Drowning Machines: Low Head Dam Hydraulics and Hazard
Remediation Options
Anita Rogacs, Cole Marr, Anizka Garcia
Rose-Hulman Institute of Technology, Terre Haute, Indiana
Introduction
1.1 Introduction
A father and two sons set out for a day of excitement as they head off to Licking River,
Kentucky. Chad, the youngest, has never been kayaking and this is his big chance to
‘learn the ropes’. With life jackets fastened, all three embark on their quest for fun as
they start into the water. Slipping through the waves, there are bright smiles on their
faces and excitement in their eyes, when the father, Larry Ratliff, catches sight of a
menacing horizon up ahead. He recognizes the danger and looks for his sons. Chad is
too far away to be warned and as his father watches in horror, his youngest son drops out
of sight. In a panic Larry paddles over the low-head dam after his son, thinking that
somehow he will save Chad. Larry is immediately pulled into the hydraulic as well.
Both father and son struggle, but ultimately lose their battle. Both are pronounced dead
at the scene. (“Kentucky”)
Many more tragic stories just like the one related above happen every year, and have
been occurring since the creation of low-head dams. A low head dam is a water control
structure usually below 10 feet high, (Elverum, 2003) and has several uses. These uses
include: ensuring a constant water supply in low flow conditions (White River, 2005),
grade control, aesthetics, and protection for utility crossings. They also have recreational
uses; they provide pools of water in the river for fishing and boating, and are jumps that
canoeists and kayakers paddle over for a thrill. (Low Dams)
Figure 1: Rafters at low-head dam ( Popular Mechanics)
1.2 History
Powering mills was one of the main reasons for the development of the low-head dam.
Water wheels were used to power mills in the 19th century, and these wheels required a
constant supply of water. Low head dams fulfilled this need because they enable the
storage of water for use in low flow conditions. (Colley)
Figure 2: Mabry Mill, Virginia ( Davis, Allen)
Figure 3: Reed Springs Mill, Missouri ( Davis, Allen)
Low-head dams also came into use as early settlers became concerned with the storage of
irrigation water. Originally local water supplies held enough water for their limited
needs. Unfortunately, this dependence on natural water resources forced them to cope
with the varying seasonal discharge. During the late 1880’s and early 1890’s a few dams
were built, but they were “make-shift affairs,” in some cases beaver dams were upgraded.
Orcharding accelerated technological growth due to the increased need for more
elaborate irrigation works and an increased need for storage of water. In the early 1900’s
dams of varying sizes and qualities were built, including earth dams. Earth dams were
common because of the availability of construction materials, and their relatively low
cost. (“Irrigation Technology”)
1.3 Types of Dams
Dams consist of timber, rock, earth, masonry, concrete, or a combination of the afore
mentioned materials. (dam, 2005) Four basic types of dams will now be considered.
These are: 1) Concrete Gravity Dams, 2) Earth Dams, 3) Earth and Rock Fill Dams, and
4) Concrete Faced Rock Fill Dams. These structures can be as simple as a flat-topped
weir or as complicated as a multiple arch dam. Concrete Gravity Dams rely on their own
weight to withstand the applied forces. (Woodward, “Types” 2004) If the water flowing
over the dam produces any cavitation or turbulence, it will slowly erode the structure, to
reduce this effect, many of these dams are made in an Ogee style. ( Encyclopedia:Dam)
Earth Dams are consist completely of homogenous, impermeable earth material. Earth
and Rock Fill Dams have an impermeable earth or clay core, covered with a permeable
rock fill outer layer. Concrete Faced Rock Fill dams mainly consist of permeable rock
fill, which is then covered on the upstream face with an impermeable concrete slab.
(Woodward, “Types” 2004)
Figure 4: Concrete Gravity Dam (ASDSO)
Figure 5: Ogee spillway
Figure 6: Earth Dam
Figure 7: Earth and Rock Fill Dam
Figure 8: Concrete Faced Rock Fill Dam
1.4 Cost
The cost of construction varies widely due to the many variables involved in an estimate.
The type of dam influences the amount of manpower needed and the type of construction
materials required. (“Concrete”)
In the case of an Earth and Rock Fill Dam or a
Concrete Faced Rock Fill Dam, many times the most economical way to obtain the large
volume of rock needed is to use the rock that needs to be excavated during the building of
the spillway. This may not be possible if the quality of the rock acquired from the
spillway is not acceptable for construction. Another important variable to take into
account is the distance that the construction materials must be hauled to get them to the
work site. (Woodward, “Construction” 2004) Also, the river on site has to be redirected
in order to be able to build the dam. This cost depends on how large the river is and how
accessible a place to redirect it is. If, for example, we looked at a 15 ft. wide by 5’ tall
dam, with a road into the site, with no materials at the site (all material and equipment
