Copyright
by
Kathryn Shirley Benson
2004
Hydraulic Effects of Safety End Treatments on Culvert Performance
by
Kathryn Shirley Benson, B.S., B.S.
Thesis
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science in Engineering
The University of Texas at Austin
May, 2004
Hydraulic Effects of Safety End Treatments on Culvert Performance
APPROVED BY SUPERVISING
COMMITTEE:
Randall Charbeneau
Ben Hodges
George Herrmann
Dedication
To my family, friends, and teachers  without you I would not be who I am.
vi
Acknowledgements
I would to thank the Texas Department of Transportation for providing the
funding for this thesis research.
I would like express my admiration, appreciation, and respect for Dr. Randall
Charbeneau. It has been both a pleasure and a privilege to work with you. Thank you for
being a mentor, teacher, and inspiration throughout this life changing experience at The
University of Texas at Austin.
I wish to express gratitude to the fellow members of the Dr. Charbeneau research
team. My research partner, Jun Xia, and Lee Sherman who helped me make a successful
transition into graduate school and become part of the research team. I appreciate the
assistance of Masatsugu Takamatsu, Lee Guethle, Jennifer Trub, and Natalie Bartosh.
Thank you to Dr. Ben Hodges and George Herrmann, P.E. for assistance with this
manuscript.
I would like to thank my parents, Beverly and Walter, for their love, support,
encouragement, and belief in me always. I would like to thank to my siblings: Keith,
Kevin, and Kimberly. I am so fortunate to have you, your spouses, and children in my
life. Your guidance has been instrumental in obtaining my personal, professional, and
academic goals. Also, thank you to Jennifer Hasting, Jennifer Sorenson, and Meghan
Strand for their continued friendships.
vii
May 2004
viii
Abstract
Hydraulic Effects of Safety End Treatments on Culvert Performance
Kathryn Shirley Benson, M.S.E.
The University of Texas at Austin, 2004
Supervisor: Randall Charbeneau
Safety end treatments (SETs) are designed and installed at inlets and outlets of
culverts to reduce potential impacts from vehicular collision with these structures. SETs
must be designed with minimal size to limit interference with water flow while
maintaining sufficient strength to support a vehicle. SETs are proposed for extensive use
on new culvert projects as well as retrofitting existing culvert projects by the Texas
Department of Transportation (TxDOT). It is necessary to understand the impacts of
SETs on culvert hydraulics to ensure they do not affect the functionality of the culvert.
SETs function as flow barriers and can affect the hydraulic performance of the
culvert in two main ways. First, the ?backwater? effect from the installation of SETs
may cause an increase in the upstream headwater depth and entrance head losses.
Second, SET installation may cause clogging. Both of these effects may lead to flooding
of upstream properties since the influence of SETs on headwater depth is usually not
ix
accounted for in culvert design procedures. The purpose of this study is to evaluate the
impact of safety end treatments (SETs) on the hydraulic performance of culverts. The
research conducted focuses on the nature of water level difference upstream of the culvert
due to SET presence and the vortex phenomenon presence, the development of minor
loss coefficients, and understanding the impacts on culvert performance curves. The
overall conclusion of this thesis research is that SETs do not have a significant effect on
culvert hydraulic performance.
x
Table of Contents
List of Tables ........................................................................................................xiii
List of Figures .......................................................................................................xiv
Chapter 1: Introduction...........................................................................................1
1.1 Overview................................................................................................1
1.1.1 Culverts ................................................................................2
1.1.2 Safety End Treatments.........................................................3
1.1.3 Vortex Phenomenon.............................................................4
1.2 Study Objectives ....................................................................................5
1.3 Approach................................................................................................6
1.4 Thesis Overview ....................................................................................6
Chapter 2: Literature Review ..................................................................................7
2.1 Energy in Open Channel Flow...............................................................7
2.2 Culvert Design .......................................................................................9
2.3 Culvert Hydraulics ...............................................................................11
2.3.1 Inlet Control Unsubmerged Case................................................13
2.3.2 Inlet Control Submerged Case ....................................................15
2.3.3 Entrance Loss Coefficients .........................................................16
2.4 Vortex Phenomenon.............................................................................16
2.5 Texas Department of Transportation SET Design Standards ..............22
2.6 Impacts of SETs on Culvert Hydraulics ..............................................25
2.6.1 Drag Force...................................................................................25
2.6.1.1 Definition of Drag Force.................................................25
2.6.1.2 Relationship between Drag Forces and Upstream Water
Level Difference ................................................................27
2.6.2 Minor Losses...............................................................................28
2.6.3 Previous Studies of SETs ............................................................28
2.7 SharpCrested Weir..............................................................................31
2.8 Physical Modeling ...............................................................................33
xi
Chapter 3: Methodology ........................................................................................35
3.1 Physical Model Design ........................................................................35
3.1.1 Culvert Model Design........................................................35
3.1.2 Safety End Treatment Design ............................................38
3.2 Description of the Physical Model.......................................................39
3.2.1 Water Supply...............................................................................40
3.2.2 Outside Channel........................................................................41
3.2.3 Culvert and SET Models....................................................43
3.2.3.1 Vertical Headwall Culvert and SET Model at a 0degree
Skew...................................................................................44
3.2.3.2 Mitered Headwall Culvert and SET Model at a 0degree
Skew...................................................................................45
3.2.3.3 Mitered Headwall Culvert and SET Model at a 30degree
Skew...................................................................................48
3.3 Data Acquisition..................................................................................49
3.3.1 Channel Discharge ......................................................................49
3.3.2 Water Depth................................................................................53
3.3 Data Processing....................................................................................59
3.3.1 Velocity.......................................................................................59
3.3.2 Velocity Head .............................................................................60
3.3.3 Specific Energy...........................................................................61
3.3.4 Barrel Minor Loss Coefficient ....................................................61
3.3.5 Approach Minor Loss Coefficient ..............................................62
Chapter 4: Results .................................................................................................64
4.1 Water Level Difference........................................................................64
4.1.1 Water Level Distributions Across the Channel .................65
4.1.2 Water Level Difference due to the Vortex Phenomena .....70
4.1.3 Water Depth Difference due to the SET model component 73
4.2 Culvert Performance ............................................................................77
4.2.1 Performance Equation Evaluation ..............................................77
4.3 Minor Loss Coefficient ........................................................................81
xii
Chapter 5: Summary and Conclusions..................................................................89
5.1 Summary..............................................................................................89
5.2 Conclusions ..........................................................................................90
5.3 Implications..........................................................................................92
5.4 Suggested Future Work........................................................................93
Appendix................................................................................................................95
References............................................................................................................108
Vita ....................................................................................................................110
xiii
List of Tables
Table 2.1: Standard pipe sizes and maximum pipe runner length.........................24
Table 3.1: Testing Identification............................................................................58
Table 4.1: Minor Loss Coefficients ......................................................................83
xiv
List of Figures
Figure 1.1a and 1.1b: Definition sketches for a culvert...........................................2
Figure 1.2: Pipe grate safety end treatment for a culvert.........................................4
Figure 1.3: Antivortex plate developed for this study............................................5
Figure 2.1: Specific energy curve with respect to water depth...............................8
Figure 2.2: Skewed culverts (taken from Norman et al., 2001)............................11
Figure 2.3: Spiral vortex (from Lugt, 1983) .........................................................17
Figure 2.4: Intake vortex (from Lugt, 1983) .........................................................18
Figure 2.5: Vortex Formation ...............................................................................19
Figure 2.6: Effect of Vortices on the HeadDischarge Relationship for a Culvert on a
Steep Slope (from Blaisdell, 1966)...............................................................21
Figure 2.7: Typical installation of SETs for cross drainage and parallel drainage23
Figure 2.8: Bottom anchor pipe installation options.............................................24
Figure 2.9: Simplified flow conditions near the culvert with and without SETs
(modified from Xia, 2003). ...........................................................................27
Figure 3.1: Schematic view of the physical model................................................40
Figure 3.2: Channel headbox and discharge straighteners (upstream end of channel)
.......................................................................................................................42
Figure 3.3: Channel tailgate (downstream end of the channel) ............................42
Figure 3.4: Vertical Headwall Model (during construction) ................................44
Figure 3.5: Vertical Headwall Model (during installation) ..................................45
Figure 3.6: Vertical Headwall Model (during operation) .....................................45
Figure 3.7: Initial Mitered Headwall Model (during operation) ...........................46
Figure 3.8: Mitered Headwall Model (during installation)...................................47
Figure 3.9: Mitered Headwall Model (antivortex plate)......................................48
xv
Figure 3.10: 30degree Skew Model (during installation and operation) .............49
Figure 3.11: Sharpcrested weir used for flow measurement. The point gage and
stilling well are shown to the right................................................................51
Figure 3.12: Large tank reservoir used for weir calibration .................................52
Figure 3.13: Weir Calibration...............................................................................53
Figure 3.14: Schematic of water depth measurement system...............................54
Figure 3.15: Manometer Board and Flushing Tube..............................................55
Figure 3.16: Pitot Tube Configuration..................................................................56
Figure 4.1: Pitot tube locations .............................................................................65
Figure 4.2: Typical Water Level Distribution for Vertical Headwall Model
Configuration (Q= 2.85 cfs, unsubmerged conditions) ................................67
Figure 4.3: Typical Water Level Distribution for Vertical Headwall Model
Configuration (Q= 6.95 cfs, submerged conditions) ....................................67
Figure 4.4: Typical Water Level Distribution for Mitered Headwall Model
Configuration (Q= 2.59 cfs, unsubmerged conditions) ................................68
Figure 4.5: Typical Water Level Distribution for Mitered Headwall Model
Configuration (Q= 6.35 cfs, submerged conditions) ....................................68
Figure 4.6: Typical Water Level Distribution for 30degree Skew Model
Configuration (Q= 2.82 cfs, unsubmerged conditions) ................................69
Figure 4.7: Typical Water Level Distribution for 30degree Skew Model
Configuration (Q= 5.67 cfs, submerged conditions) ....................................69
Figure 4.8: Typical Water Level Distribution for Mitered Headwall Model
Configuration (Q= 7.94 cfs, submerged conditions) ....................................72
Figure 4.9: Water Depth Difference and Discharge relationship for Mitered Headwall
Model Configuration.....................................................................................73
Figure 4.10: Water depth difference due to SET presence ...................................74
Figure 4.11: Percent difference in water depth due to SET presence as a function of
discharge .......................................................................................................76
Figure 4.12: Legend for the box culvert performance data ..................................78
xvi
Figure 4.13: Plot of data collected for the box culvert performance ....................78
Figure 4.14: Performance curve with standard error.......................................81
Figure 4.15: Approach Minor Loss Coefficient as a function of DHW ................84
Figure 4.16: Approach Minor Loss Coefficient as a function of ??
?
?
???
?
gDA
Q ........85
Figure 4.17: Approach Minor Loss Coefficient as a function of gVb2
2
..................86
Figure 4.18: Approach Minor Loss Coefficient as a function of gVa2
2
..................86
Figure 4.19: Barrel Minor Loss Coefficient as a function of ??
?
?
???
?
gDA
Q ..............88
1
Chapter 1: Introduction
This thesis is related to Texas Department of Transportation (TxDOT) research
project number 02109 ?Evaluation of Effects of Channel Improvements, Especially
Channel Transitions, on Culverts and Bridges? conducted by a team of researchers at the
Center for Research in Water Resources (CRWR), which is part of the University of
Texas at Austin (UT). The results from earlier work are reported in ?Hydraulics of
Channel Expansions Leading to LowHead Culverts? by Charbeneau et al., (2002). The
purpose of this study is to evaluate the impact of safety end treatments (SETs) on the
hydraulic performance of culverts.
SETs have been proposed for extensive use on new culvert projects as well as
retrofitting existing culvert projects by TxDOT. Previous studies conducted by other
investigators evaluate various aspects of the effects of SETs on the hydraulic
performance of culverts, but there is not specific guidance for design engineers to
quantify the effects of SETs in the hydraulic design process for retrofitting culverts with
SETs or applying SETs to new culverts. This study attempts to address this issue. This
chapter provides an overview of the study, introduces relevant terminology and concepts,
and discusses specific goals for this research.
1.1 OVERVIEW
Culverts, safety end treatments, and the vortex phenomenon are the fundamental
components of this study. Each concept is discussed and related to the study in this
chapter in order provide the reader information on the critical elements of this study.
2
1.1.1 Culverts
A culvert is a structure that conveys surface water through a roadway
embankment or away from the highway rightofway. Culvert design involves both
hydraulic and structural aspects. A culvert must carry construction, highway traffic, and
earthen loads and allow natural stream flows to pass beneath the road to ensure adequate
drainage and preserve the structural integrity of the road. Culverts have numerous cross
sectional shapes including circular, box (rectangular), elliptical, pipearch, and arch.
Figure 1.1a shows the profile of a box culvert, which is the shape focused on in this
study. The height of a culvert opening is called the rise (D) and the width of a culvert
opening is called the span (B) as shown in Figure 1.1b.
Figure 1.1a and 1.1b: Definition sketches for a culvert
Performance equations are used to predict crosssectional area needed to pass
flows expected to result from storm events of specified recurrence intervals (i.e. the 10,
Headwall Wingwall
3
25, or 50year storm). The following factors influence culvert type selected in the
design process: fill height, terrain, foundation condition, shape of the existing channel,
roadway profile, allowable headwater, stream stage discharge, frequencydischarge
relationships, cost, and service life. This study focuses on single barrel box culverts.
Inlet control for a culvert is when the flow capacity is controlled at the entrance
by the depth of headwater, entrance geometry, and barrel shape. Outlet control for a
culvert is when the hydraulic performance is determined by inlet conditions, barrel length
and roughness, and tailwater depth. Culverts are usually designed to operate with the
inlet submerged if conditions permit, allowing for increased discharge capacity.
1.1.2 Safety End Treatments
SETs are designed and installed at inlets and outlets of culverts to reduce potential
impacts due to vehicular collision with these structures. The term SET according to
TxDOT consists of a number of particular features including sloping ends, clear zone
slopes, concrete slope paving, metal appurtenances, and safety pipe runners. For the
purposes of this report, SET refers to the safety pipe runners. SETs must be designed
with minimal size to limit interference with water flow while maintaining sufficient
strength to support a vehicle. Commonly there are two types of safety end treatments:
pipe safety grates and bar safety grates. This study focuses on pipe safety grates (Figure
1.2). It is necessary to understand the impacts of SETs on culvert hydraulics to ensure
they do not affect the functionality of the culvert.
4
Figure 1.2: Pipe grate safety end treatment for a culvert
SETs function as flow barriers and can affect the hydraulic performance of the
culvert in two main ways. First, the ?backwater? effect from the installation of SETs
may cause an increase in the upstream headwater depth and entrance head losses.
Second, SET installation may cause clogging. Both of these effects may lead to flooding
of upstream properties since the influence of SETs on headwater depth is not accounted
for in the design procedures for culverts.
1.1.3 Vortex Phenomenon
One factor affecting the regime of flow in submerged culverts with mitered
headwalls is vortex formation. A vortex is defined as the rotating motion of a multitude
of material particles around a common center (Lugt, 1983). For the purposes of this
study, an antivortex plate was developed to limit the formation of the vortex (Figure
1.3). This antivortex plate allowed for the examination of the system under conditions
with the vortex present and without the vortex present.
5
Figure 1.3: Antivortex plate developed for this study
1.2 STUDY OBJECTIVES
The objective of this study is to evaluate the hydraulic effects of SETs on culverts
through physical modeling and to provide the Texas Department of Transportation
guidance on the influence of SETs in the hydraulic design of culverts. A table of minor
loss coefficients will be provided to the Texas Department of Transportation to this fulfill
this objective. For the scope of this thesis, the investigations are limited to a single barrel
box culvert with a vertical headwall and parallel wingwalls at 0degree skew, a single
barrel box culvert mitered headwall and parallel wingwalls at a 0degree skew, and a
single barrel box culvert mitered headwall and parallel wingwalls at a 30degree skew.
Specifically, the objectives of this thesis research are:
1. To study the nature of water level difference upstream of the culvert due
to SET presence.
2. To compare the headwaterlevel discharge relationships with and without
SETs and with to show how SETs influence the hydraulics of culverts by
developing performance curves for box culverts operating under inlet
control, based on the experiments performed during this study, and
AntiVortex Plate
6
compare them to performance curves developed from earlier work
reported in ?Hydraulics of Channel Expansions Leading to LowHead
Culverts? by Charbeneau et al. published in October of 2002.
3. Provide Minor Loss Coefficients due to the presence to SETs that may be
used in design procedures.
