old Main Hill,Logan, UT 84322-8200.
105
Transportation Research Record: Journal of the Transportation Research Board,
No. 1904, Transportation Research Board of the National Academies, Washington,D.C., 2005, pp. 105–112.
where
Y = water depth,Z = channel invert elevation,V = flow velocity,
HL = total energy loss, andg = acceleration due to gravity.
The subscripts U and D signify locations upstream and downstreamfrom the culvert.
The energy losses include inlet, friction, exit, and any other minorlosses. Inlet losses are commonly expressed as a fraction of the pipevelocity head:
where Ke is the inlet loss coefficient.FHWA’s Hydraulic Design of Highway Culverts (2), referred to
as HDS-5, along with most fluid dynamics texts and referencebooks, gives an inlet loss coefficient of Ke = 0.5 for a square-edgedentrance, independent of any other variable. More recent studies (3)suggest that Ke may vary with the ratio of the distance from the inletinvert to the upstream total energy grade line to the culvert diame-ter (HW/D). The effects of both HW/D and Reynolds number on Ke
were evaluated in this study.
INLET CONTROL HYDRAULICS OF CULVERTS
Inlet control is described in HDS-5 as a condition when “the culvertbarrel is capable of conveying more flow than the inlet will accept.”A critical section forms (flow passes through critical depth) nearthe inlet of the culvert and transitions to supercritical flow. Theflow rate through the culvert is independent of hydraulic rough-ness of the culvert material or culvert length. The flow rate is influ-enced by the culvert shape, cross-sectional area, end treatment,and headwater depth.
Empirical equations are presented in HDS-5 for inlet control head–discharge relationships, referred to as flow performance curves.
H KV
gL einlet( ) =2
22( )
106 Transportation Research Record 1904
HDS-5 gives two equations for unsubmerged inlet control, identifiedas Form 1 (Equation 3) and Form 2 (Equation 4), and one equation forsubmerged inlet control (Equation 5). Form 1 uses specific energy atcritical depth and has two empirical constants. Form 2 is based on theweir equation and includes two empirical constants. The submergedequation (Equation 5) also has two empirical constants.
Unsubmerged Form 1:
Unsubmerged Form 2:
Submerged:
where
HWi = total energy of headwater relative to inlet controlsection invert (ft) [HDS-5 uses upstream piezomet-ric energy rather than total energy as presented here;total energy is used in this analysis];
D = interior height of culvert barrel (ft);Hc = specific energy at critical depth, dc + Vc
2/2g (ft);Q = discharge (ft3/s);A = full cross-sectional area of culvert (ft2);S = culvert slope (ft/ft);
K, M, c, Y = regression constants; andKu = 1.811 (SI units) (1.0, U.S. customary units).
In this paper, the results of the data analysis are presented in termsof Ke for outlet control conditions and the regression constants K, M,c, and Y for inlet control.
HW
Dc
K Q
ADY Si uU=
⎛⎝⎜
⎞⎠⎟
+ −0 5
2
0 5 5.
. ( )
HW
DK
K Q
ADi u
M
= ⎛⎝⎜
⎞⎠⎟0 5
4.
( )
HW
D
H
DK
K Q
ADSi c u
M
= + ⎛⎝⎜
⎞⎠⎟
−0 5
0 5 3.
. ( )
(a) (b)
FIGURE 1 Examples of buried-invert fish passage culverts.
EXPERIMENTAL METHOD
A replica or model of an elliptical culvert with a 50% invert burialdepth was fabricated out of smooth steel on all surfaces. The culvertcross-sectional shape is shown in Figure 2. It should be noted thatthe test culvert does not have a rough bottom surface as would beconsistent with a simulated streambed. The selection of the smooth-wall culvert was critical to the experimental method and was basedon the assumption that the inlet loss characteristics of a culvert aremore a function of the cross-sectional geometry, end treatment, andapproach flow condition than the hydraulic roughness of the culvertmaterial or simulated streambed in the buried-invert culvert.
The smooth-wall test culvert was important for two reasons. Pres-sure taps were installed at various locations in the floor of the testculvert and used along with a piezometer board to measure thepiezometric head in the pipe. To measure the piezometric head accu-rately with a pressure tap, the pressure tap must be oriented normal tothe streamlines and the pressure should be hydrostatic locally. Suchconditions exist with a smooth-wall flow boundary. With a corrugatedsurface, for example, this would not be the case. To calculate theinlet loss, it was necessary to isolate the energy loss associated withthe inlet relative to the energy loss due to pipe friction. The smooth-wall boundary made it possible to accurately calculate the pipe fric-tion loss in the culvert. On the basis of the limited understanding ofcomposite hydraulic roughness, this calculation could not be madeto the level of accuracy required if the culvert had a compositeroughness (bottom and side wall having different hydraulic rough-ness characteristics). A fundamental study evaluating the accuracyof predictive composite roughness coefficient techniques representsanother part of the current UWRL study (NCHRP Project 15-24).