has to be brought in), and about 20 miles from the materials, the price for the dam
construction might be around $50,000. If one was to try to use this same dam as a power
source, the construction including a power house and all the extra equipment, could cost
around $300,000-$500,000. Or, if one were to consider a bigger dam, one 200 ft. wide
and 15 ft. high, also with access to a road, and material or equipment on site, and about
70 miles from the materials, the construction cost could amount to 1-2 million dollars.
(Desrochers, 2005)
1.5 Safety
Low-head dams are found throughout the United States and pose a considerable safety
risk to the general public. The safety risk arises from the fact that the structures often
look harmless or even inviting to the recreational water user. The danger of these
overflow structures is that the downstream side of a low-head dam contains a submerged
hydraulic jump or “hydraulic” as it is referred to in the boating community (Tschantz,
2003). The hydraulic jump creates a recirculating current which can trap water-goers in a
seemingly endless cycle of being pulled under, struggling back to the surface, being
pushed back toward the falling water, and once again being pushed under (Elverum &
Smalley, 2003). These low-head dams put an unsuspecting public in danger time and
time again.
Figure 9: Roller Effect (Curry, Reed)
The exact number of low-head dam structures throughout the United States is somewhat
vague. Some states do keep track of these structures, but even in these cases the numbers
can be inaccurate. Pennsylvania maintains a list of 280 low-head structures and Virginia
estimates between 50 and 100 in their state (Tschantz, 2003). Some confusion also arises
from the fact that there are no universal definitions or dimensions available to define a
“low-head” dam. According to Leutheusser and Birk (1991), in order to “drownproof”
one of these structures the weir height would have to be increased to approximately seven
times the original height. The fact that there have been no easy or inexpensive retrofits
developed for these structures means that year after year low-head dams are claiming
lives throughout the world.
While Larry Ratliff, mentioned previously, recognized the danger of low-head dams and
would not have willingly gone over the structure if not for his son, this is exactly what
many people do. Many times canoeists and kayakers along with other pleasure-seeking
riders, willingly ride over these dams.
A typical example of this is an event in Minnesota described by Elverum and Smalley
(2003) in a brochure for the Minnesota Department of Natural Resources titled “The
Drowning Machine.” In July 1979, a 25-year-old man on an air mattress went over the
Berning’s Mill Dam, apparently on a dare. He was caught in the recirculating current and
began a cycle of being pulled down and trapped against the dam. Two canoes attempted
to help, both of which were pulled into and trapped in the recirculating current of the
dam. A state trooper and several bystanders attempted a rescue, but were unsuccessful.
In the end three people died in an event that is all too typical at low-head dams. The
structure appeared harmless in the beginning, as most do, and in the end kept its
reputation as one of the most dangerous aspects of our nation’s waterways.
1.6 History of the Charles Mill Dam
The Charles Mill is located in Marion Indiana, in Grant County, and was originally built
in 1855 by John and Jacob Secrist. At this time the mill was called Marion Mills, and
was operated by James Charles, who came from England to work for Secrist. The
building, one of the oldest in Grant County, is still in use after more than a century. In its
earlier days farmers drove their grain to the mill and waited in long lines for their turn to
unload their corn, wheat, or feed for weighing and grading. It was a grist mill, powered
by the dam built at its side. The dam was also built by Secrist, and this dam powered the
machinery in the mill until about 1940 when electricity was substituted. (Simons, 1976)
The dam on the site today is called the Old Mill Dam and was built in 1936 by the Work
Projects Administration (US Government) as a recreation area.
After a time the
ownership of Charles Mill Dam, like countless others, was lost in paperwork. As Owners
die and leave no one in charge of the dams, these structures fall into disrepair and become
the property of the state. The Charles Mill Dam is currently the property of the city of
Marion and is still in use as a recreational site, and the mill itself has shops and
apartments within. (“Low Hazard,” 2002)
Unfortunately, this historic landmark has tragedies in its past. For example, on June 15,
2003, Neil W. Cornell (45 yrs. Old) died after diving into the Mississinewa River at the
Charles Mill Dam to save his twin 11 year old sons who became trapped in the reverse
roller at the base of the dam. The sons were rescued, unfortunately the father could not be
saved.( Ross, 2005)
1.7 Project Description
The Indiana Department of Natural Resources (IDNR) Engineering and Dam Safety
Group and the IDNR Division of Law Enforcement appointed our research group to