1.3 APPROACH
Physical models of a single barrel box culvert with a vertical headwall and
parallel wingwalls at 0degree skew angle, a single barrel box culvert with a mitered
headwall and parallel wingwalls at a 0degree skew angle, and a single barrel box culvert
with a mitered headwall and parallel wingwalls at a 30degree skew angle were
constructed to collect data for conditions with and without SETs installed at the inlet end
of the culvert model. Due to the formation of a vortex under submerged inlet conditions,
an antivortex plate was developed to collect data with and without the vortex
phenomenon present in the system. Both unsubmerged and submerged culvert inlet
conditions were considered. The collected data was utilized to evaluate parameter
difference (water level, specific energy, discharge, etc.) and to calculate minor loss
coefficients.
1.4 THESIS OVERVIEW
Following this introduction, Chapter Two reviews literature relevant to this study.
Chapter Three discusses the methodology used to obtain the results including the design
and construction of the physical models and data acquisition and processing procedures.
Results are presented in Chapter Four while Chapter Five presents a summary of the
study and conclusions.
7
Chapter 2: Literature Review
Little literature was found that concerns the impact of safety end treatments on
box culvert hydraulics. This research seeks to contribute to the current body of
knowledge by addressing this issue. First, however, relevant literature and previous work
is reviewed.
2.1 ENERGY IN OPEN CHANNEL FLOW
The flow in a conduit may be either openchannel flow or pipe flow. Open
channel flow must have a free surface that is subject to atmospheric pressure (Chow,
1959). The conduit in the case of this research is a box culvert. A culvert acts as an open
channel only when the culvert is partly full, which applies to this research.
The energy equation can be written as follows in open channel flow (Chow, 1959)
Lhgvyzgvyz +++=++ 22
2
2
222
2
1
111 aa (2.1)
where z = the distance from a datum to the channel bottom, y = the water depth, gv2
2
=
velocity head, Lh = head lo ss, and a = a kinetic energy coefficient that corrects for a
nonuniform flow distribution. The acceleration of gravity is represented as the same
variable (g) throughout this entire report.
Specific energy( E ) is the energy with respect to the channel floor (i.e., z = 0) and
assuming a uniform velocity distribution (i.e., a =1) and the pressure distribution is
hydrostatic is defined as (Chow, 1959)
gvyE 2
2
+= (2.2)
In open channel flow, energy is most often dissipated via eddy losses ( eh ) caused by
changes in channel geometry and by friction losses ( fh ) caused by fluid contact with a
8
solid surface. The sum of these two terms compose the head loss ( Lh ) term found in
equation (2.1). By substituting equation (2.2) into equation (2.1) and assuming that
121 ==aa , the following equation may be written
ef hhEzEz +++=+ 2211 (2.3)
Henderson uses a rectangular channel to demonstrate the concepts of critical
depth and specific energy. He presents the equation for specific energy as
2
2
2gy
qyE += (2.4)
where q is the flow per unit width of the channel B. Assuming flow is constant, then for
a given q, one may plot the variation of E with respect to y (Figure 2.1).
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5
E (ft)
y (ft)
Figure 2.1: Specific energy curve with respect to water depth
This curve shows that there are two possible depths for a given specific energy,
considered alternate depths, except for the crest of the curve, which represents the
condition of minimum energy for a flow, also considered the critical state. On the upper
Subcritical
Critical
E = y
Supercritical
9
arm of the E curve, a flow is subcritical, which means the flow is slow, deep, and
downstream controlled. The lower arm represents supercritical conditions, which means
the flow is fast, shallow, and upstream controlled.
For the critical state, the crest of the curve, the corresponding water depth is the
critical depth, yc, which can be computed as (Henderson, 1966)
3
2
g
qy
c = (2.5)
The Froude Number (Fr) represents a comparison between inertial and
gravitational forces by a ratio between velocity and wave celerity. It can also be thought
of as the ratio between water velocity and the celerity of a wave caused by a disturbance
in the water. It is defined as follows (Henderson, 1966)
gyvFr = (2.6)
If the Froude Number is equal to one, the flow is critical. Flows for which the Froude
number is higher than one are supercritical and flows for which the Froude Number is
less than one are subcritical.
2.2 CULVERT DESIGN
A culvert is any structure under the roadway, usually for drainage, with a clear
opening of 20 feet or less measured along the center of the roadway between inside of
end walls (TxDOT Hydraulic Design Manual, 2002). Culverts are usually covered with
embankment and are composed of structural material around the entire perimeter,
although some are supported on spread footings with the streambed or concrete riprap
channel serving as the bottom of the culvert (TxDOT Hydraulic Design Manual, 2002).
Culvert design involves not only structural design component but also hydraulic design
component. For economy and hydraulic efficiency, engineers should design culverts to
operate with the inlet submerged during flood flows, if conditions permit (TxDOT
10
Hydraulic Design Manual, 2002). During culvert design the minimization of risks to
traffic, risks to property damage, and failure from floods should be given priority.
Factors to be considered in culvert design include economics, location, shape, allowable
headwater depth, outlet velocity, and traffic safety among others.
A box culvert lends itself more readily to low allowable headwater situations.
The height may be lowered and the span increased to satisfy hydraulic capacity with a
low headwater. A culvert should provide the flow it is conveying with a direct entrance
and a direct exit. Any abrupt change in flow direction at either end will retard the flow
and require a larger structure that is not economical. One approach to avoid this
additional economic expense when the centerline of the road is not perpendicular to the
flow direction is to skew the culvert to make its centerline parallel to the flow direction.
The barrel skew angle can be defined as the angle measured between the centerline of the
road and the culvert centerline. The inlet skew angle the angle measured between the line
perpendicular to the centerline of the culvert and the culvert face. TxDOT normally
considers 0 to 60degree skews in 15degree increments. Figure 2.2 illustrates the skew
angle definitions. Culverts that have a barrel skew angle often have an inlet skew angle
as well because headwalls are generally constructed parallel to a roadway centerline to
avoid warping of the embankment fill (Norman et al., 2001). The inlet skew angle varies
from 0 degrees to a practical maximum of about 45degrees, dictated by the difficulty in
transitioning the flow from the stream into the culvert fill (Norman et al., 2001). Skewed
inlets slightly reduce the hydraulic performance of the culvert under inlet control
conditions (Norman et al., 2001).
For the purposes of this research, skew angle was studied at 0degrees and 30
degrees. As time permits, analysis of a model system at a skew angle of 45degrees and
60degrees may be performed.
11
Figure 2.2: Skewed culverts (taken from Norman et al., 2001)
2.3 CULVERT HYDRAULICS
Culvert hydraulics is an important part of this project and the definition and
terminology is presented in Section 1.1.1 and Section 2.2. The rest of this section
introduces culvert hydraulics and performance equations. Overall culvert hydraulics is
complicated because the flow is controlled by many factors including the inlet geometry,
slope, size, roughness, approach conditions, and tailwater conditions.
From the hydraulic point of view, the defining feature of a culvert is that it may or
may not run full, and this distinction is often of great practical importance (Henderson,
1966). When both the inlet and outlet of a culvert are submerged, the culvert will flow
full and can be analyzed as pressurized pipe flow, which is an uncomplicated form of
analysis. However, sometimes the inlet or outlet may be unsubmerged, in which case the
analysis process is different. When both the inlet and outlet are unsubmerged, the culvert
12
operates as an open channel. The ranges of conditions under which a culvert can operate
make hydraulic analysis and design challenging. However, considerable guidance may
be found in technical literature, since culvert performance has been studied extensively.
Another factor that must be considered when analyzing or designing a culvert is
whether the culvert performance is inlet or outlet controlled. Inlet control means the
culvert barrel is capable of conveying more flow than the inlet will accept, and is thus
controlled by the inlet. Outlet control means that the culvert is capable of accepting more
flow than it can convey at the outlet.
Under inlet control, the control section is located just inside the entrance. At or
near this location, the flow regime changes from subcritical to supercritical flow and
critical depth occurs. In this case, only the headwater depth and the inlet configuration
affect the culvert performance. Inlet configuration factors include the inlet area, the
barrel shape, and the inlet edge configuration (Herr and Bossy, 1965). The inlet area may
be modified by the use of beveled or grooved inlets, which may improve culvert
performance by decreasing entrance losses and increasing effective inlet area.
Under outlet control, in addition to headwater and the inlet configuration, the
barrel length, barrel roughness, barrel slope, and tailwater depth determine culvert
performance. The design procedures and equations differ for inlet and outlet control. In
design, both conditions are analyzed separately, and that which predicts the largest
headwater value is assumed to govern.
This research involves the inlet control case of culvert hydraulics, which is the
most applicable for the design of highway culverts with limited culvert rise and
unobstructed downstream area. The terrain often dictates the need for a low profile due
to limited fill height or potential debris clogging (TxDOT Hydraulic Design Manual,
2002).
13
Plotting headwater depth or elevation versus discharge can develop performance
curves for any given culvert. This is useful in evaluating the hydraulic capacity of a
culvert for various headwater depths.
2.3.1 Inlet Control Unsubmerged Case
It is known that water achieves critical conditions when flowing through an
unsubmerged culvert entrance. Therefore, the flow rate passing through such a system
may be computed as follows for a rectangular culvert (Henderson, 1966)
ccvyBQ = (2.7)
where B = the culvert width, cy = critical depth, and cv = the critical velocity. Since the
Froude number at critical conditions is equal to one, the following expression can be
written
1==
c
c
c gy
vFr (2.8)
and
cc gyv = (2.9)
Substituting equation (2.9) into equation (2.7) for Q yields
23cygBQ = (2.10)
Henderson presents
cc Ey 32= (2.11)
where cE = specific energy at critical depth. Therefore, Q may be computed as follows
23
23
3
2
cEgBQ ??
??
?
?= (2.12)
When the approach velocity head is negligible, the specific energy may be
replaced by the flowdepth, which is a common assumption. Using these assumptions
(critical flow conditions and negligible velocity head) Henderson (1966) presents the
14
following performance equation for inletcontrolled, unsubmerged culverts (when H/D is
less than 1.2)
HgHBCQ b 3232= (2.13)
where B = the width of the culvert and Cb = a coefficient expressing width contraction in
the flow entering the culvert inlet. Henderson states that if the vertical edges are rounded
to a radius of 0.1 B or more, that there is no effect of the side contraction and Cb = 1. If
the vertical edges are left square Cb = 0.9.
Based on the studies performed by the National Bureau of Standards (now NIST),
the Bureau of Public Roads (now FHWA) developed a series of performance curves and
nomographs for calculation of culvert performance under both inlet and outlet control for
many commonly used entrance configurations and culvert materials. For unsubmerged
inlet conditions, FHWA presents the following relationship for the performance curve
(see Normann et al., 2001)
SDA QKDEDHW
M
c 5.0
5.0 ???
?
??
?+= (2.14)
where, HW is the headwater depth above inlet invert (feet), D is the interior height of
culvert barrel (feet), Ec is the specific (head) energy at critical depth (feet), Q is the
culvert barrel discharge (cubic feet per second ), A is the full cross sectional area of
culvert barrel (feet2), S is the culvert barrel slope (feet/feet), and K and M are constants.
For 0degree wingwall flares, the case of this research, the coefficients are K = 0.061 and
M = 0.75 (Normann et al., 2001). These coefficients are the same as the previous
research with 90 degree wingwall flares. This equation was used to develop nomographs
to predict culvert performance, and in the nomograph development a slope of 0.02 was
assumed (Herr and Bossy, 1965).
15
2.3.2 Inlet Control Submerged Case
When the culvert entrance is submerged, then the culvert acts either as an orifice
(Normann et al., 2001) or as a sluice gate (Henderson, 1966). To represent the culvert
performance as an orifice, the performance equation takes the form
?????? ?== 222 DHgDBChgACQ dd (2.15)
In equation (2.15), Cd is a discharge coefficient that must be evaluated for different inlet
conditions, A is the culvert inlet full area, h is the head on the culvert centroid, and H is
the upstream headwater. The discharge coefficient is approximately equal to Cd = 0.6 for
squareedge entrance conditions. The equation resulting when the culvert acts as a sluice
gate is similar. For a submerged culvert, the performance equation is (Henderson, 1966)
( )DCHgDBCQ cc ?= 2 (2.16)
In equation (2.16), Cc is a contraction coefficient that has a value of Cc = 0.6 for sharp
edged entrance conditions and Cc = 0.8 for rounded soffit and vertical edges.
For submerged inlet conditions, the data from experiments performed by NBS for
the FHWA have been fit to an equation of the form
SYDA QcDHW 5.0
2
5.0 ?+??
?
??
?= (2.17)
In equation (2.17), c and Y are coefficients that depend on the culvert inlet conditions.
For a sharpedged inlet with 0degree wingwalls, c = 0.0423 and Y = 0.82. However, in
the previous research the wingwalls were 90 degrees so the coefficients were c =0.0420
and Y= 0.80. This would increase the headwater depth for the same discharge rate.
16
2.3.3 Entrance Loss Coefficients
Calculation of the entrance head loss coefficient is a main objective of this
project. The energy equation at the inlet can be written as (converted from equation in
TxDOT Hydraulic Design Manual, 2002),
i
i
e
ia H
g
VC
g
V
g
VHW ++=+
222
222
(2.18)
where HW = headwater depth, aV = the approaching velocity to the culvert entrance, iV
= the velocity at the culvert entrance, eC = the entrance loss coefficient, and iH = the
depth of hydraulic grade line just inside the culvert at the inlet.
Then eC can be solved as following,
g
V
HgVgVHW
C
i
i
ia
e
2
22
2
22
??+
= (2.19)
If all the parameters on the right hand side are measured, the head loss coefficient
can be calculated. A model culvert approach channel is generally much wider than the
model culvert cross section (which applies to the physical model in this research), so the
approach velocity head can be neglected in equation (2.19).
2.4 VORTEX PHENOMENON
A vortex is defined as the rotating motion of a multitude of material particles
around a common center (Lugt, 1983). This definition is based on the pathlines of
material particles. Most vortices in nature have a ?spatial? structure, which means the
pathlines are not perpendicular to the axis of rotation, but have a component parallel to it.
An example of a spatial vortex is the spiral vortex shown in Figure 2.3, which is similar
to the vortex seen in the course of this research. Vortices may form in water, air, gas,
plasma and the earth. Vortices in nature can be very small or have extreme dimensions.
17
They can be generated by density and temperature differences, through friction, through
the action of electrodynamic forces or through gravity (Lugt, 1983). Vortices in nature
and technology can be invisible (Lugt, 1983).
Figure 2.3: Spiral vortex (from Lugt, 1983)
For the purposes of this explanation, a culvert can be thought of as a horizontal
rectangular suction slot. Intake and discharge vortices can be observed in symmetrical
geometric surroundings. For instance, a vortex may develop at or near a rectangular
intake, which was similar to the case of this research (Figure 2.4). Gordon (1970) studied
vortex formation by observing vortices at existing hydroelectric intakes and determined
four factors that influence the formation of a vortex in these situations: the geometry of
the approach flow relative to the intake, the flow velocity at the intake, the size of the
intake, and the submergence of the intake. These factors can result in creating angular
momentum in a flow. The angular momentum of a flowing particle is proportional to the
vector crossproduct of its velocity and its distance from the center about which it is
rotating (Lugt, 1983).
18
Figure 2.4: Intake vortex (from Lugt, 1983)
The conservation law of angular momentum explains why the high angular
velocities of vortices can occur. For simplicity, consider a single particle as it is drawn
towards the rectangular suction slot with a tiny initial angular velocity located about 10
centimeters from the opening ending up 0.1 centimeters from the opening. As it is drawn
towards the opening it must increase its azimuthal velocity at a rate inversely
proportional to the distance from the opening in order to preserve its angular momentum.
For example, at a distance 0.1 centimeters from the center of rotation the particle will
have increased its velocity 100 times. Since the angular velocity increases with the
square of the distance, the corresponding angular velocity will have increased 10,000
times. This increase in velocity makes the presence of a vortex more apparent (Lugt,
1983).
Another possible explanation of the vortex is related to the contraction of the
streamlines behind an edge. In the case of this research, the edge would be the lip of the
culvert barrel and the mitered headwall interface. Under submerged conditions there is a
separation of flow at the entrance to the box culvert and also a free surface present at the
water surface. Cavitation, formation and subsequent collapse of vapor bubbles in a
flowing fluid, is occurring around box entrance due to the zone of separation at the
19
entrance to the box culvert. Velocity is increases from less than ~1 feet per second to
~14 feet per second due to the constriction in area (the entire channel to the box culvert)
which is accompanied by a decrease in pressure in accordance with Bernoulli's equation.
Due to the curvature of the streamline there is a loss of piezometric head. Due to the
significant piezometric gradient in the normal direction (0 atmosphere to 1 atmosphere
over 1 foot of water depth) the centripetal acceleration term ( rv
2
) of equation (2.20)
increases and the vortex is formed (Bos, 1989).
dnrvP ?=?
2
1
2
r (2.20)
The spiral motion of the vortex allows air to be entrained and a drop in the free surface
occurs. This drop in free surface allows for the centripetal acceleration of vortex and
reinforces the air entrainment into the jet. This explanation is illustrated in Figure 2.5.
