Hydraulic characteristics of flow and energy dissipation over stepped spillway

1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING
AND TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 8, August (2014), pp. 68-88
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HYDRAULIC CHARACTERISTICS OF FLOW AND ENERGY DISSIPATION
OVER STEPPED SPILLWAY
aRasul M. Khalaf, bRaad H. Irzooki, cSaleh J. S. Shareef
aAsst. Prof., College of Engineering, University of Al- Mustansiriyah, Iraq
bAsst. Prof., College of Engineering, University of Tikrit, Iraq
cAsst. Lecturer, Engineering Technical College, Mosul, Iraq
68
ABSTRACT
In this research, water surface profile, piezometric head distribution and energy dissipation
(E/E0)%, were studied over a stepped spillway of semicircular crest.Different types of stepped
spillway were used. Three types of d/s slope of the spillway (=V: H=1:0.75, 1:1 and 1:125) were
used and three number of steppes (Ns= 3, 5 and 7) for every slope. Seventy two experiments were
performed in a laboratory horizontal channel of 12 m length, 0.5 m width and 0.45 m depth for a
wide range of discharge. The experimental results of the study on stepped spillway show that an
increases in (d0/dc) and (L/dc) value causes an increase in (E/E0)%, and an increases intheroughness
Froude number(F*) and number of steps (Ns)value causes decreasing in (E/E1)% value for all
stepped models. An empirical equation was established for calculating the dissipation energy.
Keywords: Hydraulic Structures; Stepped Spillway; Energy Dissipation.
I.INTRODUCTION
Spillway is a major part of a dam, which is built to release flood flow. Due to the high flow
discharge over this structure, their design and construction are very complicated and usually faced
with difficulties such as cavitations and high flow kinetic energy [1]. It becomes usual to protect the
spillway surface from cavitations erosion by introducing air next to the spillway surface using
aeration devices located on the spillway bottom and sometimes on the sidewalls [2].
When the flow is released over the spillway structure, the potential energy is converted in to
kinetic energy at the toe of spillway. Since the flow is supercritical and has a very high velocity and
hence erosive power. Therefore, this energy should be dissipated in order to prevent the possibility of
sever scouring of the downstream river bed and undermining of the foundations. For this purpose,

2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
several ways were used such as lining by rubbles and riprap, or by constructing steps at D/S ends of
weirs [3].
Stepped channels and spillways have been used for more than 3500 years. The ease of
construction and the design simplicity have led this structure to be more popular since [3]. A stepped
spillway can be defined as that hydraulic structure in which a series of steps of different shapes,
dimensions, and arrangements are built into the spillway surface at some distance from the spillway
crest and extended to the toe.
Stepped spillways allow continuously dissipating a considerable amount of the flow kinetic
energy, such that the downstream stilling basin, where the residual energy is dissipated by hydraulic
jump, can be largely reduced in dimensions. Also, the cavitation risk along the spillway decreases
significantly due to smaller flow velocities and the large air entertainment rate [4]. Many researches,
such as(Chanson [3]), (Chamani and Rajaratnam [5]), (Barani et al. [6]), (Al-Talib [7]), (Hussein et
al. [8]) and (Khalaf et al.[9]), studied and investigated the investigated energy dissipation and
characteristics of flow over stepped spillways of different step shapes and stepped weirs.
The main objectives of this paper are to study the flow characteristics, energy dissipation, and
pressure distribution over stepped spillway for mild slope channels. Furthermore, to develop modify
empirical relation for percentage of energy dissipation and pressure distribution depending on
affecting factors.
II. EXPERIMENTAL SETUP AND PROCEDURE
The experimental program of this study was carried out at the hydraulic laboratory of
technical institute in Mosul. Tests were conducted in a horizontal, glass-walled rectangular channel
of 12m long, 0.5m width and 0.45m depth. Water surface levels were measured at different locations
with an accurate point gauge reading to 0.1mm. Discharges were measured by a pre-calibrated
triangular sharp-crested weir installed at the channel inlet. U/S flow heads were started to measure at
a location (9Hw) U/S of the spillway model, where Hw is the depth of water over the spillway crest.
Twelve moulds were made from plate gage No.16, with crest radius R=6cm, width of the
moulds w=50cm and spillway height P=30cm were used to constructed spillway models from
concrete and tested to study of hydraulic characteristic of flow over traditional and stepped spillway
with semicircular crest. The models divided in tow groups depending upon the profile of spillway.
Group (No.1) contain one series. Series (No.1) divided to three models of traditional spillway
without step and classified based on the variation of downstream slope. [Model (No.1) with (V: H =
1:0.75), Model (No.2) with (V: H =1:1) Model (No.3) with (V: H = 1:1.25)]. Group (No.2)
contains three series of nine models of stepped spillway, [Series (No.1), Series (No.2) and Series
(No.3)]. Every series classified according to the variation of downstream slope. [Series (No.1) with
(V: H = 1:0.75), Series (No.2) with (V: H =1:1) Series (No.3) with (V: H = 1:1.25)]. Series (No.1)
divided to three models based on the number of steps. [Model (No.1) with Ns=3, Model (No.2) with
Ns=5 Model (No.3) with Ns=7]. Also Series (No.2) and Series (No.3), each of them divided to
three models based on the number of steps as the same as Series (No.1). Details of the testing
program are shown in Table (1) and Figure (1).
As well as to investigate the pressure distribution on the spillway surface, nine to seventeen
piezometers were installed on the stepped spillway surface. These piezometers were connected by
rubber tubing to a manometer board with scales that could be read to the nearest 1.0mm.
To ensure stability of water surface levels and uniform flow with very low turbulence, the
models were fixed by adhesive material at a distance of 6m from the channel inlet. After construction
the testing program started by flowing different discharge to overtop the spillway model. All
measurements were conducted at the center line of the channel width. In each test, U/S flow depth
(d0), water surface profile, D/S flow depth (d1), unit discharge (q) and piezometric head for
69