conduct an intensive investigation on low head dam hydraulics and affordable hazard
remediation alternatives. Since the hazards of low head dams have been recognized, over
the last few decades, various attempts have been made to eliminate the dangerous
hydraulics at these structures. However, some proving to be more effective than others.
Due to IDNR’s wide range of needs, testing will be performed on two characteristic lowhead dams, one will be a model of the Charles Mill Dam. The goal in modeling these
dams is to arrive at a suitable remediation alternative for the majority of low-head dams
in the state by designing a retrofit that reduces the dangerous hydraulics or by improving
an already existing design. The current options may serve as a useful starting point for
improved hazard remediation options. Along with the reduction of dangerous hydraulic
features, we are also concerned with the environmental impact and implementation cost
of any remediation option which may be available.
Despite the fact that our retrofit design will be applicable to similar low-head dams, only
those that have the same design as the models tested can be expected to follow the
experimental results.
The standards for classification of low-head dams, fatality
statistics, final retrofit solution, and guidelines for implementation will be provided to
IDNR in the final report.
CHAPTER 2
Literature Review
2.1 Introduction
In the last two decades attention has been drawn to the dangers that exist at low-head
dams throughout the country. The dangers include being pushed toward the dam face
and pulled under, being caught in the recirrculating current at the base of the dam, and
decreased buoyancy due to increased aeration from the recirriculating current. State
governments have published several brochures and papers warning recreational users of
these dangers. Newspaper articles show up all too often detailing the tragic drownings
that take place at low-head dams every summer; yet, to date little has been done to rectify
the problem. Some states, such as Minnesota, have started documenting low-head dam
accidents. During the 29-year period ending in 2002, The Boat and Water Safety Section
of the Minnesota Department of Natural Resources reported 53 deaths and 50 injuries at
low-head dams throughout the state (Tschantz 2003). While this is an alarming figure,
many states do not keep such specific statistics, so the aggregate effect of these
dangerous hydraulic structures can not be adequately quantified. However, it is clear that
safety concerns at low-head dams must be addressed.
Research into the components of the hydraulic characteristics found at low-head dam
structures has taken place as far back as about a half century ago. Early investigations on
the subject were chiefly concerned with the characterization of the submerged hydraulic
jump which forms at most of these low-head dam sites. The initial investigations on this
subject do not seem to acknowledge the life-threatening nature of these structures. They
simply try to characterize the phenomena occurring in these locations.
This section describes the previous research on hydraulic jumps and the recirrculating
currents produced at low-head dams. Previous research and the pertinent equations
needed to understand and control these hydraulic characteristics will be presented. In
addition proposed retrofits or alteration plans to eliminate the dangers will be discussed.
2.2 Hydraulic Jump
Hydraulic jumps occur most commonly in man-made channels as a way to dissipate
energy, often gained as water flows down an overflow structure. A hydraulic jump
occurs when flow changes from a supercritical level at the base of the dam to a subcritical
level after the hydraulic jump. According to Hwang and Houghtalen (1996), critical flow
is the flow at which a flow rate, Q, can be passed with minimum energy. This occurs at
the critical depth. Therefore, it follows that if the water level in the structure drops, the
velocity must increase in order to convey the same flow. This situation is called
supercritical flow. When the water depth is greater than the critical depth the flow is
called subcritical, which results in a lower velocity necessary to handle the same Q. The
flow regime can be characterized by a comparison of the unit inertial reaction to the unit
gravitational force or Froude number, F, (Forester & Skrinde 1949). It is defined by
Hwang and Houghtalen (1996) as follows:
F
Where:
In which:
Where:
V
gD
(1)
V = velocity of flow [m/s]
D = hydraulic depth [m]
g = gravitational acceleration [m/s2]
D = A/T
(2)
A = cross-sectional area of flow
T = top width of channel
When a rectangular channel is used for the idealization of the phenomenon, as is
common, hydraulic depth, D, is equal to d, the depth of flow in the section.
By definition when F=1 the flow is critical, when F>1 supercritical flow has developed,
and when F<1 the flow is subcritical. The water levels before and after the hydraulic
jump, or, the change from supercritical to subcritical flow, is defined by the Belanger
equation (Foster and Skrinde 1949; Leutheusser and Birk 1991; and Leutheusser and Fan
2001) :
d2 1 
2
  1  8F1  1


