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European Journal of Applied Sciences – Vol. 11, No. 5
Publication Date: October 25, 2023
DOI:10.14738/aivp.115.15756
Hady, I. A., & Mohammed, A. Y. (2023). The Discharge Coefficient for Shaft Spillway According to Inlet Shape and Tail Water
Conditions. European Journal of Applied Sciences, Vol - 11(5). 420-428.
Services for Science and Education – United Kingdom
The Discharge Coefficient for Shaft Spillway According to Inlet
Shape and Tail Water Conditions
Intisar A. Hady
Dams and Water Resources Engineering College of Engineering,
University of Mosul, Mosul, Iraq
Ahmed Y. Mohammed
Dams and Water Resources Engineering College of Engineering,
University of Mosul, Mosul, Iraq
ABSTRACT
The spillway is a hydraulic facility that drains excess water or in flood by
transferring it from the reservoir at the inlet of the dam to the outlet. It is
considered a safety element for the dam. The type of spillway depends on several
factors, including the type of dam, the topographical geological nature of the
ground, the highest discharge, and the frequency of the flood wave. The vertical
spillway is used in cases with a finite area to create another type of spillway. In this
research, three physical intake shape models were used for vertical spillway (the
circular shape C, a quadrilateral shape Q, and an octagonal shape O, with two levels
of tailwater: semi and wholly submerged state, and compared with free state, to
study the flow behaves on the spillway. The results showed that the weir flow
regime occurred in the vertical spillway intake when the ratio H/D
(Head/Diameter) > 0.5, and orifice flow regime when H/D < 0.5. When the tailwater
depth was wholly submerged, the water height upstream (H) was at the minimum
values in the weir flow regime. The height (H) decreases when the tailwater depth
is semi-submerged in the orifice flow regime. Comparison between discharge
coefficient (Cd) for three intake shapes was clear; replacing intake shape (C, Q, and
O) receptivity decreased Cd in the weir flow regime. On the contrary, the discharge
coefficient increases at the same flow conditions in an orifice flow regime.
Keywords: vertical spillway, flow regime, tail water, flow state, discharge coefficient
INTRODUCTION
The vertical spillway is usually built-in narrow valleys or in dams that are built on steep slopes,
rock, and earth dams where it is not possible to build a concrete spillway within the body of the
dam, but rather at a distance from it inside the dam reservoir to prevent erosion and decline
problems. The vertical conduit consists of an entrance, either in the form of a funnel, called the
Morning Glory Spillway (MGS), or in a zigzag form, called the Labyrinth Spillway, then a vertical
diversion conduit (Shaft); it bends at a 90-degree angle (vertical bend), the horizontal exit
conduit (Exit tunnel), and the exit tunnel ends with a stilling or jump basin. The advantages of
this type of spillway are that it has a high capacity for discharge and automatic operation with
a low head; also, it begins to operate without mechanical equipment with any slight head
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Hady, I. A., & Mohammed, A. Y. (2023). The Discharge Coefficient for Shaft Spillway According to Inlet Shape and Tail Water Conditions. European
Journal of Applied Sciences, Vol - 11(5). 420-428.
URL: http://dx.doi.org/10.14738/aivp.115.15756
increase in the water level at the inlet of the spillway, in addition; The low cost of constructing
and it does not take up a large area compared to other types of spillways.[1] & [2]
The flow on the spillway was studied experimentally following Froude similarity. A curved
vertical wall supporting downstream near the spillway, two series of tests were carried out,
one with and the other without the wall in addition to piers placed on the crest, for several
discharges, the experimental presented to ensure radial over morning–glory spillway crest
should be placed the spillway as far as from reservoir boundaries, placement of piers on the
crest is an effects way to avoid the negative effective of the vortex, the optimum number of piers
is five or six, beyond which is no improvement can be expected [3]. The effect of the angle of
the anti-vortex plates on the discharge coefficient of the vertical spillway in a laboratory way
was studied. The results showed that as the angle of the plates at the top of the stream is
reduced, the discharge coefficient increases, thus increasing the efficiency of the outlet
discharge. With increasing depth of immersion, the effect of the plates on the drainage
coefficient decreases, and the maximum discharge coefficient was when using five Anti-vortex
plates at an angle of 60 degrees.[2]. Conducted a study to determine the effect of the inlet shape
of the vertical spillway on the submergence depth. Seven entrance shapes were designed and
tested, including shapes with a square edge and bell shape, three symmetrical cone shapes, and
two eccentric cones. This study focused on a range of Froude numbers ranging from (0.25-
0.65). Experiments showed that the shape with a square edge has the highest dissipation of
vortex energy formed at the entrance than the rest of the shapes, while the depth of immersion
at the entrance of the bell shape is less when compared. Square edge shape.[4]. Water levels,