The dimensions of the elliptical culvert were 25.25 in. across thehorizontal axis and 17 in. across the vertical axis. With 50% invertburial depth, the culvert height was 8.5 in. The aspect ratio of theelliptical culvert was based on commercially available culverts. Theculvert was 20 ft long. Tremendous care was taken to minimizeshape distortion of the culvert due to excessive heat during the weld-ing process. Pressure taps were installed in the culvert bottom at twodiameter (horizontal axis dimension) intervals along the length ofthe culvert for a total of five taps.
Tullis, Robinson, and Young 107
The culvert was installed into a head box 22 ft long by 24 ft wideby 5 ft deep, as shown in Figure 3. The culvert was continuouslysupported in an effort to maintain slope uniformity. The culvertslope associated with the outlet control data presented in this paperwas approximately horizontal. The slope values for the inlet con-trol data ranged from approximately 0 to 3.2%. Only inlet loss datafor the square-edged inlet with headwall are presented here; how-ever, the performance of additional end treatments will be evalu-ated as the study progresses. All end treatments (both inlet andoutlet control) were tested with and without guide walls to deter-mine the effects of channelized versus ponded approach flow con-ditions on inlet loss coefficients and inlet control performancecurves.
Figure 4 shows the end treatment for the square-edged inlet withheadwall. The guide walls were installed with a contraction ratio of2 (wall spacing to culvert horizontal axis dimension) and orientedperpendicularly to the headwall. The downstream end of the culvertwas connected to a tail box with a stop log assembly, which facili-tated variable tailwater condition. A pressure tap located in a rela-tively low-velocity region of the head box and the pressure taps inthe culvert invert were connected to a piezometer board for mea-suring piezometric head at those respective locations. Flow rateswere quantified using calibrated, 20-, 8-, and 4-in. orifice metersinstalled in supply lines of the same size, respectively. An overviewof the test setup is shown in Figure 4c.
Outlet Control
The inlet loss coefficients were calculated as follows. For nonpres-surized flow conditions, the existence of outlet control was deter-mined by calculating the Froude number (Fr) at the center threepressure tap locations in the culvert for each run to ensure that sub-critical flow conditions (Fr < 1.0) existed. The up- and downstreampressure tap data were not typically used because of the rapidlyvarying flow conditions present at those locations. With the culvertoperating under outlet control, the total energy in the approach flowand at each pressure tap location along the culvert was determinedon the basis of experimental measurements. Since the one-dimensionaltotal energy value cannot realistically be measured at the upstreamend of the culvert because of the presence of rapidly varying flow anda nonhydrostatic pressure condition, the total energy at the upstreamend of the culvert was calculated by accounting for the change inenergy between each respective pressure tap and the pipe inlet bymeans of gradually varied flow calculations. The difference betweenthe measured approach flow total energy and the calculated totalenergy values at the upstream end of the culvert represented theenergy loss associated with the inlet.
Equation 6 was used to calculate the inlet loss coefficient, Ke:
where
HW = total energy upstream of culvert,Hinlet = total energy at upstream end of culvert, and
V = mean flow velocity in culvert.
The inlet loss coefficients calculated from each piezometric headmeasurement location were averaged to produce a representativeKe-value for each flow condition.
HW H KV
ge− =inlet
2
26( )
8.5 in.
25.25 in.
FIGURE 2 Test culvert: elliptical, 50% invert burial.
Inlet Control
Inlet control flow performance testing was also conducted with thesame experimental setup. The Froude number was monitored to ver-ify supercritical flow (Fr > 1.0), ensuring inlet control. With inletcontrol, the flow rate is dependent on HW/D. HDS-5 suggests usingHWi, which represents the water depth (piezometric head) relativeto the invert elevation at the control section. For this study, HW(total energy) was used rather than HWi to be consistent with themethodology used with other flow control structures, such as spill-ways. As mentioned previously, inlet control flow performance datawere collected for three different inlet end treatments (i.e., square-edged with headwall, projecting, and a 45-degree bevel with head-wall). All end treatments were tested with a channelized and a
108 Transportation Research Record 1904
ponded approach flow condition. The projecting end treatment, withand without guide walls, is illustrated in Figure 4.
EXPERIMENTAL RESULTS
Outlet Control
HDS-5, along with most fluid mechanics texts and reference books,gives an inlet loss coefficient of 0.5 for a square-edged entrancewith a headwall, independent of any other variables. Smith and Oak(3) showed variation in inlet loss coefficients, Ke, with the ratio ofthe distance from the inlet invert to the upstream total energy grade
(a)
(b)
FIGURE 3 Overview schematic of culvert test facility: (a) elevation view and (b) plan view.