d1 2
Where:
(3)
d1,d 2 = pair of sequent depths
F1 = Froude number at supercritical depth
The Belanger equation applies only to rectangular channels, but provides the only method
for analysis of the jump phenomenon.
Velocity of the flow rate per unit width, q, is determined by:
V
Where:
q
d
(4)
V = velocity of flow [m/s]
q = flow rate per unit width [m2/s]
d = depth of flow
The flow rate per unit width of overflow, q, can be determined using the head on the
overflow (Leutheusser and Birk 1991; and Leutheusser and Fan 2001 :
q
Where:
In which:
3
2
Cw 2 g H 2
3
(5)
Cw = Rehbock weir discharge coefficient
H = head on weir [m]
g = gravitational acceleration [m/s2]
C w  .611  .075
H
P
(6)
H = head on weir [m]
P = height of weir [m]
According to Foster and Skrinde (1949) and Leutheusser and Birk (1991) a hydraulic
jump will form when the downstream depth, d2, satisfies equation 3. From equation 3 it
can be seen that there is an ideal manner for the jump to form. In reality these conditions
do not occur readily in the field.
2.3 Submerged Hydraulic Jump
While it is know how to produce an optimal hydraulic jump, the ideal situation does not
usually occur at low-head dams. The phenomenon which takes place at these structures
is referred to as a submerged hydraulic jump. When the tail water, dt, rises to become
higher than the ideal condition would require in eq.3 the jump becomes submerged. A
submerged hydraulic jump sweeps back on itself and creates a vortex (Leutheusser &
Fan, 2001). “Vortex” is one term of many used to describe the phenomenon. Other
terms for what occurs at a submerged hydraulic jump include “hydraulic”, ‘recirrculating
current”, and “roller” which will be used throughout this paper. According to
Leutheusser and Fan (2001) this roller swirls on a horizontal axis parallel to the dam
creating a strong upstream surface velocity, pushing whatever it comes in contact with
back into the dam. Rajaratnam (1965) and Leutheusser and Fan (2001) have described
the behavior in terms of submergence of the jump using the following relationship:
S
Where:
dt  d 2
d2
dt = local tailwater depth
d2 = second in pair of sequent depths [m]
(7)
The optimal jump occurs when S = 0, the jump is swept downstream if S < 0, and the
dangerous submerged jump happens when S > 0 (Leutheusser & Fan 2001). This relation
illustrates the fact that the submerged jump occurs if the tailwater depth downstream of
an overflow structure exceeds the subcritical depth of the hydraulic jump (Leutheusser &
Fan 2001).
In review, the diagram below shows some of the possible situations at a weir, or dam.
Situation A would be an example of an optimum jump. Situation B is where the
hydraulic jump is submerged, and the reverse roller is produced. Case C is when the
roller disappears and the flow is purely directed downstream.
Early modeling of the horizontal surface velocity of the upstream directed wave was
performed by Leutheusser and Birk (1991). With their initial investigation they
developed an estimate of the surface velocity. In accordance with predicted results the
velocity directed upstream decreased as the tailwater increased (Leutheusser and Birk
1991). Generally, the velocity at low-head dams is calculated to be near this maximum
swimming velocity. It is also important to remember that a 2 m/s swimming velocity is
only achievable by Olympic class athletes and would probably not be possible over the
extended period of time necessary to escape the recirculating current.
In 2001 Leutheusser and Fan developed a more comprehensive method to predict the free
surface velocity:

Vs 
16Edm d1


V1  S  1 1  8F12  1 F12 



Where:
1
3

(8)
Vs = free surface velocity [m/s]
V1 = average velocity of supercritical jump inflow [m/s]
Edm = change in energy defined in Leutheusser & Fan 2001
d1 = first in pair of sequent depths
 = Experimental constant found in Table 1 of Leutheusser & Fan 2001
S = submergence as defined in equation 5
F1 = Froude number at supercritical depth
The change in energy, Edm , is calculated using the equation:
E dm
Where:



d1 
4

2
2

2  S  1 1  8 F1  1  F1 1  C L  
(9)
2 

2
2
2




S

1
1

8
F

1
1





CL = empirical loss coefficient


CL is defined as:
In which:
CL 
E p

q 2 d12 2 g

(10)

E p  P  H   d1  q 2 d12 2 g

(11)
The experimentation of Leutheusser and Fan supports their statement that the free surface
velocity, Vs in equation 8, is about one-third the unsubmerged jump supercritical inflow
velocity V1 (2001). Using general hydraulic methods as well as the relationships
determined by previous research it should be possible to quantify the dangerous hydraulic
features occurring at low-head dam structures.
2.4 Alternatives/Solutions
Increased Spillway Elevation
According to Leutheusser and Birk (1991) many overflow structures are constructed too
low to produce a hydraulic jump that effectively dissipates the increased kinetic energy of
the flow. Although the operational requirements of the low-head dams were satisfied,
Leutheusser and Birk claimed that engineers failed to notice that the low overflow
structures did not allow the flow to go through the optimal, free hydraulic jump. The
faulty hydraulic condition, therefore, posed great danger. The suggested method for
eliminating the dangerous rollers, produced at the base of low-overflow structures, was to
simply elevate the height of the dam. It was theorized that by using the combination of
tailwater depth and the rate of flow at the downstream end of the roller, it would be
possible to determine the required height of the overflow structure that would produce the
optimal hydraulic jump. However, Leutheusser and Birk , realized that the required
height in many cases would be so great that this design option would be impractical
(1991).
Baffled Chutes
Leutheusser and Birk (1991) suggested an alternative retrofit to eliminate the “hydraulic”
of overflow structures completely, see Figure 1. It was thought that “baffled chute
spillways” would provide “continuous energy dissipation by cascade action”
(Leutheusser & Birk 1991). Hotchkiss and Comstock (1992) later experimented with
baffled chutes and found the claim flawed. Baffled chutes dissipated energy by creating
a turbulence that presented a new safety hazard for boaters navigating through the baffles.
Physical models of the baffled chutes showed that scale model boats were often trapped
in the baffled chutes. Furthermore, the collected floating and suspended debris may
result in the overtopping of the basin and damage to the baffle blocks. This occurrence
would require regular cleaning of the blocks.
Figure 1. Baffled Chute Basin. (Dam Safety 1999)
Labyrinth Weir
Hauser et. al. (1991) proposed an alternative design, called a labyrinth weir (Figure 2),
for low-head hydropower dams. The new structure increases minimum flow between
generating periods. Hauser et. al. claim rollers are created when the discharge per unit
width is high. By enlarging the crest length the labyrinth weir has a lower discharge per
unit width reducing the chance of roller formation. Disadvantages of the design include
the difficulty of increasing the crest length and the non-navigable nature of the labyrinth.
Such disadvantages have precluded the Labyrinth Weir from becoming a viable solution.
Figure 2. Labyrinth Weir. (Physical Hydraulic 2005)
Stepped Spillways
Stepped spillways are also used as energy dissipaters for low overflow structures (Figure
3). The flow over the steps can be defined as either nappe flow or skimming flow. In
nappe flow, as water hits each step, it dissipates energy by either breaking up the water