discharges, and pressure were verified by laboratory experiments of the vertical spillway of
Labaska Dam. The model examination was divided into five alternative spillway crest models
according to the modified techniques. In each model, ten discharges were used. Two of these
models contained barriers, and the other was without barriers in the crest. The results included
comparing the measured values against calculations by the analytical method of the patterns
and conditions of pressure along the length of the spillway vicinity. When identifying the places
that are least loaded to pressure, it was found that they are concentrated at the end of the inlet
part, that is, at the top of the spillway, while the places that are most loaded to pressure are at
the end of the outlet shaft before it expands. The outlet shaft is exposed to the greatest amount
of pressure if flow barriers are used, as this high pressure contributes to the stability of the total
pressure [5]. Proposing a new design for the vertical spillway by replacing the classic circular
section of the inlet with a polygonal shape consisting of 12 sections, which allows the water jet
to enter without separation in the vertical conduit. This shape of the inner surface of the
spillway entrance allows water to flow without curvatures that cause erosion of the concrete
walls. Experiments on the model showed that the highest water level during the highest flood
discharge would decrease by 0.68 m and avoid the phenomenon of cavitation. In addition, the
new design increases the discharge coefficient from 0.46 to 0.52, increasing dam capacity.[6].
The effect of the number and characteristics of pyramidal vortex breakers with square and
triangular bases on the discharge coefficient at the entrance to the vertical spillway was studied
by creating physical groups of three, four, and six of the vortex breakers in four sizes. The
results showed that the group of six vortex breakers causes a significant increase in the
discharge coefficient by up to 50.97% at low discharges close to the crest of the spillway and
an increase of up to 16.13% in high discharges compared to the normal morning glory
spillway.[7]. To treat the problem of the water vortex that occurs when the submerged depth
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is less than the critical depth and its effect on the discharge coefficient of the vertical spillway.
Double water jet was used directed at the vertical spillway, with different vertical and
horizontal distances, and using three diameters of the spillway. The research concluded that
double water jet has a clear effect in dissipating the energy of the vortexes formed at the vertical
intake, especially in cases of orifice flow for large diameters, also as close as the level of double
water jet to the edge of the vertical spillway, it has a positive effect in increasing the discharge
coefficient. [8]. Indicated an experimental on the effect of the deflector in the throat of the
vertical spillway with the shape of a crown wheel inlet on the vortex and the coefficient
discharge, that deflector has an important role in reducing the vortex flow and stabilizing
changes in the water level in the tank. Also, the crown wheel spillway has a 19% higher
discharge coefficient than the simple vertical duct. [9]. Introduced a new shape for the entrance
to the vertical spillway, which is in the form of a bow-tied spillway at different angles (60-150)
degrees and in two cases: the first with a middle arch and the second without a middle arch, to
determine the extent of its effect on the discharge coefficient. The results showed that the
arched spillway without a middle arch led to an increase in drainage with increasing angle.
Therefore, the model with an angle of 150 degrees has a higher drainage coefficient than other
models and has a better hydraulic performance than the Majd Al-Sabah spillway by 10%. As for
the design with a central arch, changing the bend angle did not have a significant effect on the
drainage coefficient.[10]. Used an advanced computational fluid dynamics (CFD) technique to
analyze the hydraulic properties of a new type of labyrinth- vertical spillway. Three physical
models with different crest were used. The results of the analysis showed that the discharge
capacity and discharge coefficient of the vertical labyrinth spillway have higher efficiency when
compared with the vertical spillway of the inlet shape (bell-mouth) at water flows in the case
of a weir, as for high water above the edge of When H/P values are greater than 0.475 (where
H is the height of the water above the edge of the spillway and P is the height of the spillway),
the efficiency of the modern spillway is less than that of a bell mouth.. Good agreement was also
observed between the numerical results and the physical model results, with a slight deviation
due to scale effects in the physical model and convergence of errors in the numerical model.
(Aydin & Ulu, 2023)
This study aims to demonstrate the best case for increasing water discharge from the dam
reservoir at the peak period of the flood.
EXPERIMENTAL WORK
The experiments were conducted in a rectangular channel, 20 m long, 0.7 m glass wall high, and
0.8 m wide, in the Hydraulics Laboratory of Mosul University.