Figure 2.5: Vortex Formation
A literature search was conducted to determine how a vortex might affect the
performance of the prototype box culvert studied in this research. As will be discussed in
Section 4.1.2, a vortex was observed for the mitered headwall 0degree skew angle model
20
configuration when it was operated under submerged conditions. Most of the literature
found discusses the vortex effects on pipe culverts or hood inlets. However, it is logical
to apply some of these findings to the box culvert. Vortices are commonly observed
phenomenon of culvert hydraulics. Once the culvert entrance is submerged and full flow
is established a vortex often forms near the entrance, especially if the water level over the
top of the entrance is small. This vortex can be quite substantial and air is often aspirated
into the barrel. Frequently the vortex is cyclic or irregular in nature, alternately forming
and disappearing. One consistent finding is that an airentraining vortex may cause the
head and discharge relationship to vary in a random manner (Blaisdell, 1966 and French,
1955).
Blaisdell (1966) makes the following statements concerning vortices in reference
to reentrant and hood inlets:
Vortices at culvert inlets exert a considerable influence on the performance of
culverts. The magnitude of their effect can be seen by referring to Figure 3
(Figure 2.6 in this report).
Vortices have the greatest adverse effect on the culvert capacity during pipe
control with low inlet submergences. However, vortices do occur during orifice
control. Vortices form over the inlet; air is admitted to the culvert through the
vortex core; the air replaces water in the culvert and reduces the discharge. The
quantity of air admitted to the culvert varies with the vortex intensity. Because
the intensity of the vortex is no t constant, the effect of the vortex on the culvert
capacity varies with time.
Surface vortices that do not have an air core may have little effect on the culvert
capacity. At the other extreme, an airentraining vortex can reduce the capacity
from that represented by the pipe control to that represented by the orifice control
curve. Or, the vortex can produce a culvert capacity anywhere between the
orifice and pipe control curves. The shaded area in Fig. 3 (Figure 2.6 in this
report) indicates the approximate area of effect of vortices. An important fact is
that the actual discharge of the culvert at any given time cannot be determined if
airentraining vortices exist.
It is not necessary to tolerate vortices and their uncertainties. Vortices can be
controlled by simple devices. The addition of an antivortex device to a culvert
21
inlet can change the indeterminate headdischarge relationship to a dependable,
unique relationship.
Figure 2.6: Effect of Vortices on the HeadDischarge Relationship for a Culvert on a
Steep Slope (from Blaisdell, 1966)
The Kranc et al. (1990) report, which studied the hydraulic performance of culvert
grates for the Florida Department of Transportation, contains a section on the influence of
vortex formation. Kranc et al. studied vortex formation but the actual influence of the
vortex was not determined, and consistent with most of the literature, they focus on pipe
culverts. It was concluded by Kranc et al. that it was difficult to see any reduced
performance due to the vortex but this could be a result of the scale of the facility the
experiments were performed. However, it was stated that the circulation pattern might
have an influence on bank erosion and on the accumulation of debris.
22
Other researchers have examined vortex suppressors. One method incorporates a
vertical plate oriented along the axis of the barrel protruding from the entrance treatment,
which is a very effective method to reduce the vortex (Blaisdell, 1960 and Kranc et al.,
1990). Kranc et al. (1990) stated
Experiments were conducted to determine the effect of the entrance vortex on the
head discharge characteristic using the flat plate aligned with the flow?The data
show that either inlet or outlet control can be maintained and that little difference
in performance is observed when compared with the results when a vortex is
allowed to form. Operation in transition zones between inlet and outlet control
modes have been observed. It appears that one effect of the plate is to stabilize
the mode of operation and may limit sudden jumps from inlet to outlet control.
Another possible way to eliminate the vortex phenomenon could be to
significantly raise the tailwater datum, which elevates both the headwater and the
tailwater (Kranc et al., 1990). This corresponds to statements made earlier by Blaisdell
(1966) in relation to the vortex not being present at significant headwater depth. In
review of Figure 2.6, it seems that the area of effect of vortices would be from DHW
ratios of approximately 1.2 to 3.0. The maximum value of DHW for the mitered headwall
model configuration of this thesis research was less than 2.0.
2.5 TEXAS DEPARTMENT OF TRANSPORTATION SET DESIGN STANDARDS
SET standards issued by the Bridge Division of Texas Department of
Transportation will be reviewed in this section. This thesis research focuses on pipe
safety grates. These design standards were utilized when developing the SET model
component.
There are two kinds of drainage, cross drainage and parallel drainage. Cross
drainage means the traffic is across the flow and parallel drainage means the direction of
traffic is parallel to the direction of the flow. Correspondingly, there are two kinds of
installation of SETs, which are shown in Figure 2.7 (Safety End Treatment Standards,
23
TxDOT, 2000). Only the cross drainage SETs were studied in this research. There are
three main parts of safety grates: cross pipe, pipe runner, and bottom anchor pipe.
Figure 2.7: Typical installation of SETs for cross drainage and parallel drainage
The cross pipe is flush with the top of the wingwall that runs across the culvert.
There are two options for the construction of cross pipe. The first option is constructing
it discontinuously, with one segment for each barrel and sleeve pipes serving as
connections outside the wingwalls. The other alternative is making the cross pipe
continuous across the inside wingwalls, so that the sleeve pipes are omitted. The total
length of the cross pipe should be about the same as the culvert width, which can be seen
from Figure 2.7. The size of cross pipe should be the same diameter as that of the pipe
runner (diameter determination explained below).
The slope of the pipe runner is the same as the slope of the wingwalls
(embankment), and should be no steeper than 3:1 (horizontal: vertical). Recommended
values of slope are 3:1, 4:1, and 6:1 for SET installation. The length of the pipe runners
can be determined from the wingwall length (height) and the slope. All the pipe runners
are equally spaced based on the centerline of each pipe runner. The maximum allowable
pipe runner spacing ranges from 2.5 feet maximum to 2.0 feet minimum measured from
24
the centerline of the pipe runners. The number of pipe runners is determined as a
function of maximum allowable pipe runner spacing. The size of the pipe runner should
be as shown in Table 2.1 (Safety End Treatment Standards, TxDOT, 2000).
Table 2.1: Standard pipe sizes and maximum pipe runner length
STANDARD PIPE SIZES & MAXIMUM PIPE RUNNER LENGTH
Pipe Size Pipe O.D. Pipe I.D. Max Pipe Runner Length
2" STD 2.375" 2.067" N/A
3" STD 3.500" 3.068" 10'0"
4" STD 4.500" 4.026" 19'8"
5" STD 5.563" 5.047" 34'2"
There are two options to construct the bottom anchor pipe as shown in Figure 2.8
(modified from Safety End Treatment Standards, TxDOT, 2000). For the development of
the SET model component used in this research option 2 was selected.
Figure 2.8: Bottom anchor pipe installation options
25
2.6 IMPACTS OF SETS ON CULVERT HYDRAULICS
The impacts of SETs on the hydraulic performance of culverts is analyzed based
on drag force in the following sections. Minor losses and previous studies concerning the
effects of SETs will be reviewed as well.
2.6.1 Drag Force
Any solid body in a flow has a drag force exerted on it by the fluid and causes
energy losses in the flow. The drag force caused by the SETs in this research and its
relationship with the water level difference upstream are discussed below.
2.6.1.1 Definition of Drag Force
Drag forces on SETs cause energy loss in the flow and consequent water level
increase upstream of the obstacle for subcritical flows. For flows with no free surface,
the total drag on a body is the sum of the friction drag and the pressure drag
pfD FFF += (2.21)
where Ff is due to the shear stress on the surface of the object and Fp is due to the
pressure difference between the upstream and downstream surfaces of the object.
For open channel flow, the drag consists of three components. First, the surface
drag, which is due to the shear stress acting on the surface of the SET. Second, the Form
drag, which is due to the difference between the higher pressure on the upstream side of
the SET (where the flow impacts on the SET and where the depth is greater) and the
lower pressure in the wake or separation zone on the downs tream side of the SET. Third,
wave drag, which is due to the force required to form the standing surface waves around
a SET.
The drag force ( FD ) can be expressed as (Roberson and Crowe, 1993)
SET
2
A2VrDD CF = (2.22)
26
where CD = drag coefficient, ? = fluid density, ASET = projected area of the submerged
part of a SET onto a plane perpendicular to the flow direction, and V = flow velocity.
The functional dependence of SET drag coefficients for rectangular channels can
be written as
???
?
???
?=
y
B,
B
BFr,,I,
B
k,Re shape, SETfC SETSET
T
SET
SET
SETD (2.23)
where Re SET = SET Reynolds number, which is given by
n
SET
SET
BV *Re = (2.24)
where V = flow velocity, BSET = width of SET perpendicular to the flow, ? = kinematic
viscosity, kSET = roughness of SET surface, IT = turbulence intensity in the approach
flow, Fr = Froude number, which is given by
gy
VFr =
(2.25)
where y = flow depth.
When Reynolds number (Re) is sufficiently high, the form drag becomes the
major component of the total drag force and DC becomes virtually independent of Re.
Under such conditions the pressure distribution is the primary cause of drag and the drag
coefficient can be obtained by integrating the dimensionless pressure coefficient, 'p ,
defined as (Henderson, 1966),
2
0
0
2
1' V
ppp
r
?= (2.26)
over the projected area of the solid body. In equation (2.26), p is the pressure on the
body surface and 0p is the freestream pressure on the body.
27
2.6.1.2 Relationship between Drag Forces and Upstream Water Level Difference
The water level difference (?h) upstream of the culvert with and without the SETs
and the flow conditions are simplified and schematically illustrated in Figure 2.9 (Xia,
2003).
Figure 2.9: Simplified flow conditions near the culvert with and without SETs (modified
from Xia, 2003).
Equation (2.27) can be developed to give the relationship between the drag force and the
water level difference. A detailed explanation of this development can be found in
Section 2.4 of ?Impacts of Safety End Treatments on Culvert Hydraulics? by Jun Xia
(2003).
?
?
?
??
? ?++
?+?= )2()( 111
2 h
hgBhhBh QhFD r (2.27)
where r = the fluid density, ?h = water level difference upstream of the culvert with and
without the SETs, Q = discharge, B = width of the channel, 1h = water level without SET
model component present, and g = acceleration of gravity.
x
Culvert
Safety Grate
FD
1 2
h2
h1
?h Water Surface without
SETs
y
28
2.6.2 Minor Losses
In general, when a flow encounters changes in the shape configurations in a flow
passageway, form losses are imposed on the flow in addition to those resulting from
surface frictional resistance. All form losses in turbulent flow through conduits can be
expressed in the general form as (Zipparro and Hasen, 1993)
g
VKH
eL 2
2
= (2.28)
where LH = form loss and eK = coefficient of form loss. The loss in the flow energy
caused by the SETs in this research can be viewed as minor losses, which under some
circumstances, can be much smaller than other losses and may be neglected. However,
for many conditions, form loss can be the major resistance to flow.
2.6.3 Previous Studies of SETs
Most of the previous SETs studies are related to pipe or circular culverts, not box
culverts. Circular culverts can behave differently than box culverts.
Some observations on the hydraulic performance of safety grates were reported
by S. C. Kranc, M. W. Anderson and A.A. Villalon in June of 1989 and November of
1990 to the Florida Department of Transportation and U. S. Department of Transportation
Federal Highway Administration. Their investigation was restricted to circular culverts
with nine types of end sections. Both bar safety grates and pipe safety grates were tested.
Headwater elevationdischarge correlations of openended and gratedended culverts
were compared. It was concluded that, in general, the additional losses incurred by
adding the grate on the performance of inlet endsection treatment were small. However
in some cases, especially for culverts with box endsections, the culvert capacity under
weir control could be reduced. In other cases, such as the mitered endsections with
grates, the presence of the grate seems to accelerate the transition to outlet control.
29
However, it was not recommended that designs rely on this effect. Overall the flared
endsection had the best performance. It was also observed that the bar safety grates had a
greater negative effect on the culvert performance than the pipe safety grates but the style
of the grate matters only slightly. Regarding clogging, it was found that the effect of inlet
blockage was highly variable. Generally, modest accumulations could be tolerated, but a
substantial build up of debris could lead to added losses under outlet control and reduced
discharge coefficients for inlet control. A 10% to 20% blockage may not justify cleaning
but 50% blockage may demand immediate attention. Outlet endsection treatments were
not found to be particularly critical, assuming that blockage with debris does not occur.
Vortices did develop and a vortex suppressor was studied. It was determined that the
reduction of the vortex did not have a noticeable effect on performance, at least over the
range of data for the study.
Another investigation on the hydraulic performance of culverts with safety grates
was conducted by University of Texas at Austin for the Texas State Department of
Highways and Public Transportation in 1983. Box culvert and pipe culvert models were
studied. The slope of the headwalls for both culverts was fixed as 4 to 1. The box
culvert was tested with both bar grates and pipe grates, and the pipe culvert was tested
with only pipe grates. It was found that for box culvert, the effect of the pipe safety
grates was negligible while there was an increase in headwater depth for bar safety
grates. When comparing the entrance head loss coefficients, the pipe grates showed little
or no effect while the bar grates showed a more consistent increase in entrance head loss
coefficient for all flow regimes tested for culvert slopes of 0.008 and 0.0108. When
comparing the headwater depth and discharge relationship, pipe grates had no effect on
the headwater depth; however, bar grates caused an increase in headwater depth. For the
pipe culvert, the pipe safety grates had a greater effect on the culvert performance
30
because the entrance loss coefficient was substantially increased and more significant at
higher discharges. It was also concluded that the entrance head loss coefficient varied
with culvert slope, headwater depth, tailwater depth, and/or discharge. With regard to
clogging, it was stated that the efficiency of a box culvert was substantially decreased
when clogging was greater than 45%.
In ?Model Study of Safety Grating for Culvert Inlet? by Richard Weisman (1989)
a 1:10 scale model of a prototype 15 feet wide culvert that has a bottom circular arc,
giving a height of 5.5 feet in the center and 5.0 feet at each edge, with 0degree
wingwalls (perpendicular to the flow) and a distance of 30 feet between each wingwall
was studied. This configuration allows for 7.5 feet of headwall on each side of the
culvert barrel in the prototype. The safety grating studied was parabolic in the vertical
plane and consisted of 96 bars with 3.75 inch spacing and a 1.1 inch diameter in the
prototype. It was concluded that the changes measured in headwater were not significant.
At high flows the water surface contains waves and other disturbances that made
measurements quite difficult. It was recommended that wider spacing with smaller bars
would cause even smaller increases in water surface elevation. It was also stated vortices
formed at the corners where the wingwall meet the headwall at high flows in which the
headwater depth exceeds the culvert height. The vortices appeared and dissipated
periodically and typically alternated from one side to the other. The presence of the grate
had no effect on the occurrence of vortices.
In ?Hydraulics of Safety End Sections for Highway Culverts? by Bruce M.
McEnroe (1994), pipe culverts with end sections designed specifically for collision safety
were studied. Scale models of 10 safety end sections were studied. The end sections
tested were the parallel and crossdrainage versions of the 24, 36, 48, and 60inch end
sections with 6:1 slopes and the 60inch end section with a 4:1 slope. It was concluded
31
the measured inletcontrol rating curves for end sections of the same size were virtually
identical, regardless of the slope of the end section and the arrangement of the safety
bars. Therefore, the differences in the designs of safety end sections did not affect their
performance under inlet control. It was concluded that the effect of safety end sections
could cause some favorable hydraulic characteristics because they force the inlet to flow
full whenever the inlet was submerged even if it was hydraulically short. In cases where
a culvert with a standard end section would not flow full, a safety end section would
provide superior hydraulic performance. The entrance loss coefficients for safety end
sections were only slightly higher than for standard manufactured sections. Therefore,
installation on existing highway culverts to meet collisionsafety criteria without
significantly reducing their hydraulic capacities could occur.
2.7 SHARPCRESTED WEIR
There are a variety of discharge measurement structures available such as weirs,
flumes, and orifices. There are different forms of weirs, such as a normal sharpcrested
weir, parabolic sharpcrested weir, triangular sharpcrested weir, triangular broadcrested
weir, etc. The one selected for the purposes of this research was a normal sharpcrested
weir, also considered a ?thinplate? weir. In general, sharpcrested weirs will be used
where highly accurate discharge measurements are required (Bos, 1989). A sharpcrested
weir is usually comprised of a thin plate mounted perpendicular to the flow. The basic
theoretical development of weirs is based on the assumption that the pressure above and
below the nappe is atmospheric.
Measurement of discharge using weirs is based on a fact that a significant barrier
in an open channel may act as a control, and there is a consistent relation between the
head and the discharge at the control point. The geometry of the barrier determines both
the discharge coefficient and the exponent in the equation (Rouse, 1949)
32
nCLhQ = (2.29)
where Q is the discharge, C is the discharge coefficient, L is the length of the crest, h is
the head of fluid above the weir crest upstream from the weir, and n is the exponent
coefficient. The head of the fluid is usually measured by point gage or Pitot tube at a
sufficient distance upstream from the crest to avoid effects of surface curvature near the
weir crest which could lead to under estimation of the head, and therefore, the discharge.