flow in air or mixing the flow on each step. This process may or may not form partial
hydraulic jump on the step (Rajaratnam 1990). In the skimming flow, the flow from each
step travels as a consistent stream, “skimming” over each step creating recirculating
rollers. The momentum transfer to these rollers enhances the energy dissipation over the
structure. Christodoulou (1992) conducted experiments to validate Rajaratnam’s
estimates on the energy loss over stepped spillways. It was found that the amount of
energy lost is mainly governed by the ratio of the critical depth of the water flow passing
over the spillway to the step height (dc/h), and the number of steps N. Furthermore,
greater number of steps and decreasing values of dc/h result in increased energy
dissipation over the spillway. With further experimentation Chamani and Rajaratnam
(1994) were able to present a method to estimate the energy loss within the nappe region
flow and find a relationship for the variation of energy loss at each step. To retrofit a low
head dam, Freeman and Garcia (1996) constructed a four- and a six-step spillway. The
conclusion reached was that even though the six-step spillway performed better, the fourstep arrangement is more cost effective and a more feasible solution.
Figure 3. Four-step spillway. (Freeman 1996)
Rock Arch Dam Conversion
Rock arch rapids are a new retrofit for low-head dams that is currently being investigated
by Dr. Luther Aadland, who is currently taking data at multiple locations where the
design has been implemented. The retrofit design uses three different sized field stones,
which are placed as seen in Figure 4. The downstream end of the rock arch rapids curves
and then becomes flat as it approaches the dam crest. The slope of the rapid is
approximately 5%, which allows fish to swim upstream. The slope of the weirs varies to
match the grade. “Weirs are integrated into the bank and gaps between the large boulders
near the bank are filled with smaller stones to reduce leakage and create pools” (Aadland
2005).
The rock arch dam conversion utilizes varying sized stones. The different sizes are
necessary since each serves a specific purpose. Boulders function as strengthening
elements that add stability to the flow and direct the rapids towards the mid-channel,
therefore, reducing the flow velocity and stress on the river banks. The size of the field
stones or boulders range between three and six feet in diameter. They are set one foot
above the grade and are spaced according to the slope for a maximum of one foot head
loss per weir (Aadland 2005). “Cobble” is used for filling voids near the crest. The size
of these smaller field stones change from one foot to three feet depending on the shear
stress exerted on the rocks due to the varying flow rates. The size of a cobble can be
between one and six inches in diameter.
Aadland claims that the retrofit completely eliminates the “hydraulic” and provides a
pathway for migrating fish. The primary concern with the design is the mobile nature of
stones, which has led to questions regarding the permanence of the structure.
30o ANGLE OF WIER TO BANK
FLOW
5% slope
or lower
SLOPE
D
A
M
C
R
E
S
T
Figure 4. Rock Arch Dam Conversion (Aadland 2005).
CHAPTER 3
Project Approach
3.1 General expectations
To carry out our project successfully, we first conducted an intensive literature search on
low head dam structures, hazards and fatality statistics. After obtaining the necessary
background information, two characteristic low head dams were be chosen for
experimentation. The phenomenon was tested by numerical modeling using Flow3D
(Flow Science Inc.), a fluids modeling software that utilizes finite element analysis. Both
quantitative and qualitative testing was conducted on the velocities and flow direction of
the recirculating and eddy currents using different flow rates. A physical model was then
built to verify the accuracy of the numerical model. Furthermore, successful simulation