The inclination of the channel is controlled by a circular lever fixed to the ground, as shown in
Fig (1). The water entering the tank can be changed using a gate valve connected to pipes and
a pump. Two water depth measuring devices measured the water's height upstream and
downstream of the channel.
The vertical spillway was set at a distance of 2.5m from the front of the channel using a glass
wall attached to the sides of the canal so that water did not leak except through the spillway.
Three physical models of vertical spillway intake shape were designed: the circular shape C, a
quadrilateral shape Q, and an octagonal shape O with 10cm diameters of the vertical spillway
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Hady, I. A., & Mohammed, A. Y. (2023). The Discharge Coefficient for Shaft Spillway According to Inlet Shape and Tail Water Conditions. European
Journal of Applied Sciences, Vol - 11(5). 420-428.
URL: http://dx.doi.org/10.14738/aivp.115.15756
as the Fig (2). The height of the vertical spillway edge to the bed was 34 cm, and the horizontal
space to the transparent wall was 20cm. The parameter length for each model was calculated
using the software AutoCAD2021, as in Table (1). The depth of the tailwater outlet in the
spillway was changed by a plywood barrel to obtain two tailwater conditions: semi-state and
submerged state, as the Fig (3)
Ninety tests were made, starting with shape C in free tail water state, the water depth over the
vertical spillway crest (H) reading 1.9cm at the beginning and increased to get ten water
depths; five of them obtained low heads less than the radiuses of the spillway (R) which it
classified the free weir regime and the other were greater than (R) which is the state of
submerged orifice regime. The discharge rate was pumped between (2.8-10.5) l/s. Then, the
tailwater condition was changed to semi-submerged and wholly submerged with all preceding
measurements. The crest shape was removed and replaced with (Q and O) in the same
discharge of previous experiments.
Figure (1): section of the laboratory channel
O Q C
Figure (2): The cross-section of the vertical intake shapes
Table 1: the area and perimeter of the shaft spillway entrance shapes
Shaft spillway diameter Area and circumference Shapes
C Q O
(10 cm) Area/cm2 31.41 64.84 100.5
circumference/cm 78.54 171.12 185.23
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a b
Figure (3): shows the type of tail water condition: a- partially tail water state b-fully submerged
tail water condition.
THEORETICAL BACKGROUND
Calculating the Real Discharge
The real discharge was computed with a sharp rectangular crested weir at the terminus of a
channel [12]:
Qr= (0.4(
z⁄v) + 3.22)(l − 0.003)(z + 0.003)
3/2
(1)
Where,
Qr: real discharge (ft3/s)
z: water head measured above the weir (ft)
l: length of the weir crest (ft)
v: height of the weir (ft)
Calculating the Theoretical Discharge of the Weir Flow
Qtheo =2
3
√2g L H3/ 2 )2(
Cd=Qr/ Qtheo (3)
Where,
Qtheo: theoretical discharge m3/s, [13]
Cd: discharge coefficient )-(
H: water head on vertical spillway edge) m)
g: ground acceleration(m/s2)
L: the wetted circumference of the vertical spillway intake (m) and its take from Table (1)
Calculation of the Theoretical Discharge in Orifice Flow
Qtheo = A √2g(H + P) (4)
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Hady, I. A., & Mohammed, A. Y. (2023). The Discharge Coefficient for Shaft Spillway According to Inlet Shape and Tail Water Conditions. European
Journal of Applied Sciences, Vol - 11(5). 420-428.
URL: http://dx.doi.org/10.14738/aivp.115.15756
Where,
A = the area of the vertical spillway (m2)
P = the distance between the outlet hole's center and the spillway's intake edge, m, and its value
is 15cm. (Jalil et al., 2020).
In the case of wholly submerged tail water, H is the difference between the water heights at the
inlet H1 and outlet H2 of the vertical spillway since H=H1–H2 (cm).
RESULTS AND DISCUSSION
The study includes three intake shapes (C, Q, and O) used on a 10cm diameter of vertical
spillway, changes the tailwater depth into two levels, and compares with free outlet flow. Ten
water head (H) were done; five of them less than detective the dimensionless ratio H/R>1, and
the other five achieved H/R<1 as shown in table (2).
It can be seen in Fig (4) that rating curves for three models were used; in a constant discharge,
a circular intake shape gave (H) greater than the other two shapes (Q and O), respectively, in
weir and orifice flow regime, it showed increase the values of (H) in shape (C) more than the
shape (O) with 27.7% and 9.3% in weir and orifice flow regime respectively.