This distance is usually at least 3 times the value of the head above the weir.
A normal sharpcrested weir is generally a crest plate of metal with a top width of
1/16 to 1/8 of an inch, a bevel on the downstream side of the top, and extends the full
width of the channel. These are the conditions of the weir installed at CRWR for the
purpose of this research. Figure 2.7 shows the elevation view of a normal sharpcrested
weir.
Figure 2.7: A normal sharpcrested weir in elevation view
The equation for this kind of weir can be written as (Rouse, 1949)
23232 LhgCQ d= (2.30)
There are different expressions for the coefficient Cd, among which the 1913 Rehbock
formula is typical,
33
)(305108.0605.0 fthwhCd ++= (2.31)
where w is the weir height. Normally, the last term in the equation is very small and
omitted. In application, the value for the constant in the equation may be slightly
different from 0.605.
2.8 PHYSICAL MODELING
Often in hydraulic engineering studies, physical models are employed to study
phenomena that are difficult to model mathematically. Experimental study is a way to
examine complex fluid flow phenomena. This method is based on the principles of
hydraulic similitude, which is a known and usually limited correspondence between the
behavior of a physical model and that of its prototype (Warnock, 1950). Complete
similitude requires the physical model be geometrically, kinematically, and dynamically
similar to the prototype. The following relationships were developed in or, generalized in
form (Warnock, 1950).
The fullsized object of interest is called the prototype, represented by subscript p,
whereas the scaled down version is called the model, represented by subscript m. The
length ratio of prototype to model is called the geometric length ratio pmr LLL := . It
makes this ratio must be consistent througho ut the model to maintain similarity of linear
dimensions. This consistency is called geometric similarity.
Kinematic similarity is similarity of motion. It exists between two states of
motion if the ratios of the components of velocity at all homologous points in two
geometrically similar systems are equal. The velocity component in prototype is piv )( ,
the velocity component at the homologous point in the physical model is miv )( , and then
the scale ratio is pimir vvv )(:)()( = .
34
In order for the model to behave as the prototype, the forces in the model and the
prototype must also be the same, which is known as dynamic similarity. For the purposes
of this hydraulic study, dynamic similarity means that the Froude Numbers of the model
and prototype must be equal as shown in equation (2.32).
m
m
p
p
gy
v
gy
v = (2.32)
From this equation, one may solve for the ratio of velocities as follows:
m
p
m
p
L
L
v
v = (2.33)
or rr LV = (2.34)
Therefore, the flow ratio can be compute as
2rrr LVQ = (2.35)
Substituting equation (2.25) into (2.26) yields
25rr LQ = (2.36)
or
25
???
?
???
?=
m
p
m
p
L
L
Q
Q (2.37)
In this way, various characteristics between the model and prototype can be related. In a
situation where viscous forces are dominant, the Reynolds number must be considered to
achieve dynamic similarity.
35
Chapter 3: Methodology
The objectives of this study are to evaluate the hydraulic effects of SETs on
culverts through physical modeling and to provide the Texas Department of
Transportation (TxDOT) guidance on the influence of SETs in the hydraulic design of
culverts. This chapter describes the physical model as well as the equipment and
experimental methods used to measure discharge and water depth in this study.
3.1 PHYSICAL MODEL DESIGN
The culvert and SET models were designed using the physical model similitude
principles presented in Section 2.8 and the TxDOT SET standards presented in Section
2.5. As concluded in that section, equation (2.37) can be used to relate discharges
between a prototype and model. The prototype for this research is a single barrel box
culvert with a 6 foot rise and a 10 foot span with the SET dimensioned in accordance
with TxDOT specifications for a 3:1 slope.
3.1.1 Culvert Model Design
Henderson (1966) states the critical flow rate passing through a culvert with a
rectangular cross section may be computed as follows:
ccvyBQ = (3.1)
where B is the culvert width, cy is critical depth, and cv is the critical velocity. The
Froude number at critical condition ( cFr ) is equal to one, therefore the following
expression can be written
1==
c
c
c gy
vFr (3.2)
and
cc gyv = (3.3)
36
Substituting into the equation for Q gives
23cygBQ = (3.4)
Henderson (1966) presents the relationship between the specific energy ( cE ) and the
water depth ( cy ) at critical condition as
cc Ey 32= (3.5)
Therefore, Q may be computed as follows
23
23
3
2
cEgBQ ??
??
?
?= (3.6)
Due to the absence of downstream obstructions, the culvert is assumed to be inlet
controlled and critical flow should occur near the culvert entrance (Henderson, 1966). It
is assumed that energy losses are insignificant and the allowable headwater elevation is
equal to the height of the barrel. Therefore, the specific energy at critical condition ( cE )
is 6 feet for the prototype. By solving equation (3.5) the water depth at critical condition
( cy ) is 4 feet for the prototype. By solving equation (3.3) the velocity at critical
condition ( cV ) is 11.4 feet/second for the prototype.
The span of the culvert (B) is 10 feet for the prototype. Therefore, the design
discharge is Q = 10 ft * 4 ft * 11.4 ft/s = 454 ft3/s, which is the discharge for the
prototype ( pQ ). The maximum discharge available for the model, mQ , at the Center for
Research in Water Resources (CRWR) is approximately 8 ft3/s. The modeltoprototype
scale ratio can be determined using equation (3.7), previously developed in Section 2.8.
19.04548
5/25/2
25 =?
?
??
?
?=
???
?
???
?==
p
m
rr Q
QLQ (3.7)
Thus a scale of 1:6 was used in this research. The prototype dimensions are 6 feet wide
and 10 feet high and the corresponding model dimensions are 5/3 feet wide and 1 foot
high.
37
The project started with the simplest case, a culvert model with a vertical
headwall and parallel wingwalls at a 0degree skew. A culvert model with a mitered
headwall and parallel wingwalls at a 0degree skew was investigated next. The third
culvert model investigated had a mitered headwall and parallel wingwalls at a skew angle
of 30degrees. As time permits, a 45degree and 60degree skew angles may be
investigated in continuing research.
The wingwall and embankment slope in this research was 3:1 (S=3). In the
vertical headwall configuration model the heights of the wingwalls ( wH ) were equal to
the height of the culvert opening, 1 foot. The length of the wingwalls were determined
by
ftftSHL ww 33*1* === (3.8)
For the mitered headwall configurations the same principal was applied to calculate
wingwall length. To obtain the mitered headwall configurations, the 3:1 slope was
extended above the height of the culvert opening and ranged in length from 1.5 to 4.5 feet
depending on the desired level of submergence. In all models the wingwalls had a 0
degree flare.
The width of the model channel is 5 feet. The lengths of the embankment slopes
for the model were 5/3 feet. This was calculated by taking the width of the channel,
subtracting the width of the culvert opening, and dividing that value by two.
Embankments with different slopes (4:1 or 6:1) may be considered as time permits.
For the culvert model with a 30degree skew angle the above principles were
applied but the model was developed at a 30degree orientation to the flow of water in the
channel.
The various culvert models utilized for this thesis research are described in
Section 3.2.3.
38
3.1.2 Safety End Treatment Design
The SET models were designed in accordance with the TxDOT Standards
discussed as in Section 2.5. The length scale of 1:6 was applied to the SET models as
determined by the culvert model design procedures discussed in Section 3.1.1. To
calculate the runner length and diameter for the model, the prototype dimensions must be
determined first.
The height of the wingwall is 6 feet and the length of the wingwall is 18 feet for
the prototype. To establish the pipe runner length ( cP ) equation (3.9) was modified from
the TxDOT specifications. End of pipe clearance is not an issue in the SET model
components constructed for this research. Therefore, this term can be excluded from the
original TxDOT equation. K1 represents the constant value based on slope (3:1 in the
case of this thesis research) from the TxDOT specifications.
ftftKLP wc 97.18)054.1*18()1*( === (3.9)
From Table 2.1, the 4 inch standard pipe with an outer diameter of 4.5 inches and
an inner diameter of 4.026 inches should be used based on the maximum pipe runner
length of 18.97 feet. The maximum allowable spacing range is 2.5 feet maximum to 2.0
feet minimum measured from the center line of the pipe runners. The prototype culvert
width is 10 feet, so the number of pipe runners required is 4 based on the maximum
allowable spacing. According to TxDOT specifications the cross pipe should be the same
size as the pipe runner.
Therefore, for the corresponding physical model, there should be four pipe
runners spaced every four inches on center connected to a cross pipe, with an outer
diameter of 0.75 inches and an inner diameter of 0.67 inches. The length of the pipe
runners should be 3.16 feet long.
39
The various SET models utilized for this thesis research are described in Section
3.2.3.
3.2 DESCRIPTION OF THE PHYSICAL MODEL
Figure 3.1 details the layout of the physical model. The channel is divided into
three sections to be able to better describe water flow through the channel. These
sections are described in detail in Section 3.2.2. The upstream section leads from the
headbox shown to the left of the figure downstream to the model section. The model
section of the channel contains the culvert and SET models, described in Section 3.2.3.
The third channel section is the downstream section and contains the return channel
contains the sharpcrested weir and allows the water to return to the distribution reservoir
creating a recycled water system.
40
Figure 3.1: Schematic view of the physical model
3.2.1 Water Supply
The water used for the physical model experiments is pumped into the outside
channel through a water distribution system from a halfmillion gallon reservoir located
outside the CRWR laboratory. Two water supply lines lead from the distribution
reservoir to the selected destination, each with its own pump. Valves located throughout
the system are used to control the magnitude of channel discharge and also to direct the
discharge to different destinations in the distribution system. There are three indoor
destinations, the out door channel destination, and the discharge measurement tank
destination. After flowing through the destination, the water is discharged to a return
Upstream Section
n
Headbox with Flow
Straighteners
Return
Channel
Model Section Downstream Section
Water
Reservoir
Sharpcrested Weir
Point Gage &
Stilling Well
Discharge
Measurement
Tank
Tailgate
Return
Channel
41
channel, which allows the water to return to the distribution reservoir creating a recycled
water system.
3.2.2 Outside Channel
The outside channel is rectangular, with a width of 5 feet, a depth of 2.6 feet and a
length of 110 feet. The channel bottom measured by a previous research team was found
to be approximately horizontal (Charbeneau et al., 2001). The side slopes of the channel
are zero. At the head of the upstream section, shown to the left in Figure 3.1, water is
pumped into a headbox and then through discharge straighteners before entering the
upstream channel section. Baffles are located in the headbox to stabilize the discharge
before entering the upstream channel section. Baffles are made of several layers of
cinder blocks that are overlapped so that the water must follow a tortuous path and have
significant contact with the blocks before it enters the discharge straighteners. The
tortuous discharge path and contact with cinder blocks helps to stabilize the discharge.
Discharge straighteners, located just downstream of the headbox, are used to eliminate
secondary currents as the water enters the upstream section of the channel. The discharge
straighteners are made from sheet metal and extend 5 feet in the direction of the
discharge and across the entire width and height of the channel. They have a lateral
spacing of approximately 0.5 feet. Figure 3.2 shows the vertical delivery pipe, the
downstream end of the set of baffles, and the discharge straighteners.
42
Figure 3.2: Channel headbox and discharge straighteners (upstream end of channel)
The model section of the channel contains the culvert model and SET model. It is
located approximately 72 feet from the headbox. Detailed descriptions of the culvert and
SET models used in this research can be found in Section 3.2.3 and Section 3.2.4.
The downstream section of the channel includes a tailgate which allows for easy
modification of the water level by changing the gate opening (Figure 3.3). The tailgate
was used in the level pool procedure discussed in Section 3.3.2.
Figure 3.3: Channel tailgate (downstream end of the channel)
43
3.2.3 Culvert and SET Models
Various culvert and SET models were built approximately 72 feet downstream
from the headbox using a scale of 1:6 as determined in Section 3.1.1. The models of the
culvert and embankment slopes were constructed from wood, metal bracing, screws, and
bolts. The models were then primed and painted to prevent water damage. Caulk was
used to create a water tight seal with the model edge and rectangular channel wall. The
model culvert had a 1 foot rise and 5/3 feet span. The length of the barrel was a function
of the individual model configuration. Metal angle braces with one side attached to the
culvert model and the other side attached to the rectangular channel wall were installed to
prevent model deformation due to the force of the water movement. Model
reinforcement with cinder blocks was also required to reduce the potential for
deformation.
The SET models were built on a 1:6 scale, using the same scale as the culvert
model. The slope of the SET model was 3:1. The cross pipe and four pipe runners were
made of PVC pipes with an outer diameter of 0.75 inches. The pipe runners were
connected to the cross pipe using PVC Tconnections in the vertical headwall and
mitered headwall model configurations. The pipe runners were glued to the cross pipe
using PVC end connections drilled with a hook for the 30degree skew model
configuration. The cross pipe was connected to the culvert model using hose clamps or
Ubrackets. The bottom anchor pipes were constructed from 90degree PVC connections
glued to the pipe runner portion of the model. The ends of the 90degree PVC
connections were beveled to have flush contact with the channel floor by cutting, filing,
and filling the connections with epoxy. The PVC pipes were filled with sand to prevent
vibrations. In the mitered headwall and 30degree skew models, a plexiglass plate was
added to increase stability at the base of the pipe runners.
44
3.2.3.1 Vertical Headwall Culvert and SET Model at a 0degree Skew
The vertical headwall model at a 0degree skew, referred to as the vertical
headwall model for the purposes of this report, was initially constructed in two pieces 
the culvert model and the embankment model (Figure 3.4). After installation, it was
determined the twopiece model was not feasible. Therefore, the embankment slopes
were then constructed freestanding, weighed down with cinder blocks, and attached to the
face of the culvert model with metal bracing (Figure 3.5). The model reinforcement is
also apparent in Figure 3.5.
The rise of the culvert barrel was 1 foot and the width of the barrel was 5/3 feet.
The vertical headwall extended approximately 1.5 feet above the culvert opening while
the wingwall height matched the rise of the culvert barrel. The culvert barrel length was
1 foot.
Figure 3.4: Vertical Headwall Model (during construction)
45
Figure 3.5: Vertical Headwall Model (during installation)
The SET model was attached to the vertical headwall using hose clamps. During
model operation the test conditions with and without the SET could be created without
detachment of the entire SET model (Figure 3.6).
Figure 3.6: Vertical Headwall Model (during operation)
3.2.3.2 Mitered Headwall Culvert and SET Model at a 0degree Skew
The mitered headwall culvert model at a 0degree skew, referred to as the mitered
headwall model for the purposes of this report, was initially constructed to extend 1.5 feet
above the culvert opening (Figure 3.7). After installation, it was determined the level of
46
submergence required for the range of experiments was greater than allowed using the
initial configuration. The mitered headwall was expanded to approximately 4.5 feet to
obtain a greater level of submergence (Figure 3.8). A wood bracing system was
developed to support the increased headwall length under the weight of water (Figure
3.8). The rise of the culvert barrel and the width of the barrel remained the same, at 1
foot and 5/3 feet respectively. The culvert barrel length was 3 feet. The SET model was
attached to the mitered headwall using Ubrackets and bolts. A plexiglass plate was
attached to the bottom anchor pipes of the SET model to provide additional stabilization.
During model operation the test conditions with and without the SET could be created
with complete detachment of the entire SET model.
Figure 3.7: Initial Mitered Headwall Model (during operation)
47
Plexiglass Plate
Figure 3.8: Mitered Headwall Model (during installation)
Vortices formed at the corners where the wingwall meet the headwall at high
flows for submerged conditions. The vortices appear and dissipate periodically and
typically alternate from one side to the other. The presence of the SET model component
has no effect on the occurrence of vortices. An antivortex plate was developed to
prevent the formation of a vortex (Figure 3.9). The antivortex plate was constructed
from ? inch thick plywood and was triangular in shape to conform to the 3:1 slope of the
mitered headwall. The antivortex plate was 3 feet in length and 1 foot in height. A 1
inch by 1 inch notch was cut into the antivortex plate to allow the plate to fit over the
SET model and flush against the 3:1 sloped mitered headwall. The antivortex plate was
secured during operation by fastening it between two Lbrackets permanently attached to
the mitered headwall.
48
Figure 3.9: Mitered Headwall Model (antivortex plate)
3.2.3.3 Mitered Headwall Culvert and SET Model at a 30degree Skew
The mitered headwall culvert model at a 30degree skew, referred to as the 30
degree skew model for the purposes of this report, was constructed to extend 1.5 feet
above the culvert opening (Figure 3.10). The rise of the culvert barrel was 1 foot, the
width of the barrel was 5/3 feet, and the length of the culvert barrel was 3 feet. A similar
bracing system was created as shown in Figure 3.8 to support the mitered headwall
against deformation. The mitered headwall was extended 1.5 feet to prevent the
formation of the vortex phenomenon. This limits the range of discharge rates that can be
examined. The SET model was attached to the mitered headwall using Ubrackets and
screws. A plexiglass plate was attached to the bottom anchor pipes of the SET model to
provide additional stabilization. During model operation the test conditions with and
without the SET could be created with complete detachment of the entire SET model.