of a retrofit that results in a significant reduction of the dangerous hydraulics was tested
on the physical models as well. For the physical modeling the characteristics of both the
recirculating and eddy currents were observed. Using objects of varying size and material
we will also assess the reaction of a human body that comes in contact with the
recirculating current. The data from the analytical and physical models will be compared,
and if they do not agree we will revise the computer model to be in line with the physical
model. The agreeing models will be re-tested and the final data compiled.
3.2 Experimental Procedure
Two types of Dams were tested in the laboratory, an ogee style dam, and a straight dam.
To see the dimensions and composition details of these models see Appendix # .
Figure 14: Straight Dam
Figure 15: Ogee Dam
Three different flow rates were used on each dam, one of high, one of low, and one of
medium intensity. The tailwater depth was controlled by using a flat panel which was
slid up and down to trap water, or let more pass underneath.
Figure 16: Tailwater Depth Control Weir
In order to determine the reach of the roller created, styrofoam was placed in the water to
see which direction it drifted. The height where the current changed from a reverse
current to a forward flowing current was estimated using an air pump connected through
a tube to a fine pointed syringe. The small bubbles created were used to determine the
direction of the flow deeper in the water.
In order to accurately determine the flow rate, the water pump was calibrated. A series of
tests were done and yielded a chart which could be used to identify the calibration factor
needed for each flow rate. (See Appendix# )
3.3 Numerical Modeling
Notation:
The following are used in the paper:
g = acceleration due to gravity
F = Froude number
F1 = Froude number at jump inflow
d1= supercritical depth
d2 = subcritical depth
dc = critical depth
N = number of steps
h = step height
H = head on weir
Cw = weir coefficient
q = flow rate per unit width
S = submergence
dt = local tailwater depth of channel
Vs = surface velocity
Edm = change in energy defined in Leutheusser & Fan 2001
 = Experimental constant found in Table 1 of Leutheusser & Fan 2001
References
Aadland, Luther “Rock Arch Dam Conversion Design” Email to Anita Rogacs. June 9,
2005.
Chamani, M.R., and N. Rajaratnam. “Jet Flow on Stepped Spillways.” Journal of
Hydraulic Engineering. ASCE. Vol. 120, No. 2. (1994): pp 245-259.
Christodoulou, G. C.. “Energy Dissapation on Stepped Spillways.” Journal of
Hydraulic Engineering. ASCE. Vol. 119, No. 5. (1993): pp 644-650.
Forester, J.W., and Raymond A. Skrinde. “Control of the Hydraulic Jump by
Sills.” Transactions of the American Society of Civil Engineers. Vol. 115. (1949):
pp. 973-1022.
Freeman, J.W., and Marcelo H. Garcia., “Hydraulic Model Study for the Drown
Proofing of Yorkville Dam, Illinois,” Hydraulic Engineering Series No. 50.
University of Illinois, Civil Engineering Studies. (1996).
Hauser, G. E., R. M. Shane, and W.G. Brock. “Innovative Regulation Weirs for
Dam Releases.” Proc. 1991 Nat. Conf. on Hydr. Eng.. ASCE. Jul. 29- Aug 2.
(1991): pp 178-183.
Hoctkiss, R., and M. Comstock. Discussion of “Downproofing of Low Overflow
Structures.” Journal of Hydraulic Engineering. ASCE. Vol. 118, No. 11. (1992):
pp 1586-1588.
Leutheusser, Hans J., and Jerry J. Fan. “Backward Flow Velocities of Submerged
Hydraulic Jumps.” Journal of Hydraulic Engineering. ASCE. Vol. 129. (2001):
pp. 514-517.
Leutheusser, H. J., and W.M. Birk.. “Downproofing of Low Overflow Structures.”
Journal of Hydraulic Engineering. ASCE. Vol. 117, No. 2. (1991): pp 205-213.
“Physical Hydraulic Modeling of the Dam.” City of Waco. Water Utility Services.
June 20 2005 <www.waco-texas.com/brazosdesign.htm>.
Rajaratnam, Nallamuthu. “Skimming Flow in Stepped Spillways.” Journal of
Hydraulic Engineering. ASCE. Vol. 116, No. 4. (1990): pp 587-591.
Rajaratnam, Nallamuthu. “Submerged Hydraulic Jump.” Journal of Hydraulics.