On the other hand, the water height (H) decreases in the wholly submerged tail water state
more than the free state by 9.3% in the weir flow regime. In the orifice flow regime, the depth
(H) decreases in semi-submerged tail water than in the free state by 7.3%, as shown in Fig (5).
When studying the characteristics of flow for the test data by dimensional analysis process, the
comparison between the dimensionless factors discharge coefficient (Cd) with the ratio
Head/Diameter (H/D) for three models (C, Q, and O) in the weir flow regime as shown in fig(6),
it is noted increase (Cd) with increase (H/D) and the greater values of (Cd) were in model (O).
The effect of tailwater depth changing was the best in wholly submerged, where gave the
maximum values of discharge coefficient. Otherwise, in the orifice regime, the intake shape
influence was reversed where the shape (O) obtained the maximum values of (Cd) with the
semi-submerged tail water state, as shown in Fig (7).
Figure 4: The relationship of the real discharge and the water height (H) with the effect
of three intake shapes and free flow condition
0
2
4
6
8
10
12
14
0 5 10 15
Qr(l/s)
H(cm)
C-free
Q-free
O-free
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Figure 5: The relationship of the real discharge and the water height (H) with the effect
of tail water condition
Figure 6: The relationship of Cd vis H/D for three models and the conditions of
tailwater in the weir flow regime
Figure 7: The relationship of Cd vis H/D for three models and the conditions of
tailwater in the orifice flow regime
0
2
4
6
8
10
12
14
0 5 10 15
Qr(l/s)
H(cm)
Q-free
Q-sub
Q-semi
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 0.2 0.3 0.4 0.5 0.6
Cd
H/D weir
C-free
Q-free
O-free
C-sub
Q-sub
O-sub
C-semi
Q-semi
O-semi
0.4
0.5
0.6
0.7
0.8
0.9
0.4 0.6 0.8 1 1.2 1.4
Cd
H/D orifice
C-free
Q-free
O-free
C-sub
Q-sub
O-sub
C-semi
Q-semi
O-semi
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Hady, I. A., & Mohammed, A. Y. (2023). The Discharge Coefficient for Shaft Spillway According to Inlet Shape and Tail Water Conditions. European
Journal of Applied Sciences, Vol - 11(5). 420-428.
URL: http://dx.doi.org/10.14738/aivp.115.15756
Table 2: The values of water height over the vertical spillway crest for all cases of
tailwater and intake shapes.
C- semi C- wholly-sub C- free
3.1 1.8 1.9
3.2 2.5 2.8
3.5 2.8 3.4
4.5 3.5 4.4
5.5 4.2 5.3
6.1 6.9 6.6
7 7.3 7.1
8.2 8.5 8.3
9.5 9.8 9.6
10.5 10.9 10.7
Q – semi Q - wholly-sub Q -free
2.6 1.4 1.6
2.8 2 2.4
3.2 2.6 2.9
.39 3.3 3.6
5.3 4.1 4.8
6 6.0 6.5
6.7 7 6.9
8.1 8.3 8.2
8.5 9.2 8.9
10.4 10.8 10.6
O – semi O - wholly-sub O -free
2.4 1.3 1.4
2.8 1.9 2.1
3.2 2.3 2.9
3.6 2.8 3
4.5 3.3 4.4
5 5.6 5.2
6.5 6.9 6.5
7.6 8.2 7.7
8.5 9 8.7
10.2 10.7 10.5
CONCLUSION
1. The height of the water upstream of the vertical spillway decreases with an increase in
the crest intake length of the spillway, and the minimum height H is at the O model for
all tail water states: semi-submerged, wholly submerged, and free flow.
2. When H/D ratio (Head/Diameter) is less than 0.5, the vertical spillway represents a weir
flow regime, while at H/D higher than 0.5, the flow acts like an orifice flow.
3. The larger water height (H) values in the weir flow at a semi-submerged tail water state
and lower it in a fully submerged state.
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4. In the orifice flow regime, the water height (H) decreases when changing the tailwater
state from free to semi-submerged and increases in wholly submerged tailwater
conditions.
5. The discharge coefficient was at maximum values in a fully submerged tailwater state
with the inlet model C for the weir flow regime.
6. The best model recommended to increased spillway discharge is octagonal shape (O
model) with submerged tail water condition.
List of Abbreviations
H = the height of the water over crest vertical spillway, cm, D = diameter of the vertical spillway,
cm, Q = discharge m3/s, Cd = discharge coefficient, g = ground acceleration m/s, L = the crest
intake length of the spillway, m, a = cross-sectional area of the spillway intake shape m2, Pc =
the distance from the CREST vertical spillway to the center of the horizontal part, m
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