AntiVortex Plate
Vortex
49
Figure 3.10: 30degree Skew Model (during installation and operation)
3.3 DATA ACQUISITION
The data collected in this investigation are the channel discharge and the water
depth. From the data collected water velocity, velocity head, specific energy, and minor
loss coefficients were calculated. The following sections describe the methods used to
collect these data and the calculations that were performed.
3.3.1 Channel Discharge
Accurately determining the flow rate was an integral part of the experiments since
this value would be used to compute many other parameters (i.e. flow velocity). Channel
discharge was typically measured with a normal sharpcrested weir calibrated against
tank measurements. These methods are described below. Section 2.6 contains
information on sharpcrested weirs.
To determine the required dimensions for a sharpcrested weir equation (3.10)
must be solved, which is a combination of the 1913 Rehbock formula for Cd and the
sharpcrested weir equation (Bos, 1989). The sum of the h (head) and w (height of the
50
weir) cannot exceed the return channel height of 3 feet. Based on known quantities, a
maximum weir height of 2.29 feet was obtained by solving equation (3.10)
2/32)08.0605.0(
3
2 hLg
w
hQ += (3.10)
The sharpcrested weir was constructed of a thin plate of metal and erected
perpendicular to the flow near the downstream end of the return channel to the reservoir
(Figure 3.10). The upstream face of the weir plate is smooth except for a small bypass
door (1 feet wide and 8 inches high) located in the center of the bottom of the weir. This
door allows for complete drainage of water in the return channel when necessary. The
weir extends horizontally the full width of the channel, 5 feet. For safety purposes, a
weir height of 2 feet was utilized to allow for adequate freeboard. The weir was attached
to the return channel walls using angle iron. The weir is reinforced on the downstream
side with a horizontal brace to prevent deformation.
The sharpcrested design caused the nappe to spring free, as seen in Figure 3.11.
The lower half of the point gage was placed in the stilling well (transparent plastic tube),
shown in Figure 3.11, to reduce the impacts of water waves while measurements are
taken. The point gage and stilling well were located about 16 feet upstream from the
weir to ensure it was beyond the zone of appreciable surface curvature. Nappe aeration
tests were performed using a four inch diameter PVC pipe to ensure this was an adequate
distance for the point gage and stilling well placement.
51
Figure 3.11: Sharpcrested weir used for flow measurement. The point gage and
stilling well are shown to the right.
The weir flow was computed from (Bos, 1989)
(3.11)
where Cd = 0.618, L= width of weir crest = 5 feet, and H = measured head.
The measured head was determined by point gage measurements. This tool is a
marked pointer that can measure the elevation of the water surface by adjusting the tip of
the pointer to the water surface and reading the dial configuration (thousandth decimal
place accuracy). The datum weir crest height was determined by averaging a series of
point gage measurements taken when the water just reached the weir crest. This datum
value is subtracted from discharge point gage measurements to determine the measured
head value. Each discharge point gage measurement was taken at least 30 minutes after
any change in discharge rate to ensure stabilization had occurred.
An alternative method of measuring channel discharge was employed to calibrate
the sharpcrested weir. This method involves redirecting all channel discharge into the
large tank reservoir shown in Figure 3.12. The tank reservoir has a capacity of 9,300
gallons with dimensions of 12 feet in diameter and 11 feet in height. The channel
discharge is redirected to the inlet pipe located at the top of the tank and discharged
2/32
3
2 HLgCQ
d=
52
through the outlet pipe controlled by a valve. The water level inside the tank can be
viewed through a vertically mounted spyglass on the outside of the tank. When the water
level in the tank (meniscus in the spyglass) is no longer fluctuating, the system has
reached steady state. Once steady state is achieved, the outlet valve is closed quickly and
the elapsed time is recorded for the meniscus in the spyglass to move from the steady
state level to a level near the top of the spyglass. Using the change in water level, cross
sectional area of the tank, and the lapsed time, the discharge rate is determined. This
process was performed at several discharge rates and used to calibrate the weir.
Calibration results are shown in Figure 3.13.
Figure 3.12: Large tank reservoir used for weir calibration
When discharging from the large tank reservoir a strong wave existed near the
point gage which impacted the discharge point gage measurement. To minimize this
effect, a 1.3 feet high by 3 feet wide dam constructed of cinder blocks was built between
the outlet pipe and the point gage. This dam allowed for enough energy dissipation that
53
the wave no longer existed; therefore, the discharge point gage measurement was
accurate.
0
2
4
6
8
0 2 4 6 8
Tank Reservoir Flow (cfs)
Weir Flow (cfs)
Figure 3.13: Weir Calibration
Figure 3.13 shows results from a calibration run. This figure shows the discharge
measured in the storage tank from change in water level, versus the discharge measured
by the weir. The solid line marks exact onetoone correspondence. This line is a good
fit to the data points; thus shows the weir and tank reservoir discharge measurements do
indeed correspond to each other, and therefore measuring discharge using the weir
equation is an accurate method. The standard deviation of the weir flow rate minus the
tank flow rate divided by the tank flow rate is 0.0205.
3.3.2 Water Depth
It was essential to this research to obtain accurate measurements of small changes
in water depth. For the purpose of this report, the terms ?water depth?, ?water level? and
54
?static head? will be considered synonymous and the terms will be used interchangeably.
The static ports of Pitot tubes were connected to an inclined manometer board via flexible
plastic tubing to obtain the accurate measurements of the small changes in water level
required (Figure 3.14). The inclined manometer board allows precise measurement of
water depth. A Pitot tube can measure both total hydraulic head and static hydraulic
head. Only the static hydraulic head measurements were utilized in this research.
wavy watersurface
Pitot
tube
static ports
point gage
stilling well
outside of
channel
PVCtube
Figure 3.14: Schematic of water depth measurement system
The inclined manometer board and flushing tube were constructed for the
purposes of this research using both new and existing materials from the CRWR
hydraulics laboratory (Figure 3.15). The flushing tube is a PVC pipe that is
approximately four feet in length, 3 inches in diameter, and has barbs for the attachment
of the flexible plastic tubing and a water source (provided by a water hose). By forcing
water through the system, the air is ?flushed? out of the flexible plastic tubing as well as
the hard plastic tubes on the inclined manometer board. The inclined manometer board
consists of 28 transparent hard plastic tubes with barbs for flexible tubing connection at
each end and 13 measurement tapes mounted on a 1 inch thick plexiglass sheet attached
to an adjustable metal frame. Each hard plastic tube has an inner diameter of 3/8 inch
Flexible Plastic Tubing
Manometer
Board
55
and a length of 4.46 feet. A water depth reading is determined by correlating the
meniscus of the water column in the hard plastic tube with the measurement tape located
to the right of the hard plastic tube.
Figure 3.15: Manometer Board and Flushing Tube
The slope of the manometer board determines the amplification of water depth
readings. However, the slope of the manometer board must be shallow enough that the
meniscus of the water column can be read throughout the desired range of experiments.
For this research, the desired range of water depth is approximately 2 feet; therefore, the
slope of the manometer board was fixed at 1 : 2.41 (vertical : hypotenuse), which means
that vertical water readings were amplified 2.41 times. Thus,
41.2
A
v
HH = (3.12)
where vH = the vertical position of the water surface and AH = the reading from the
inclined manometer board.
Six Pitot tubes were installed at two crosssections upstream from the culvert and
SET model (Figure 3.16). Two pieces of angle iron were fixed across the channel at
positions 5 feet and 9 feet upstream from the culvert entrance. One set of three Pitot
tubes were attached to each angle iron by Cclamps. In each set of Pitot tubes, one was
56
attached in the middle of the channel and the other two were offset 1.5 feet from the
center Pitot tube. All the Pitot tube bottoms were approximately 2 inches from the floor
of the channel.
Figure 3.16: Pitot Tube Configuration
The static head values measured by a Pitot tube must be referenced to a datum in
order to be converted into water depth. In order to establish the datum a level pool
calibration must be performed. A level pool was created in the channel by passing a very
low discharge rate through the channel and allowing the system to reach steady state. A
small discharge was required because of leakage through the tailgate. Velocities in the
pool were very low so that every point on the horizontal surface of the pool had
approximately the same elevation for the entire channel length. Thus, it was considered a
level pool.
The Pitot tube datum was established by creating a level pool in the channel and
marking the static head readings on the manometer board under the level pool condition.
Next, the depth was measured at the location of all Pitot tubes with a point gage. These
depths corresponded to the static head readings obtained from the manometer board
Culvert & SET
Model
5? Upstream
9? Upstream
57
reading. The differences in those readings were measured by the deviation of the
meniscus from the level pool readings on the manometer board.
For the three model configurations, numerous scenarios were created by varying
the discharge rate to create two sets of flow conditions (unsubmerged or submerged),
varying the presence of the SET model component, and if necessary, varying the
presence of the antivortex plate (See Table 3.1). The first digit of each scenario
corresponds to the model configuration (where 1 = the vertical headwall model, 2 =
mitered headwall model, and 3 = 30degree skew model). The second digit represents
the scenario flow condition (where 1 = unsubmerged, 2 = submerged and 3 = submerged
with antivortex plate), while the letter ?a? indicates the SET model component was
present and the letter ?b? indicates the SET model component was not present.
Two sets of water depth measurements were taken at each discharge rate for each
scenario at the six Pitot tube locations were configured and averaged arithmetically
(Figure 3.16). By comparing the ?a? and ?b? scenarios the effect of the SETs could be
determined. By comparing scenario 22a to scenario 23a the effect of the vortex
phenomena could be determined.
58
Table 3.1: Testing Identification
Model
Configuration
Scenario
Number
Unsubmerged
Subme
rged
With SETs
Without SETs
With Anti

Vortex Plate
Without Anti

Vortex Plate
11a X X N/A N/A
11b X X N/A N/A
12a X X N/A N/A
Vertical
Headwall
Model
12b X X N/A N/A
21a X X N/A N/A
21b X X N/A N/A
22a X X X
22b X X X
23a X X X
Mitered
Headwall
Model
23b X X X
31a X X N/A N/A
31b X X N/A N/A
32a X X N/A N/A
30degree
Skew Model
32b X X N/A N/A
At the beginning of each experiment, there was no water in the channel. The
experiment started by flushing water through the Pitot tubes for about 20 minutes to
eliminate air bubbles from the flexible plastic tubing as well as the hard plastic tubes on
the inclined manometer board. Air bubbles could create an error in water depth
measurement. Figure 3.15 shows the configuration used for the flushing process. While
the flushing process was occurring, the Pitot tubes were checked and, if necessary,
cleaned with a needle to ensure that all the static ports of each Pitot tube were not
clogged (shown in Figure 3.14).
While the flushing process was still taking place and after verifying each Pitot
tube was clean, the required discharge rate was set by configuring the valves and turning
59
on the appropriate pumps. When the water depth in the channel rose above the Pitot
tubes the flushing process continued for approximately twenty to thirty minutes to
prevent air from reentering any tubing. At least thirty minutes after the flushing process
was completed, the first set of water depth and flow measurements were obtained. Once
the first set of readings was finished, the scenario was changed according to what was
required (i.e. the removal/insertion of the SET model component or the removal/insertion
of the antivortex plate). As before, the second group of measurements was performed at
least thirty minutes later, allowing enough time for the flow conditions to stabilize. Two
sets of water level readings were taken for each measurement set and averaged
arithmetically to ensure accuracy of the water level readings obtained before changing the
discharge.
3.3 DATA PROCESSING
From the acquired data of channel discharge and water level, many other
components were calculated. These calculations included velocity, velocity head,
specific energy, approach minor loss coefficient, barrel minor loss coefficient, and culvert
performance curves.
3.3.1 Velocity
Water velocities at the position of each Pitot tube for the appropriate scenario
were determined by dividing the discharge rate (measured by the weir) by the cross
sectional area (the product of channel width times the water level measured by each Pitot
tube). This is considered the approach velocity.
A
QV
a = (3.13)
Where, aV = approach velocity, Q = discharge and A = crosssectional area.
60
To determine the barrel velocity for unsubmerged conditions, the unit discharge (q ) is
first determined by dividing the discharge rate (Q ) by the width of the culvert (B= 5/3
feet). Critical depth ( cy ) for the barrel is then determined by equation (3.14).
cyg
q =
???
?
???
? 3/12 (3.14)
The barrel velocity ( bV ) is then determined for unsubmerged conditions by equation
(3.15). This is the critical velocity equation which is presented as equation (3.3) and
developed in Section 3.1.1.
( ) 2/1cb ygV = (3.15)
For submerged conditions, the barrel velocity is calculated by equation (3.16).
DBQVb
3
2= (3.16)
where Q is the discharge, D is the culvert rise (D = 1 foot), and B is the culvert width (B
= 5/3 feet). The 2/3 factor is related to the fact the depth within the entrance is assumed
to be 2/3 of the area regardless of the headwater level is because of the flow regime. The
2/3 factor is derived and explained in detail in ?Hydraulics of Channel Expansions
leading to LowHead Culverts? by Charbeneau et al. 2003.
3.3.2 Velocity Head
Velocity head ( vh ), either barrel or approach, is determined by using the
appropriate velocity in the calculation of equation (3.17).
g
Vh
v 2
2
= (3.17)
For this research, it was found that barrel velocity head is typically one order of
magnitude larger than approach velocity head.
61
3.3.3 Specific Energy
The specific energy, E, is defined as the sum of the water depth, y, and the
velocity head ( vh ) as shown in equation (3.17). The specific energy at all six Pitot tube
locations were calculated for each scenario. The water depth was measured as explained
in Section 3.3.2 and the approach velocity head value was used in this equation
(calculated as explained in the previous section). Specific energy is also explained in
Section 2.1.
vhyE += (3.18)
3.3.4 Barrel Minor Loss Coefficient
The barrel minor loss coefficient represents the losses in the flow energy
associated with the movement of the water past the SET based on the barrel velocity
head. Based on equation (2.19) developed in Section 2.3.3, the barrel minor loss
coefficient bLK due to the SET presence can be calculated by,
???
?
???
?
?=
g
V
EK
b
bL
2
2
(3.19)
To compute minor losses due to SETs for a discharge, the arithmetic average of the
change in specific energy for the six Pitot tube measurements due to the presence of the
SETs model component was used as the numerator in equation (3.19). This value is
calculated by subtracting the specific energy for a scenario ?b? (without the SET model
component present) from the specific energy for a scenario ?a? (with the SET model
component present) at each Pitot tube location for a specific discharge, then averaging
these six values arithmetically. For the same discharge, the arithmetic average of the
barrel velocity head for the six Pitot tubes for the scenario without the SET model
component was used as the denominator in equation (3.19). The barrel minor loss
62
coefficient could be obtained for the various scenarios listed in Table 3.1 at a range of
discharge rates corresponding to each scenario.
Barrel velocity head is typically one order of magnitude larger than the approach
velocity head for this research. The appropriate velocity head value is in the denominator
of the minor loss coefficient formulas. Approach minor loss coefficients (explained in
Section 3.3.5) were calculated because they are an order of magnitude larger than the
barrel minor loss coefficients because of the velocity head relationship stated above. This
allows for greater visibility of trends. However, in design procedures the barrel minor
loss coefficient values would be used since these values are more closely tied to the drag
forces on SETs. Entrance loss is a function of the velocity head in the barrel according to
the FHWA, therefore the barrel minor loss coefficients calculated should be used in any
design procedure (Norman et al., 2001).
3.3.5 Approach Minor Loss Coefficient
The approach minor loss coefficient represents the losses in the flow energy
associated with the movement of the water past the SET based on the approach velocity
head. Based on equation (2.19) developed in previous Section 2.3.3, the approach minor
loss coefficient due to the SET presence can be calculated by,
???
?
???
?
?=
g
V
EK
a
L
2
2
(3.20)
To compute minor losses due to SETs for a discharge, the arithmetic average of the
change in specific energy for the six Pitot tube measurements due to the presence of the
SET model component was used as the numerator in equation (3.20). This value is
calculated by subtracting the specific energy for a scenario ?b? from the specific energy
for a scenario ?a? at each Pitot tube location, then averaging these six values
63
arithmetically. For the same discharge, the arithmetic average of the approach velocity
head for the six Pitot tubes for the scenario ?b? (without the SET model component
present) was used as the denominator in equation (3.20). The approach minor loss
coefficient could be obtained for the various scenarios listed in Table 3.1 at a range of
discharge rates that corresponded with each scenario.
64
Chapter 4: Results
The overall goal of this research is to evaluate the hydraulic effects of SETs on
culverts through physical modeling and to provide the Texas Department of
Transportation guidance on the influence of SETs in the hydraulic design of culverts.