ASCE Vol. 91. (1965): pp. 71-96.
Elverum, Kim A. and Tim Smalley. (2003). The Drowning Machine. Retrieved on June
10, 2005, from the Boat and Water Safety Section Minnesota Department of
Natural Resources <http://files.dnr.state.mn.us/education_safety/safety/boatwater/
drowningmachine.pdf >.
Leutheusser, Hans J., and Warren M. Birk. Drownproofing of Low Overflow
Structures. Journal of Hydraulic Engineering. February, 1991. Vol.117, No.2.
Tschantz, Bruce A. Public Hazards at Low-head Dams: Can We Make Them Safer?
National Dam Safety Conference Proceedings, 2003 Dam Safety Conference,
Minneapolis, September 2003.
“Kentucky.” American Whitewater. Accessed 20 June 2005
<www.americanwhitewater.org/safety/archive/year/1997/>.
Elverum, Kim, and Tim Smalley. “The Drowning Machine.” Boat and Water Safety
Section. Minnesota Department of Natural Resources, 2003.
White River Citizen’s Advisory Council Meeting. Indianapolis DPW Engineering Office.
Meeting Summary, 12 Jan. 2005
<www.in.gov/idem/mycommunity/wrac/meetsums/jan_12_05.html>.
“Low Dams.” Miami Conservancy District. Accessed 20 June 2005
<www.miamiconservancy.com/Bike_Trails_&_Recreation/Low_Dams/Default.htm>.
“Irrigation Technology.” Living Landscapes. Royal BC Museum. 22 June 2005
<www.livinglandscapes.bc.ca/thomp-ok/irrigating-of-okanagan/chapter/wilch4.html>.
Colley, Brent. “The History of Mills and Dams Along the Norwalk River.” Norwalk
River Watershed Association,Inc. 22 June 2005
<www.norwalkriver.org/historyofmills.htm>.
Woodward, Richard. “Types of Dams.” The Dam Site. 2004. 22 June 2005
<http://members.optusnet.com.au/~engineeringgeologist/page6.html>.
“dam.” encyclopedia.com. 2005. Columbia Encyclopedia, Sixth Edition. 22 June 2005
<www.encyclopedia.com/printable.asp?url=/ssi/dl/dam.html>.
“Concrete Dam Construction.” The Internet for Civil Enigneers. 22 June 2005
<www.icivilengineer.com/Hydraulic_Engineering/Dam_Construction/>.
Woodward, Richard. “Construction Materials.” 2004. 22 June 2005
<http://members.optusnet.com.au/~engineeringgeologist/page13.html>.
“Rafters at low-head dam.” Online image. Popular Mechanics.com. 27 June 2005
<http://www.popularmechanics.com/outdoors/boating/1277026.html?page=3&c=y>.
Davis, Allen. “Mabry Mill, Virginia.” Online image. The Old Mill Photo Gallery. 27
June
2005 <www.marketcorner.com/photos/watermill.htm>.
Davis, Allen. “Reed Springs Mill, Missouri.” Online image. The Old Mill Photo Gallery.
27 June 2005 <www.marketcorner.com/photos/watermill.htm>.
“Concrete Gravity Dam.” Online image. ASDSO-Kids and Careers. 27 June 2005
<http://new.damsafety.org/layout/subsection.aspx?groupid=12&contentid=69>.
“Earth dam.” Online image. Wahlstrom, Ernest Dams, Dam Foundations and Reservoir
Sites. 27 June 2005 < http://www.dur.ac.uk/~des0www4/cal/dams/foun/gr4.htm>.
“Earth and Rock Fill Dam.” Online image. Wahlstrom, Ernest Dams, Dam Foundations
and Reservoir Sites. 27 June 2005
<http://www.dur.ac.uk/~des0www4/cal/dams/foun/gr4.htm>.
“Concrete Faced Rock Fill Dam.” Online image. Wahlstrom, Ernest Dams, Dam
Foundations and Reservoir Sites. 27 June 2005
<http://www.dur.ac.uk/~des0www4/cal/dams/foun/gr4.htm>.
Curry, Reed. “Roller Effect.”2000.Online image. Below the Millpond. 22 June 2005
<www.overmywaders.com/articles/lowheaddam.jpg>.
Desrochers, Bob. “Cost Estimates.”Personal Interview by Phone. 27 June 2005.
“Ogee dam.”Online image.Batavians. 13 June 2005
<http://bataviansforahealthyriver.org/dam_issues.htm>
“Encyclopedia:Dam.” Nationmaster.com. 13 June 2005
<www.nationmaster.com/encyclopedia/Dam>
Simons, Richard. “Home in The Mill.” Indianapolis Star Magazine.13 June 1976
“Low Hazard In-Channel Dam Visual Inspection Report.” Indiana Department of Natural
Resources. 4 March 2002.
Ross, Whitney. “Safety First- caution needed anytime, anywhere when you’re heading
into the water.” Chronicle Tribune.com. 3 July 2005. 15 July 2005.
<http://www.chronicle-tribune.com/apps/pbcs.dll/article?AID=/20050703/NEW
S01/507030304/1002>