Tullis, Robinson, and Young 109
(a) (b)
(c)
FIGURE 4 Elliptical, 50% invert-burial test culvert with square-edged inlet with headwall and projecting end treatments (with and without guide walls): (a) ponded approach condition, (b) channelized approach condition, and (c) test setup overview.
line to the culvert diameter (HW/D). In this study, the inlet losscoefficients were calculated for a range of headwater energy valuesrelative to the culvert diameter (HW/D), where the diameter, D, rep-resents the vertical axis dimension from the streambed invert in theculvert to the culvert crown. In addition to HW/D effects, the effectsof the Reynolds number on Ke were evaluated by collecting datasuch that the Reynolds number was held approximately constantwhile the HW/D-value varied. To achieve these data, the flow ratethrough the culvert had to be decreased through tailwater control asthe HW/D-value increased. The water temperature was also monitoredfor each run. This process was repeated for a range of Reynoldsnumbers up to the maximum allowable Reynolds number that couldbe achieved based on the depth of the head box and culvert size.
The Reynolds number is defined as a characteristic velocity timesa characteristic length divided by the kinematic viscosity. Four timesthe hydraulic radius was used as the characteristic diameter. The aver-age flow velocity and the flow depth (used to calculate the hydraulicradius) were calculated by using data from the three center pressure taplocations.
The inlet loss coefficient testing results for the 50% invert burialdepth, elliptical culvert with a square-edged inlet with headwall arepresented in Figure 5. The inlet loss coefficient data are plotted as afunction of the dimensionless ratio HW/D. The data are also identi-fied by Reynolds number and approach flow condition (i.e., chan-nelized or ponded). Figure 5 indicates that Ke is approximately equalto 0.6 for an elliptical culvert with 50% invert burial depth and asquare-edged inlet with headwall for HW/D-values of 1.5 and greater.This finding corresponds well with the Ke = 0.59 result published bySmith and Oak (3) for the same end treatment. It is interesting tonote that Smith and Oak (3) reported inlet loss coefficients that var-ied with HW/D for all end treatments tested, with the exception ofthe square-edged inlet with headwall. For HW/D < 1.5, Ke decreasesslightly, with the range of Ke-values falling between 0.4 and 0.6.
110 Transportation Research Record 1904
Inlet Control
The data for inlet control flow performance are presented in Figure 6for the three end treatments tested. The data are identified by approachflow and submergence conditions. The square-edge-with-headwalland the 45-degree-bevel data show no variation with approach flowconditions (channelized or ponded). There are no shifts or offsetsin the data at the transition from unsubmerged to submerged inletconditions. The beveled inlet is slightly more efficient than thesquare-edged inlet, as would be expected.
For the projecting inlet, there is some difference between thechannelized and ponded data, particularly in the submerged inletrange. The culvert is more efficient with the channelized approach.The channelized approach likely reduced the amount of contractionas the flow enters the projecting culvert inlet, relative to the pondedcondition. There is also a small offset between the channelized dataat the transition from unsubmerged to submerged inlet.
The regression coefficients for the Form 1 and Form 2 (unsub-merged) inlet control equations and the submerged inlet controlequation are summarized in Table 1. The channelized and pondedapproach data were analyzed together for the square-edged and thebeveled inlets, as the data sets showed no variation with approachflow condition. For the projecting end treatment, coefficients arereported for each approach condition. The regression coefficientsfor several related culverts listed in HDS-5 are included in Table 1for comparative purposes.
CONCLUSIONS
Outlet Control
From the results presented, the following conclusions can be made.The inlet loss coefficient for elliptical culverts with the invert buried
0.0
0.2
0.4
0.6
0.8
1.0
0.0 1.0 2.0 3.0 4.0 5.0
HW/D
Ke
Ponded, Re=80k
Ponded, Re=160k
Ponded, Re=320k
Channelized, Re=80k
Channelized, Re=160k
Channelized, Re=320k
FIGURE 5 Inlet loss coefficients for elliptical culvert with 50% invert-burial depth and square-edged inlet with headwall. Inletloss coefficient data segregated according to approach condition (ponded or channelized) and Reynolds number.
to the culvert spring line (50% burial) and a square-edged entrancewith a headwall is constant over the range of Reynolds number andHW/D-values tested. The Ke-value for the square-edged headwallinlet was approximately 0.6, with a small amount of scatter. Thisfinding differs from the Ke = 0.5 referenced in HDS-5 and mosthydraulics reference books for this type of inlet. At smaller HW/D-values, the inlet loss coefficient varies somewhat between 0.4 and0.6. Using Ke = 0.6 is recommended for the elliptical culvert with50% invert burial and a square-edged inlet with a headwall, whichrepresents a more conservative value relative to published valuesfor traditional square-edged inlets with headwall (i.e., 0.5).