Important specific research objectives are to study the nature of water level difference
upstream of the culvert due to SET presence; to compare the headwaterlevel discharge
relationships with and without SET presence to show how SETs influence the hydraulics
of culverts by developing performance curves for box culverts operating under inlet
control, based on the experiments performed during this study, and compare them to
performance curves developed from earlier work reported in ?Hydraulics of Channel
Expansions Leading to LowHead Culverts? by Charbeneau et al., (2002); and, finally, to
provide Minor Loss Coefficients due to the presence of SETs that may be used in design
procedures. The analysis of collected data is presented in this chapter. For the purpose
of this report, the terms ?water depth?, ?water level? and ?static head? will be considered
synonymous and the terms will be used interchangeably.
4.1 WATER LEVEL DIFFERENCE
The water level difference upstream of the culvert can be examined in two ways:
distribution across the channel for a specified discharge and average water level
difference due to the presence of SETs or the vortex. Water level can also be considered
static head. First, the water level difference distributions across the channel can be
compared by creating two channel crosssections ? one for the three Pitot tubes that are
installed 5 feet upstream of the culvert model and one for the three Pitot tubes that are
installed 9 feet upstream of the culvert model. These crosssections can be compared to
see if trends exist under different flow conditions for different model configurations.
65
Water level difference is calculated by subtracting the water level for a scenario ?b?
(without the SET model component present) from the water level for a scenario ?a? (with
the SET model component present) at each Pitot tube location for a specific discharge,
then averaging these six values obtained arithmetically. Secondly, the arithmetic
averages of water level differences from the six Pitot tubes were compared to see if
general trends exist for the various model configurations. This process allows for the
exhibition of the water level difference due to the SETs and the vortex clearly.
4.1.1 Water Level Distributions Across the Channel
Figure 4.1 can be used to determine Pitot tube locations in relation to the culvert
and SET model, which assists in the interpretation of Figure 4.2 through 4.7. Figure 4.2
shows a typical water level distribution across the channel for unsubmerged conditions
while Figure 4.3 shows a typical water level distribution across the channel for
submerged conditions for the vertical headwall model. Figure 4.4 shows a typical water
level distribution across the channel for unsubmerged conditions while Figure 4.5 shows
a typical water level distribution across the channel for submerged conditions for the
mitered headwall model. Figure 4.6 shows a typical water level distribution across the
channel for unsubmerged conditions while Figure 4.7 shows a typical water level
distribution across the channel for submerged conditions for the 30degree skew model.
Figure 4.1: Pitot tube locations
Culvert & SET
Model
5? Upstream
9? Upstream
1
1 2.5
2.5
5
5
Traverse Position (ft)
66
As stated in Section 3.2.2, the bed of the channel is essentially horizontal; this
indicates that the depth at a crosssection should be approximately equal. By comparing
Figures 4.2 through 4.7, the water level distribution is found to be similar for
unsubmerged and submerged conditions for all model configurations. The range of the y
axis is the same for Figures 4.2 through 4.7. The water level across the crosssection 9
feet upstream of the culvert entrance is consistent but the water level across the cross
section 5 feet upstream of the culvert entrance is somewhat variable. It does seem the
water level is slightly higher at the crosssection 5 feet upstream of the culvert entrance
compared to the crosssection 9 feet upstream of the culvert entrance. The water level is
always slightly higher when the SET model component is present which will be
discussed in more detail in Section 4.1.3.
It can be concluded that the small variance in water level at the crosssection 5
feet upstream of the culvert entrance could be due to unevenness of the bed channel or
the slight increase in depth, especially near the channel center, could be associated with
the conversion of kinetic energy to depth in order to build up the energy to accelerate the
flow through the culvert entrance section. However, in sum the differences in water level
depths across the channel are so slight they can be neglected. Thus, the water levels of
the 5 feet crosssection and the 9 feet crosssection can be viewed as approximately static
and the arithmetic average of these six water depths measured by the Pitot tubes can be
taken to represent water level for each scenario data was collected for (Table 3.1).
67
0.650
0.660
0.670
0.680
0.690
0.700
0.710
0.720
0.730
0.740
0.750
0.0 1.0 2.0 3.0 4.0 5.0
Traverse Position (ft)
Water level (ft)
5 ft upsteam; w/ SET5 ft upstream; w/o SET
9 ft upstream; w/ SET9 ft upsteam; w/o SET
Figure 4.2: Typical Water Level Distribution for Vertical Headwall Model Configuration
(Q= 2.85 cfs, unsubmerged conditions)
1.390
1.400
1.410
1.420
1.430
1.440
1.450
1.460
1.470
1.480
1.490
0.0 1.0 2.0 3.0 4.0 5.0
Traverse Position (ft)
Water Level (ft)
5 ft upsteam; w/ SET
5 ft upstream; w/o SET
9 ft upstream; w/ SET
9 ft upsteam; w/o SET
Figure 4.3: Typical Water Level Distribution for Vertical Headwall Model Configuration
(Q= 6.95 cfs, submerged conditions)
68
0.630
0.640
0.650
0.660
0.670
0.680
0.690
0.700
0.710
0.720
0.730
0.0 1.0 2.0 3.0 4.0 5.0
Traverse Position (ft)
Water Level (ft)
5 ft upsteam; w/ SET5 ft upstream; w/o SET
9 ft upstream; w/ SET9 ft upsteam; w/o SET
Figure 4.4: Typical Water Level Distribution for Mitered Headwall Model Configuration
(Q= 2.59 cfs, unsubmerged conditions)
1.390
1.400
1.410
1.420
1.430
1.440
1.450
1.460
1.470
1.480
1.490
0.0 1.0 2.0 3.0 4.0 5.0
Traverse Position (ft)
Water Level (ft)
5 ft upsteam; w/ SET
5 ft upstream; w/o SET
9 ft upstream; w/ SET
9 ft upsteam; w/o SET
Figure 4.5: Typical Water Level Distribution for Mitered Headwall Model Configuration
(Q= 6.35 cfs, submerged conditions)
69
1.290
1.300
1.310
1.320
1.330
1.340
1.350
1.360
1.370
1.380
1.390
0.0 1.0 2.0 3.0 4.0 5.0
Traverse Position (ft)
Water Level (ft)
5 ft upsteam; w/ SET
5 ft upstream; w/o SET
9 ft upstream; w/ SET
9 ft upsteam; w/o SET
Figure 4.6: Typical Water Level Distribution for 30degree Skew Model Configuration
(Q= 2.82 cfs, unsubmerged conditions)
1.050
1.060
1.070
1.080
1.090
1.100
1.110
1.120
1.130
1.140
1.150
0.0 1.0 2.0 3.0 4.0 5.0
Traverse Position (ft)
Water Level (ft)
5 ft upsteam; w/ SET
5 ft upstream; w/o SET
9 ft upstream; w/ SET
9 ft upsteam; w/o SET
Figure 4.7: Typical Water Level Distribution for 30degree Skew Model Configuration
(Q= 5.67 cfs, submerged conditions)
70
4.1.2 Water Level Difference due to the Vortex Phenomena
In this research, a vortex developed under submerged conditions for the mitered
headwall model configuration. Vortices formed at the corners where the wingwall meet
the headwall at high flows for submerged conditions. The vortices appear and dissipate
periodically and typically alternate from one side to the other. The presence of the SET
model component has no effect on the occurrence of vortices, meaning they occurred
both when the SET model component was present and when it was not present. A vortex
did not develop throughout the course of data collection for the vertical headwall model
configuration, the initial model configuration studied. The mitered headwall length of the
30degree skew angle was reduced to prevent the vo rtex phenomenon from developing.
This also limits the range of data that can be collected. First, the vortex phenomenon
must be understood before any interpretation of the submerged mitered headwall
condition scenarios can be completed. The vortex pheno menon is explained in detail in
Section 2.4.
An antivortex plate was developed which is believed to lessen the vortex
phenomenon. A vortex effectively reinforces itself once the spiral motion has developed
by entraining air. It is believed the antivortex plate developed for the purposes of this
research lessens the vortex phenomenon by changing the streamline pattern shown in
Figure 2.5. By placing the antivortex plate perpendicular to the spiral motion of the
vortex, the vortex itself is suppressed because the waterair circulation pattern that causes
vortex reinforcement can no longer occur. However, occasionally vortices would
develop even with the antivortex plate in place. This could potentially impact the results
obtained. Also, as presented in Section 2.4 the vortex phenomenon can be invisible, so
even if the vortex was not present visually the potential impact on collected experimental
data still exists.
71
It was observed for the mitered headwall model configuration operating under
submerged conditions when the vortex is present, a large ?sucking? sound is produced. If
an object was placed in the approach channel upstream of the vortex, an observer could
watch the object be caught up in the swirling motion due to the spiral vortex circulation
pattern before it entered the culvert barrel. This could be considered an ?attractive
nuisance? especially in the case of children, meaning children could be attracted to the
culvert due to this phenomenon, and could be classified as a detrimental phenomenon
from a safety perspective.
Further study of the vortex phenomenon should occur to be able to fully discuss
the effects of the vortex but was outside the defined scope of this project, therefore, not
fully examined in this research. Results obtained for the mitered headwall configuration
under submerged conditions are not predictable due to the vortex phenomenon occurring.
Preliminary results indicate the vortex can be beneficial to the system from a
hydraulic perspective. An example of this benefit can be found in Figure 4.8, which
represents a typical water level distribution across the channel with the vortex and
without the vortex phenomenon present. In Figure 4.8 the water level upstream of the
culvert barrel without the vortex phenomenon present is higher than when the vortex
phenomenon is present for the same discharge rate. In fact, results obtained from this
experimental program indicate the impact of the SETs on the water levels is significantly
less than the impact of the vortex phenomenon. When a strong vortex is present, the
velocity field is strongly multidimensional. Minor loss coefficients are used in a one
dimensional analysis of a flow system. These experiments show that the multi
dimensional effects of the vortex are equally, if not more significant than the one
dimensional effects of SETs on upstream water levels.
72
1.820
1.840
1.860
1.880
1.900
1.920
1.940
1.960
1.980
0.0 1.0 2.0 3.0 4.0 5.0
9' Upstream Crosssection  Traverse Position (ft)
Water Level (ft)
without vortex; w/ SET
without vortex; w/o SET
with vortex; w/ SET
with vortex w/o SET
Figure 4.8: Typical Water Level Distribution for Mitered Headwall Model Configuration
(Q= 7.94 cfs, submerged conditions)
Figure 4.9 further illustrates that the impact of the SETs on the water depth
difference is significantly less than the impact of the vortex phenomenon for a range of
submerged conditions. Water level difference is calculated by subtracting the water level
for a scenario ?b? (without the SET model component present) from the water level for a
scenario ?a? (with the SET model component present) at each Pitot tube location for a
specific discharge, then averaging these six values arithmetically. The negative results
obtained occur due to the way water level difference is calculated and indicate for those
specific situations the water level for a scenario ?a? is actually higher than the water level
for a scenario ?b?. It is the opinion of this author that this is due to the unpredictable way
the system behaves due to the vortex phenomenon occurring.
73
0.06
0.04
0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
Discharge (cfs)
Water Depth Difference (ft)
Due to SET presence
Due to vortex presence
Figure 4.9: Water Depth Difference and Discharge relationship for Mitered Headwall
Model Configuration
4.1.3 Water Depth Difference due to the SET model component
As stated in Section 2.6 the SET model component should increase the water level
upstream of the culvert because of the drag force imposed to the flow. The experimental
data shows that the water depths increase when there are SETs present. The water level
differences due to the presence of SETs for all scenarios are shown in Figure 4.10. Each
y value is calculated by subtracting the water depth for a scenario ?b? (without the SET
model component present) from the water depth for a scenario ?a? (with the SET model
component present) at each Pitot tube location for a specific discharge, then averaging
these six values arithmetically. For the mitered headwall submerged conditions, with or
without antivortex plate, some of these values were negative due to the potential reasons
explained in Section 4.1.2.
74
0.02
0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.0 2.0 4.0 6.0 8.0 10.0
Discharge (cfs)
Water depth difference due to SET presence
(ft)
Vertical HW Submerged
Vertical HW Unsubmerged
Mitered HW Submerged with plate
Mitered HW Submerged without plate
Mitered HW Unsubmerged
30 Degree Skew Submerged
30 Degree Skew Unsubmerged
Figure 4.10: Water depth difference due to SET presence
Figure 4.10 clearly indicates that there is a trend in water level difference
increasing as the discharges increases under submerged conditions and the water level
difference remaining relatively constant for unsubmerged conditions. The approximate
dividing value of the discharge, 5 cubic feet per second, allows for the data to be
classified in submerged or unsubmerged categories. When the discharge is higher than 5
cubic feet per second, the flow is submerged. When the discharge value is less than 5
cubic feet per second, the flow is unsubmerged. This corresponds the water depth ( cy ) at
critical condition = 0.654 feet and specific energy ( E ) = 0.98 feet. In the previous study
?Hydraulics of Channel Expansions Leading to Lowhead Culverts? conducted by
Charbeneau et al. (2002) it was found if E/D was less than 1 the conditions were
unsubmerged. Therefore, the values calculated for unsubmerged and submerged
75
conditions for this research correspond with the relationship determined in the previous
research.
Most importantly, the water depth differences are small, most of which are less
than 0.01 feet, and the differences are consistently of the same magnitude for the range of
discharges classified as unsubmerged for all model scenarios. This difference scales to
be 0.06 feet for the prototype system. The 30degree skew model configuration data is
slightly higher than the mitered headwall configuration data, which is slightly higher than
the vertical headwall configuration data. Overall, the impact of SETs for all model
configurations can be considered relatively small because the change in water level
would scale to be less than one inch for the prototype.
For submerged conditions, there is a trend in water level difference increasing as
the discharges increases. This is extremely apparent for the vertical headwall model
configuration. For the mitered headwall model configuration submerged conditions the
results are scatted and some values are negative, potentially due to the reasons discussed
in Section 4.1.2. The largest measured water level differences are less than 0.053 for the
model configurations, which scale to represent a 0.318 feet increase for water level in the
prototype. This could be considered noteworthy because the culvert flow will be in the
submerged region during flooding conditions so the current estimates of backwater may
underestimate the actual impacts due to SETs.
However, if the percent difference in water depth is considered due to the SET
presence for the above example it would only represent a 2.8% change in water level.
This value is calculated by taking the water depth difference and dividing it by the
measured water depth without the SET model component present at the measured
discharge. For the example used in the above paragraph, the following sample
calculation was performed to illustrate this concept: %87.2100*844.1 053.0 =??
?
?
???
?
feet
feet . The
76
results of this percent increase calculation are shown in Figure 4.10 for all the data points
shown in Figure 4.9.
For the unsubmerged conditions, since a relatively constant value was discovered
for water level difference, it is found the lower the discharge the larger the percent depth
difference due to the SET presence. This is due to the fact the water depth itself is less
for the lower discharges but the water level difference remains constant.
For submerged conditions a trend similar to the water depth difference exists; the
larger the discharge the larger the percent difference in water depth.
However, all values indicate less than a 3% increase in water level due to the
presence of the SET model component. Therefore, it seems that the overall impacts of
SETs are small for the range of experiments performed for this thesis research.
1.50
1.00
0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.0 2.0 4.0 6.0 8.0 10.0
Discharge (cfs)
Percent difference in water depth due to SET
presence (%)
Vertical HW Submerged
Vertical HW Unsubmerged
Mitered HW Submerged with plate
Mitered HW Submerged without plate
Mitered HW Unsubmerged
30 Degree Skew Submerged
30 Degree Skew Unsubmerged
Figure 4.11: Percent difference in water depth due to SET presence as a function of
discharge
77
4.2 CULVERT PERFORMANCE
Refer to ?Hydraulics of Channel Expansions Leading to LowHead Culverts? by
Charbeneau et al. (2002) for details on previous research conducted that is compared to
the current research in this section. This includes the development of performance curve
equations and the fitting of the performance curves for the previous research. The inlet
control equation describes the flow under both conditions, with and without the SETs.
4.2.1 Performance Equation Evaluation
The performance data for the experiments presented in this thesis research are
compared to the data for previous experiments are shown in Figure 4.13. Data collected
from the culvert system located in the outdoor channel is labeled as VHW for the vertical
headwall model configuration, MHW for the mitered headwall configuration and 30
degree skew for the 30degree skew model configuration. The abbreviation AVP
represents the antivortex plate while sub is for submerged conditions and unsub is for
unsubmerged conditions. The 2, 4, and 6barrel data sets are for the indoor channel with
an abrupt expansion. The data set labeled 1barrel is for the single barrel culvert in the
outdoor channel, while the set labeled 1barrel (n) is from the outdoor channel with the
culvert barrel having the smaller span. The legend to be applied to Figure 4.13 and 4.14
is presented in Figure 4.9 for visibility purposes.