Additional culvert shapes with varied invert burial depths will betested in conjunction with this study to determine appropriate inletloss coefficients. Smith and Oak (3) published results indicating thattraditional circular culverts exhibited variations in Ke with HW/D for
Tullis, Robinson, and Young 111
all end treatments tested, with the exception of the square-edgedinlet with headwall.
Inlet Control
For inlet control flow conditions, both forms of the unsubmerged inletcontrol flow equations (i.e., Form 1 and Form 2) match the experi-mental data set quite well, with the appropriate regression constants,as does the submerged inlet control flow equation. This paper pre-sents coefficients that can be used to predict inlet flow capacity foran elliptical culvert with 50% invert burial and square-edged inletwith headwall, projecting, or a 45-degree bevel with headwall inletend treatment.
0.0
1.0
2.0
3.0
4.0
5.0
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Q (ft3/s)
Sq.-edge w/Hdwall, Ponded, Unsub. Sq.-edge w/Hdwall, Ponded, Sub. Sq.-edge w/Hdwall, Channel., Unsub.
Sq.-edge w/Hdwall, Channel., Sub. Proj., Ponded, Unsub. Proj., Ponded, Sub.
Proj., Channel., Unsub. Proj., Channel., Sub. Bevel, Ponded, Unsub.
Bevel, Ponded, Sub. Bevel, Channel., Unsub. Bevel, Channel., Sub.
HW
(ft
)
FIGURE 6 Flow performance curve for square-edged inlet with headwall, projecting, and 45-degree bevel withheadwall end treatments for ponded and channelized approach flow conditions.
TABLE 1 Inlet Control Equation Regression Constants for Elliptical Culvert with 50% Invert Burial and HDS-5 Regression Constants for Related Traditional Culverts
Unsubmerged Submerged
Form 1 Form 2
Model K M K M c Y
HDS-5 elliptical inlet face, tapered — — 0.547 0.800 0.0598 0.75inlet thin-edge projecting
HDS-5 horizontal ellipse, concrete, 0.0100 2.00 — — 0.0398 0.6sq.-edge w/hdwl.7
UWRL projecting (ponded) 0.1247 0.59 0.528 0.669 0.0650 0.46UWRL projecting (channelized) 0.0966 0.54 0.498 0.667 0.0649 0.13UWRL square headwall 0.0838 0.43 0.489 0.650 0.0431 0.61UWRL 45 degree bevel 0.0555 0.60 0.454 0.696 0.0318 0.68
Since a significant amount of work remains to be completed inthis study (i.e., different culvert shapes, end treatments, and invertburial depths), the generality of the conclusions drawn from the datapresented is yet to be determined with respect to the performance ofnontraditional culvert shapes associated with environmentally sen-sitive installations. The specific results presented here can be incor-porated into a standard HDS-5-type culvert design analysis for anelliptical culvert with 50% invert burial for the end treatments testedin this study. These specific culvert designs would likely only beused in conjunction with fish passage, debris passage, or other envi-ronmentally sensitive designs. The results would also be applicableto calculating the inlet loss for an elliptical culvert that has beensilted in with streambed material to the springline.
The experimental method implemented in this study was basedon the assumption that the inlet loss is independent of the hydraulicroughness associated with the culvert and the simulated streambed,which composes the bottom flow boundary of the culvert. As theability to better predict energy loss due to friction in a compositeroughness system improves, the likelihood of being able to accu-rately quantify inlet loss in a culvert with a simulated streambed andfully verify the assumptions made in this study will also improve.Evaluating methods for determining representative roughness coef-ficients for a composite roughness conveyance system is one of sev-
112 Transportation Research Record 1904
eral objectives associated with NCHRP Project 15-24, currently inprogress at the UWRL, at Utah State University.
ACKNOWLEDGMENTS
Funding for this research was provided by NCHRP Project 15-24.The authors thank the NCHRP oversight panel for their participationand assistance with this project.
REFERENCES
1. Bates, K., B. Barnard, B. Heiner, J. P. Klavas, and P. D. Powers. Fish Pas-sage Design at Road Culverts: A Design Manual for Fish Passage at RoadCrossings. Washington Department of Fish and Wildlife, Habitat andLands Program, Environmental Engineering Division, 2003. www.wsdot.wa.gov/TA/T2Center/FishPassage.pdf. Accessed April 2005.
2. Norman, J. M., R. J. Houghtalen, and W. J. Johnston. Hydraulic Designof Highway Culverts. Hydraulic Design Series Number 5 (HDS-5).FHWA, U.S. Department of Transportation, 2001.
3. Smith, C. D., and A. G. Oak. Culvert Inlet Efficiency. Canadian Journalof Civil Engineering, Vol. 22, 1995, pp. 611–616.
The Committee on Hydrology, Hydraulics, and Water Quality sponsored publication
of this paper.