78
Figure 4.12: Legend for the box culvert performance data
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Q/[A((gD)^0.5)]
HW/D
Figure 4.13: Plot of data collected for the box culvert performance
79
In general, the data for the current research is higher than the data from the
previous research, especially under submerged conditions. The higher data indicates that
for the same headwater levels a reduction in discharge would occur, this is considered a
reduction in hydraulic performance. However, when the difference in the performance
relationship for the same model configuration due to the SET presence is compared, the
overall decrease in the performance due to SET presence can be considered minor.
One explanation due to the difference in overall performance of the system model
in this thesis research compared to the previous research could be the change in wingwall
configuration from perpendicular to the culvert barrel to parallel to the culvert barrel
combined with the impact of wingwall slope. The wingwalls models for this thesis
research are all on a 3:1 slope. It appears the model configurations studied in this thesis
research may impact the performance more than the SET presence. This is especially
true under submerged conditions, which is consistent with the constants used for inlet
control design equations presented by FHWA (Norman et al., 2001).
Previous research by the FHWA indicates that for unsubmerged conditions the
miter slope appears to have no effect, however, under submerged conditions a 3:1
wingwall miter seems to be more hydraulically efficient than a 2:1 wingwall miter
(Graziano et al., 2001). Therefore, a lower wingwall miter such as 6:1 may increase
efficiency which, could be examined in future studies to confirm this effect.
It is known that skewed inlets can slightly reduce the hydraulic performance of a
culvert under inlet control conditions (Normann et al., 2001). This is consistent with the
findings of this thesis research.
In the previous research, the least squares method was used to fit the data in order
to find the best values for the coefficients DC , cC , and bC . The values that produced the
smallest standard error (E = 0.0376) were Cb = 1.08 and Cc = 0.601, which together give
80
Cd = 0.649. However, the maximum theoretical value of the contraction coefficient Cb is
1 for perfectly rounded inlet walls. Thus, the value for Cb was constrained to 1, which
yielded Cb = 1.0, Cc = 0.667, Cd = 0.667 with a minimum standard error of S.E. = 0.0484.
The data fit the curve quite well. Figure 4.24 shows the data plotted along with the
performance curve equations plus or minus one standard error, which was calculated
from equation (4.1).
2
1
1.. ?
= ??
???
??
???
???
?
???
??
???
?
???
?= N
i dimi gDA
Q
gDA
Q
NES (4.1)
If the same analysis is performed to include the data from the current experiment
the performance curve would most likely increase under submerged conditions. In future
research, the least squares method that was used to fit the data in order to find the best
values for the coefficients DC , cC , and bC could be applied to the current research as a
whole and the with SET presence and without SET data sets individually. This could
also be done for the entire data set. The comparison of these coefficients would indicate
the relationship change due to the change in model configurations and the change due to
SET presence.
81
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Q/[A((gD)^0.5)]
HW/D
Figure 4.14: Performance curve with standard error
4.3 MINOR LOSS COEFFICIENT
In this section, the minor loss coefficients are provided and the relationships of
minor loss coefficient and other variables such as discharge or velocity head are
examined. Both the approach minor loss coefficients and the barrel minor loss
coefficients associated with the movement of water past the SETs are presented in Table
4.1. The values in Table 4.1 represent the averages of all data for each model
configuration for either unsubmerged or submerged conditions. The values for the
mitered headwall configuration submerged conditions are not present due to the vortex
phenomenon that developed (refer to Section 4.1.2). Approach minor loss coefficients
are calculated because they are an order of magnitude larger than the barrel minor loss
82
coefficients (refer to Section 3.3.4 and Section 3.3.5). This allows for greater visibility of
the trends. However, in design procedures the barrel minor loss coefficient values would
be used since these values are more closely tied to the drag forces on SETs. Entrance
loss is a function of the velocity head in the barrel according to the FHWA (Norman et
al., 2001); therefore, the barrel minor loss coefficients calculated for this research may be
used in any design procedure not the approach minor loss coefficients.
According to the TxDOT Hydraulic Manual (2002) the Entrance Loss Coefficient
for a reinforced box culvert with wingwalls parallel (extension of sides) with a square
edge at crown the entrance loss coefficient is 0.7 and for a reinforced box culvert
wingwall at 10 to 25 degrees to barrel squareedged at crown is 0.5. It is also stated in
the traffic safety section, part of Section 2 of the TxDOT Hydraulic Manual, mitered end
sections should be used carefully because they may increase hydraulic head losses.
Compared with these values, the minor loss coefficient values calculated for SETs can be
considered insignificant.
The approach minor loss coefficient relationship with DHW , ??
?
?
???
?
gDA
Q , barrel
velocity head, and approach velocity head are shown in Figures 4.15 through 4.18. It is
important to look at these relationships as well as the average values of the minor loss
coefficients found in Table 4.1. The same relationship trends exist for the barrel minor
loss coefficient as the approach minor loss coefficient. The negative values of the
mitered headwall submerged conditions are not shown on these graphs because a
negative minor loss coefficient is not feasible.
83
Table 4.1: Minor Loss Coefficients
Model Configuration Approach Minor Loss Coefficient Barrel Minor Loss Coefficient
Vertical Headwall Model ?
Unsubmerged Conditions 0.506 0.023
Vertical Headwall Model ?
Submerged Conditions 1.508 0.033
Mitered Headwall Model ?
Unsubmerged Conditions 0.869 0.037
30degree Skew Model ?
Unsubmerged Conditions 0.936 0.036
30degree Skew Model ?
Submerged Conditions 0.868 0.027
On the whole, the minor loss coefficient increases as the headwater level
increases as shown in Figure 4.15. It is shown when the headwater depth  culvert barrel
rise ratio is lower than 1, the minor loss coefficients tend to be about the same magnitude
and the value of the minor loss coefficient is small. However, for small discharge
conditions (when DHW is less than 0.6) the minor loss coefficient values are more
significant. This is especially true for the 30degree skew model configuration. When
the headwater depthculvert barrel ratio is around 1.0, the minor loss coefficients are the
smallest. When the headwater depthculvert barrel ratio is greater than 1.0, the minor
loss coefficient increases as the headwater level increases. In this regime, the SETs have
larger influence on the culvert hydraulic performance, especially when DHW is greater
than 1.5.
84
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.0 0.5 1.0 1.5 2.0
HW/D
Approach Minor Loss Coefficient
Vertical HW Submerged
Vertical HW Unsubmerged
Mitered HW Submerged with fin
Mitered HW Submerged without fin
Mitered HW Unsubmerged
30 Degree Skew Submerged
30 Degree Skew Unsubmerged
Figure 4.15: Approach Minor Loss Coefficient as a function of DHW
As a general rule, the minor loss coefficient increases as the discharge increases,
especially under submerged conditions, as shown in Figure 4.16. It is shown when
???
?
???
?
gDA
Q is lower than 0.5, the minor loss coefficients tend to be about the same
magnitude and the value of the minor loss coefficient is small. However, for small
discharge conditions (when ??
?
?
???
?
gDA
Q is less than 0.2) the minor loss coefficient values
are more significant. This is especially true for the 30degree skew model configuration.
When the ??
?
?
???
?
gDA
Q is greater than 1.0, the minor loss coefficient increases as the
discharge increases. In this regime, the SETs have larger influence on the culvert
hydraulic performance especially when ??
?
?
???
?
gDA
Q is greater than 0.8.
85
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.0 0.2 0.4 0.6 0.8 1.0
Q/A((gD)^0.5)
Approach Minor Loss Coefficient
Vertical HW Submerged
Vertical HW Unsubmerged
Mitered HW Submerged with fin
Mitered HW Submerged without fin
Mitered HW Unsubmerged
30 Degree Skew Submerged
30 Degree Skew Unsubmerged
Figure 4.16: Approach Minor Loss Coefficient as a function of ??
?
?
???
?
gDA
Q
Similar trends as discussed above exist for the approach minor loss coefficient
and barrel minor velocity head relationship shown in Figure 4.17. Generally, it seems a
consistent relationship type for the approach minor loss coefficient relationship
with DHW , ??
?
?
???
?
gDA
Q , and barrel velocity head can be observed. However, the
relationship between the approach minor loss coefficient approach velocity head is
unpredictable. In Figure 4.18 there is a significant amount of scatter associated with the
approach velocity head so the relationship between the approach minor loss coefficient
approach velocity head is considered indiscriminate.
86
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
Barrel Velocity Head (ft)
Approach Minor Loss Coefficient
Vertical HW Submerged
Vertical HW Unsubmerged
Mitered HW Submerged with fin
Mitered HW Submerged without fin
Mitered HW Unsubmerged
30 Degree Skew Submerged
30 Degree Skew Unsubmerged
Figure 4.17: Approach Minor Loss Coefficient as a function of gVb2
2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.000 0.005 0.010 0.015 0.020 0.025
Approach Velocity Head (ft)
Approach Minor Loss Coefficient
Vertical HW Submerged
Vertical HW Unsubmerged
Mitered HW Submerged with fin
Mitered HW Submerged without finMitered HW Unsubmerged
30 Degree Skew Submerged
30 Degree Skew Unsubmerged
Figure 4.18: Approach Minor Loss Coefficient as a function of gVa2
2
87
In design procedures the barrel minor loss coefficient values would be used since
these values are more closely tied to the drag forces on SETs. Entrance loss is a function
of the velocity head in the barrel according to the FHWA (Norman et al., 2001);
therefore, the barrel minor loss coefficients calculated for this research should be used in
any design procedure. As a general rule, the barrel minor loss coefficient range from
0.002 to 0.077 and average to be approximately 0.03 for the entire data set, as shown in
Figure 4.19. The SETs have larger influence on the culvert hydraulic performance
especially for small and large values of the parameter ??
?
?
???
?
gDA
Q (less than 0.2 or grater
than 0.8). This figure emphasizes the barrel minor loss coefficient due to the presence of
SETs is very small; therefore, the overall impact of SETs on culvert performance is
small.
88
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0 0.2 0.4 0.6 0.8 1.0Q/A((gD)^0.5)
Barrel Minor Loss Coefficient
Vertical HW Submerged
Vertical HW Unsubmerged
Mitered HW Submerged with fin
Mitered HW Submerged without fin
Mitered HW Unsubmerged
30 Degree Skew Submerged
30 Degree Skew Unsubmerged
Figure 4.19: Barrel Minor Loss Coefficient as a function of ??
?
?
???
?
gDA
Q
89
Chapter 5: Summary and Conclusions
This chapter presents a summary and conclusions of the research contained in this
thesis. Section 5.1 contains a summary of the approach and progress made on the
research objectives. Section 5.2 presents conclusions while Section 5.3 discusses the
implications of this research. This chapter concludes with suggestions on future work.
5.1 SUMMARY
The overall goal of this research is to evaluate the hydraulic effects of SETs on
culverts through physical modeling and to provide the Texas Department of
Transportation guidance on the influence of SETs in the hydraulic design of culverts.
Important specific research objectives are the following:
1. To study the nature of water level difference upstream of the culvert due
to SET presence.
2. To compare the headwaterlevel discharge relationships with and without
SET presence to show how SETs influence the hydraulics of culverts by
developing performance curves for box culverts operating under inlet
control, based on the experiments performed during this study, and
compare them to performance curves developed from earlier work
reported in ?Hydraulics of Channel Expansions Leading to LowHead
Culverts? by Charbeneau et al., (2002).
3. To provide Minor Loss Coefficients due to the presence of SETs that may
be used in design procedures.
To meet the thesis research objectives, physical models of a single barrel box
culvert (prototype dimensions of 10 feet by 6 feet) were constructed and studied on a
90
scale of 1:6. The configurations included a vertical headwall model configuration, a
mitered headwall model configuration with a 0degree skew angle, and a mitered
headwall model configuration with a 30degree skew angle. The slope of the
embankment and pipe runners were 3:1 for all model configurations. Conditions with
and without SETs installed at the inlet end of the culvert model were examined. Due to
the formation of a vortex under submerged inlet conditions an antivortex plate was
developed to collect data with and without the vortex phenomena. Experiments were
performed under inlet control for both submerged flow and unsubmerged flow.
Discharge and water level measurements were acquired for various scenarios. The
collected data (discharge and water level) was utilized to evaluate parameter difference
due to the SET presence and/or the vortex presence and to calculate minor loss
coefficients.
5.2 CONCLUSIONS
The following conclusions were made based on the research conducted and
presented in this thesis.
The conclusions related to Objective 1 are the following:
? The water level can be taken as approximately uniform across the channel.
? The water level increases when there are SETs present. In general, the
water level difference increases as the discharge under submerged
conditions. The water level difference remains approximately constant for
unsubmerged conditions.
? When the vortex phenomenon is present the headwater level is typically
less than when the vortex is not present for the same discharge. In fact,
results obtained from this experimental program indicate the impact of the
SETs on the water levels is significantly less than the impact of the vortex
91
phenomenon. When a strong vortex is present, the velocity field is
strongly multidimensional. Minor loss coefficients are used in a one
dimensional analysis of a flow system. These experiments show that the
multidimensional effects of the vortex are equally, if not more significant
than the onedimensional effects of SETs on upstream water levels.
? Values for the range of data collected indicate less than a 3% increase in
water level due to the presence of the SET model component. Therefore,
it seems that the overall impacts of SETs on water level are small for the
range of experiments performed for this thesis research.
The conclusions related to Objective 2 are the following:
? The inlet control equation describes the flow under both conditions, with
and without the SETs.
? When the differences in the performance relationship for the same model
configuration due to the SET presence are compared, the overall decrease
in the performance due to SET presence can be considered minor.
? There is an apparent decrease in overall culvert performance for the
current research when compared to culvert configuration of the previous
research, especially under submerged conditions.
? It appears the model configurations studied in this thesis research may
impact the performance more than the SET presence. This is especially
true under submerged conditions which are consistent with the constants
used for inlet control design equations presented by FHWA (Norman et
al., 2001).
The conclusions related to Objective 3 are the following:
92
? The barrel minor loss coefficients range from 0.002 to 0.077 and average
to be approximately 0.03 for the entire data set. The barrel minor loss
coefficient due to the presence of SETs is very small; therefore, the overall
impact of SETs on culvert performance is small.
? It seems a consistent relationship for the minor loss coefficient
with DHW , ??
?
?
???
?
gDA
Q , and barrel velocity head can be observed. The
minor loss coefficient increases in relation to these variables, especially
under submerged conditions. For small discharge within the unsubmerged
range, the minor loss coefficient is higher.
? It was determined that the relationship between the minor loss coefficient
and approach velocity head is unpredictable.
? The SETs have larger influence on the culvert hydraulic performance,
especially for small and large values of the parameter ??
?
?
???
?
gDA
Q (less than
0.2 or greater than 0.8).
5.3 IMPLICATIONS
The overall conclusion of this research is the impacts of SETs on culvert
performance are small and may not be significant for most applications. In general, the
minor loss coefficient values calculated can be considered small, however, for submerged
conditions, SET influence on the minor loss coefficient may be considered in culvert
design procedures, especially when the DHW is greater than 1.5 or ??
?
?
???
?
gDA
Q is greater
than 0.8.
93
5.4 SUGGESTED FUTURE WORK
The research related to this thesis is ongoing at the Center for Resources in Water
Research at The University of Texas of Austin. The work discussed in the following
section could help obtain more definitive relationships between the various model
configurations. However, it is the opinion of this author that SETs do not have a
significant impact on culvert performance.
? Construct new culvert and safety end treatment models using the slope of
4:1 or 6:1 and the culvert skew of 45degrees.
? Further investigation into the relationships between the model
configurations studied in this thesis research and their impact on the
culvert performance curves may be useful for further interpretations of the
trends observed.
? The least squares method that was used to fit the data in the previous
research could be completed in order to find the best values for the
coefficients DC , cC , and bC . This method could be applied to the current
research as a whole, as well as, the data set with SET presence and the
data set without SET data sets individually. New values could also be
generated for the entire data set (current and previous research). The
comparison of these coefficients would indicate the relationship change
due to the change in model configurations and the change due to SET
presence.
? Clogging caused by SETs could be examined for barrel blockage ranges
3070% which indicated a more significant impact in previous SET
studies.
94
? Parallel drainage configurations of SETs could be studied and compared to
the trends found for cross drainage SETs.
95
Appendix
96
Summary Raw Data Table for Vertical Headwall Model ? Unsubmerged Conditions
Date Discharge Condition Average depth w/ SET (ft) Average depth w/o SET (ft)
08/12/03 1.296 unsubmerged 0.4190 0.4149
07/28/03 1.307 unsubmerged 0.4278 0.4201
08/01/03 1.458 unsubmerged 0.4524 0.4477
08/01/03 1.708 unsubmerged 0.5058 0.5018
07/31/03 1.743 unsubmerged 0.5149 0.5113
05/21/03 1.801 unsubmerged 0.4006 0.3981
08/12/03 1.897 unsubmerged 0.5382 0.5332
08/01/03 2.144 unsubmerged 0.5934 0.5897
08/13/03 2.169 unsubmerged 0.6149 0.6108
08/15/03 2.246 unsubmerged 0.6049 0.5995
05/21/03 2.269 unsubmerged 0.4972 0.4918
08/14/03 2.601 unsubmerged 0.6633 0.6603
07/28/03 2.696 unsubmerged 0.6897 0.6857
08/13/03 2.847 unsubmerged 0.7128 0.7087
08/14/03 2.973 unsubmerged 0.7390 0.7352
05/21/03 3.001 unsubmerged 0.6395 0.6359
08/14/03 3.289 unsubmerged 0.7958 0.7913
07/23/03 3.304 unsubmerged 0.7927 0.7881
05/21/03 3.311 unsubmerged 0.7047 0.6992
07/31/03 3.319 unsubmerged 0.7913 0.7827
08/13/03 3.877 unsubmerged 0.9006 0.8958
07/29/03 3.892 unsubmerged 0.8933 0.8868
05/21/03 4.189 unsubmerged 0.8639 0.8544
06/04/03 4.315 unsubmerged 0.9243 0.9223
06/09/03 4.329 unsubmerged 0.9508 0.9458
06/03/03 4.372 unsubmerged 0.9184 0.9105
06/06/03 4.530 unsubmerged 0.9797 0.9718
08/12/03 4.531 unsubmerged 0.9926 0.9840
06/09/03 4.633 unsubmerged 0.9978 0.9836
07/29/03 4.812 unsubmerged 1.0238 1.0166
07/30/03 4.829 unsubmerged 1.0331 1.0281
08/05/03 4.829 unsubmerged 1.0379 1.0309
Note: The average depth column with SET or without SET is the average of the 6
individual Pitot tubes located upstream of the culvert model. Samples the individual Pitot
tube readings and the average of them are labeled individual raw data and located after
the summary raw data tables.
97
Summary Raw Data Table for Vertical Headwall Model ? Submerged Conditions
Date Discharge Condition Average depth w/ SET (ft) Average depth w/o SET (ft)
05/20/03 5.025 submerged 1.0069 1.0003
08/05/03 5.151 submerged 1.0897 1.0793
05/13/03 5.274 submerged 0.9777 0.9745
08/04/03 5.568 submerged 1.1426 1.1299
08/05/03 5.728 submerged 1.1659 1.1544
08/15/03 5.943 submerged 1.2046 1.1942
07/23/03 6.070 submerged 1.2326 1.2263
07/30/03 6.070 submerged 1.2609 1.2498
08/06/03 6.197 submerged 1.2587 1.2496
05/23/03 6.288 submerged 1.1263 1.1112
07/30/03 6.308 submerged 1.2883 1.2831
08/15/03 6.437 submerged 1.3267 1.2978
07/31/03 6.661 submerged 1.4003 1.3785
05/23/03 6.768 submerged 1.1944 1.1781
07/25/03 6.888 submerged 1.4358 1.4213
08/06/03 6.946 submerged 1.4559 1.4509
07/28/03 6.965 submerged 1.4598 1.4279
08/04/03 7.003 submerged 1.4758 1.4417
07/23/03 7.041 submerged 1.4844 1.4577
05/22/03 7.044 submerged 1.2881 1.2702
06/09/03 7.118 submerged 1.4740 1.4478
08/06/03 7.195 submerged 1.5376 1.5136
05/22/03 7.249 submerged 1.3304 1.3001
07/24/03 7.351 submerged 1.5600 1.5355
05/20/03 7.420 submerged 1.4356 1.4012
08/08/03 7.527 submerged 1.6403 1.6149
08/08/03 7.527 submerged 1.6403 1.6149
08/04/03 7.566 submerged 1.6104 1.5891
08/07/03 7.566 submerged 1.6559 1.6339
08/11/03 7.566 submerged 1.6760 1.6387
08/07/03 7.606 submerged 1.6839 1.6425
06/04/03 7.709 submerged 1.5568 1.5269
07/25/03 7.764 submerged 1.6860 1.6618
08/11/03 7.804 submerged 1.7151 1.6943
06/10/03 7.905 submerged 1.6285 1.6120
05/23/03 7.925 submerged 1.5215 1.4966
08/08/03 8.044 submerged 1.8219 1.7751
08/11/03 8.104 submerged 1.7744 1.7543
05/22/03 8.124 submerged 1.5335 1.5104
06/12/03 8.144 submerged 1.6894 1.6543
07/28/03 8.145 submerged 1.8102 1.7785
07/25/03 8.389 submerged 1.8794 1.8536
08/07/03 8.471 submerged 1.9054 1.8644
05/23/03 8.927 submerged 1.7321 1.6866
98
Summary Raw Data Table for Mitered Headwall Model ? Unsubmerged Conditions
Date Discharge Condition Average depth w/ SET (ft) Average depth w/o SET (ft)
09/10/03 1.141 unsubmerged 0.3848 0.3762
10/17/03 1.536 unsubmerged 0.5544 0.5488
09/26/03 2.208 unsubmerged 0.6127 0.6048
10/10/03 2.587 unsubmerged 0.6800 0.6701
10/07/03 2.750 unsubmerged 0.7175 0.7084
10/13/03 3.496 unsubmerged 0.8401 0.8345
10/13/03 3.496 unsubmerged 0.8401 0.8345
09/05/03 3.708 unsubmerged 0.8639 0.8549
09/25/03 3.831 unsubmerged 0.8937 0.8878
09/26/03 4.207 unsubmerged 0.9522 0.9431
09/05/03 4.223 unsubmerged 0.9408 0.9347
09/26/03 4.465 unsubmerged 0.9893 0.9819
10/07/03 4.779 unsubmerged 1.0515 1.0363
09/04/03 4.779 unsubmerged 1.0320 1.0179
09/09/03 4.913 unsubmerged 1.0410 1.0227
09/04/03 4.779 unsubmerged 1.0320 1.0179
99
Summary Raw Data Table for Mitered Headwall Model ? Submerged Conditions
Date Discharge Condition Average depth w/ SET (ft) Average depth w/o SET (ft)
10/20/03 5.603 submerged 1.2317 1.2073
09/08/03 5.781 submerged 1.1721 1.1465
09/08/03 6.197 submerged 1.2059 1.1961
10/22/03 5.710 submerged 1.2594 1.2544
10/10/03 6.124 submerged 1.3837 1.3762
09/08/03 6.474 submerged 1.2481 1.2327
09/08/03 6.605 submerged 1.2628 1.2506
09/26/03 7.080 submerged 1.6299 1.6313
10/17/03 5.341 submerged without fin 1.1621 1.1508
10/08/03 5.533 submerged without fin 1.1878 1.1864
10/15/03 6.345 submerged without fin 1.4444 1.4308
10/07/03 6.437 submerged without fin 1.4481 1.4426
10/16/03 6.512 submerged without fin 1.4950 1.4930
10/01/03 6.605 submerged without fin 1.5070 1.5186
10/01/03 6.907 submerged without fin 1.5891 1.5961
10/06/03 6.927 submerged without fin 1.7132 1.7181
10/03/03 7.370 submerged without fin 1.7086 1.7032
10/02/03 7.944 submerged without fin 1.8980 1.8444
Date Discharge Condition Average depth w/ SET (ft) Average depth w/o SET (ft)
10/17/03 5.341 submerged with fin 1.1177 1.1102
10/08/03 5.533 submerged with fin 1.2020 1.1966
10/15/03 6.345 submerged with fin 1.3816 1.3805
10/07/03 6.437 submerged with fin 1.4803 1.4567
10/16/03 6.512 submerged with fin 1.5059 1.5157
10/01/03 6.605 submerged with fin 1.5268 1.5363
10/01/03 6.907 submerged with fin 1.6304 1.6236
10/06/03 6.927 submerged with fin 1.7313 1.7397
10/03/03 7.370 submerged with fin 1.7680 1.7853
10/02/03 7.944 submerged with fin 1.9762 1.9689
100
Summary Raw Data Table for 30degree Skew Model ? Unsubmerged Conditions
Date Discharge Condition Average depth w/ SET (ft) Average depth w/o SET (ft)
03/03/04 0.925 unsubmerged 0.3721 0.3637
03/03/04 1.436 unsubmerged 0.4619 0.4558
02/09/04 1.559 unsubmerged 0.5191 0.5154
01/23/04 1.570 unsubmerged 0.5363 0.5272
02/05/04 1.731 unsubmerged 0.5803 0.5703
02/16/04 2.336 unsubmerged 0.6823 0.6766
03/03/04 2.336 unsubmerged 0.6835 0.6794
02/09/04 2.520 unsubmerged 0.7159 0.7113
02/05/04 2.737 unsubmerged 0.7590 0.7481
01/23/04 2.819 unsubmerged 0.7730 0.7689
02/19/04 3.333 unsubmerged 0.8916 0.8825
02/17/04 3.586 unsubmerged 0.9043 0.8980
03/01/04 3.861 unsubmerged 0.9608 0.9560
03/02/04 3.877 unsubmerged 0.9751 0.9664
02/06/04 4.017 unsubmerged 1.0234 1.0141
02/18/04 4.319 unsubmerged 1.0526 1.0442
01/27/04 4.416 unsubmerged 1.0680 1.0674
01/23/04 4.613 unsubmerged 1.1020 1.0896
01/28/04 4.662 unsubmerged 1.1102 1.1016
02/05/04 4.679 unsubmerged 1.1100 1.0871
03/02/04 4.879 unsubmerged 1.1592 1.1433
02/17/04 4.896 unsubmerged 1.1574 1.1440
101
Summary Raw Data Table for 30degree Skew Model ? Submerged Conditions
Date Discharge Condition Average depth w/ SET (ft) Average depth w/o SET (ft)
02/18/04 5.014 submerged 1.1941 1.1794
03/01/04 5.082 submerged 1.2050 1.1837
01/27/04 5.117 submerged 1.2293 1.2145
02/09/04 5.134 submerged 1.2070 1.2018
02/09/04 5.306 submerged 1.2617 1.2497
02/16/04 5.533 submerged 1.3186 1.3088
02/16/04 5.533 submerged 1.3218 1.3120
02/16/04 5.568 submerged 1.3401 1.3365
02/18/04 5.568 submerged 1.3456 1.3401
03/03/04 5.568 submerged 1.3283 1.3229
01/28/04 5.674 submerged 1.3410 1.3283
02/17/04 5.674 submerged 1.3547 1.3503
102
Individual Raw Data Table for Vertical Headwall Model ? Unsubmerged Conditions
8/12/2003 unsubmerged
Flow Rate
H1 (ft) 1.500
H2 (ft) 1.315
H0 (ft) 0.185
P (ft) 2
Cd 0.609
q (cfs/ft) 0.259
W (ft) 5.000
Q (cfs) 1.296
w/ SET
Manometer Position (ft) Depth (ft)
11 8.8 1.0 0.4192
12 8.7 2.5 0.4178
13 8.9 4.0 0.4205
21 8.7 1.0 0.4178
22 8.8 2.5 0.4192
23 8.8 4.0 0.4192
avg. 0.4190
w/o SET
Manometer Position (ft) depth (ft)
11 8.5 1.0 0.4151
12 8.4 2.5 0.4138
13 8.6 4.0 0.4165
21 8.4 1.0 0.4138
22 8.5 2.5 0.4151
23 8.5 4.0 0.4151
avg. 0.4149
103
Individual Raw Data Table for Vertical Headwall Model ? Submerged Conditions
8/5/2003 unsubmerged
Flow Rate
H1 (ft) 1.774
H2 (ft) 1.315
H0 (ft) 0.459
P (ft) 2
Cd 0.619
q (cfs/ft) 1.030
W (ft) 5.000
Q (cfs) 5.151
w/ SET
Manometer Position (ft) Depth (ft)
11 58.2 1.0 1.0897
12 57.8 2.5 1.0842
13 57.7 4.0 1.0829
21 58.4 1.0 1.0924
22 58.4 2.5 1.0924
23 58.7 4.0 1.0965
avg. 1.0897
w/o SET
Manometer Position (ft) depth (ft)
11 57.3 1.0 1.0775
12 57 2.5 1.0734
13 57 4.0 1.0734
21 57.7 1.0 1.0829
22 57.6 2.5 1.0815
23 58 4.0 1.0870
avg. 1.0793
104
Individual Raw Data Table for Mitered Headwall Model ? Unsubmerged Conditions
9/10/2003 unsubmerged
Flow Rate
H1 (ft) 1.485
H2 (ft) 1.315
H0 (ft) 0.17
P (ft) 2
Cd 0.608
q (cfs/ft) 0.228
W (ft) 5.000
Q (cfs) 1.141
w/ SET
Manometer Position (ft) depth (ft)
11 6.2 1.0 0.3738
12 6.5 2.5 0.3786
13 6.4 4.0 0.3849
21 6.3 1.0 0.3861
22 6.1 2.5 0.3938
23 6.3 4.0 0.3917
avg. 0.3848
w/o SET
Manometer Position (ft) depth (ft)
11 5.6 1.0 0.3657
12 5.8 2.5 0.3691
13 5.7 4.0 0.3754
21 5.7 1.0 0.3779
22 5.5 2.5 0.3856
23 5.7 4.0 0.3835
avg. 0.3762
105
Individual Raw Data Table for Mitered Headwall Model ? Submerged Conditions
10/20/2003 submerged
Flow Rate
H1 (ft) 1.800
H2 (ft) 1.315
H0 (ft) 0.485
P (ft) 2
Cd 0.620
q (cfs/ft) 1.121
W (ft) 5.000
Q (cfs) 5.603
w/ SET
Manometer Position (ft) depth (ft)
11 68.4 1.0 1.2201
12 68.3 2.5 1.2194
13 68.3 4.0 1.2271
21 68.3 1.0 1.2296
22 68.9 2.5 1.2482
23 69.1 4.0 1.2461
avg. 1.2317
w/o SET
Manometer Position (ft) depth (ft)
11 66.7 1.0 1.1970
12 66.4 2.5 1.1936
13 66.2 4.0 1.1985
21 66.5 1.0 1.2051
22 67.2 2.5 1.2250
23 67.5 4.0 1.2244
avg. 1.2073
106
Individual Raw Data Table for 30degree Skew Model ? Unsubmerged Conditions
3/3/2004 unsubmerged
Flow Rate
H1 (ft) 1.463
H2 (ft) 1.315
H0 (ft) 0.148
P (ft) 2
Cd 0.608
q (cfs/ft) 0.185
W (ft) 5.000
Q (cfs) 0.925
w/ SET
Manometer Position (ft) depth (ft)
11 5.3 1.0 0.3616
12 5.3 2.5 0.3623
13 5.4 4.0 0.3713
21 5.4 1.0 0.3738
22 5.5 2.5 0.3856
23 5.3 4.0 0.3781
avg. 0.3721
w/o SET
Manometer Position (ft) depth (ft)
11 4.7 1.0 0.3534
12 4.7 2.5 0.3541
13 4.9 4.0 0.3645
21 4.7 1.0 0.3643
22 4.7 2.5 0.3747
23 4.8 4.0 0.3713
avg. 0.3637
107
Individual Raw Data Table for 30degree Skew Model ? Submerged Conditions
2/18/2004 submerged
Flow Rate
H1 (ft) 1.766
H2 (ft) 1.315
H0 (ft) 0.451
P (ft) 2
Cd 0.619
q (cfs/ft) 1.003
W (ft) 5.000
Q (cfs) 5.014
w/ SET
Manometer Position (ft) depth (ft)
11 65.6 1.0 1.1820
12 65.7 2.5 1.1840
13 65.6 4.0 1.1904
21 65.4 1.0 1.1901
22 66.2 2.5 1.2114
23 66.2 4.0 1.2067
avg. 1.1941
w/o SET
Manometer Position (ft) depth (ft)
11 64.6 1.0 1.1684
12 64.6 2.5 1.1691
13 64.5 4.0 1.1754
21 64.4 1.0 1.1765
22 65 2.5 1.1951
23 65.1 4.0 1.1917
avg. 1.1794
108
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110
Vita
Kathryn Benson was born in State College, Pennsylvania on June 22, 1978 and
raised in several locations due to her father?s military service. She is the daughter of
Walter Benson, Ph.D., MBA, P.E., and Beverly Benson, CRNP. She attended the
University of South Carolina located in Columbia, South Carolina where she received a
Bachelor of Science in Civil and Environmental Engineering and a Bachelor of Science
in Marine Science. She has various published abstracts and performed many conference
presentations in the Marine Science field related to the undergraduate research program,
M.A.R.E., she cofounded. She worked in the engineering consulting field prior to
attending graduate school for 2 years. Water movement has been a passion of hers for as
long as she can remember. She has the best black Labrador Retriever in the entire world,
Malaga, who loves CRWR and was named after Malaga Cove, California where she fell
in love with the ocean.
Permanent address: 9615 Maury Road
Fairfax, Virginia, 22032
This thesis was typed by the author.