3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
traditional and stepped spillway were measured. The measurements along the spillway models were
conducted under the free flow conditions.
III. WATER SURFACE PROFILESOVER STEPPED SPILLWAY
Water surface profiles over all models of stepped spillway were shown in Figures (2 to10)
which were measured in the center line of the channel. For all models it can be seen that water
surface profiles were becomes horizontal when X/P 2.5 while in traditional spillway X/P 3 where
(P) spillway height. These water surface profiles were used to determine the average velocities and
u/s water heads over the spillway when water surface profiles were essentially horizontal. The trends
of these water surface profiles for all test runs were mostly similar, and it can be seen clearly the
effect of d/s steps on the water surface profiles.
Table1: Details of the traditional and stepped spillway models
70
Dimension of
Number steps in (cm)
of steps
(NS)
Downstream
slope ()
(V:H)
Run
No.
Model
No.
Series
No.
Crest
Height
P(cm)
Spillway
type
Group
No.
h L
Without step
1 1-6 1:0.75
30 1
Traditional
spillway
1 2 7-12 1:1
3 13-18 1:1.25
3 6 4.48
1:0.75
1 19-24
30 1
Stepped
spillway
2
2 25-30 5 4 2.98
3 31-36 7 3 2.24
3 6 6
1:1
4 37-42
30 2 5 43-48 5 4 4
6 49-54 7 3 3
3 6 7.5
7 55-60
30 3 8 61-66 1:1.25 5 4 5
9 67-72 7 3 3.75

4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
Fig. 1: Stepped Spillway and Piezometer Location. (Not to Scale)
Fig.2: Water surface profiles for all test runs for Stepped spillway (model No.1) with
d/s slope [V: H = 1:0.75] and Ns =3
Fig.3: Water surface profiles for all test runs for stepped spillway (model No.2)
with d/s slope [V: H = 1:0.75] and Ns =5
71

5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
Fig.4: Water surface profiles for all test runs for stepped spillway (model No.3)
with d/s slope [V: H = 1:0.75] and Ns =7
Fig.5: Water surface profiles for all test runs for stepped spillway (model No.4)
with d/s slope [V: H = 1:1] and Ns =3
Fig.6: Water surface profiles for all test runs for stepped spillway (model No.5)
with d/s slope [V: H = 1:1] and Ns =5
Fig.7: Water surface profiles for all test runs for stepped spillway (model No.6)
with d/s slope [V: H = 1:1] and Ns=7
72

6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
Fig.8: Water surface profiles for all test runs for stepped spillway (model No.7) with d/s slope
[V: H = 1:1.25] and Ns=3
Fig.9: Water surface profiles for all test runs for stepped spillway (model No.8) with d/s slope
[V: H = 1:1.25] and Ns=5
Fig.10: Water surface profiles for all test runs for stepped spillway (model No.9) with d/s slope
[V: H = 1:1.25] and Ns=7
Generally three types of flow occur when water flows over stepped spillway. Type1is jet flow
or partially flow or nappe flow, Type2 is Transition flow and Type3 is skimming flow. These
regimes of flow are classified as follows:
Type1: Jet flow or partially flow or nappe flow
Type one was observed over stepped spillway at low discharge and varying according to the
73
dimensions (h/l=53.13
, 45
and 38.66
) and number of steps (Ns=3, 5 and 7). Therefore; When water
flow over stepped spillway with a number of step Ns=3, jet flow developed and impinges on the
whole surface of the first step then jet to trend the bed of the channel and hit him at location
(15to17cm) from toe of spillway. The presence of a cell filled with air-between the upper flow, the
vertical face of the step, the horizontal face of the step and the part bed of the channel-is the main
characteristic of this regime. As shown in Figures. (2, 5 and 8).
When the discharge increases from (2 to11 l/sec) and a number of step to Ns=5, jet flow is
converted to partially nappe flow for spillway with downstream slope (=h/l=53.13
and 45
). While
partially nappe flow is developed and then converted to nappe flow at increased the discharge from
(2 to 8 l/sec) for spillway with the same number of step and downstream slope (=h/l=38.66
). In this
flow, the jet does not fully impinge on the whole surface of step. It is characterized by water

7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
impinges on the whole surface of the first step then jet to impinges the fourth step and then it falls
from fourth step to the next one down. The presence of a cell filled with air-between the upper flow,
the vertical face of the step and the small plunge formed over the horizontal face of the step-is the
main characteristic of this regime, as shown inFigures. (3, 6 and 9). In the partial nappe flow, energy
is dissipated in two stages, on impact with the flat surface and more significantly, in the turbulence
created by dispersal of the nappe.
More ever; When increase the discharge from (2 to11 l/sec) and a number of step to Ns=7, jet
flow is converted to partially nappe flow for spillway with downstream slope (=h/l=53.13
74
). While
partially nappe flow is developed and then converted to nappe flow at increased the discharge from
(2 to 8 l/sec) for spillway with the same number of step and downstream slope (=h/l=45
and
38.66
). In this flow, the nappe does fully impinge on the step surface. It is characterized by water
impinges on the whole surface of the first step then it falls from one step to the next one down , the
cells of air described above are alternately filled with a mesh of water and air showing a steady
rotation as shown in Figures. (4, 7 and 10).
From the above analyses it is conclude that jet flow, partially nappe flow and nappe flow
depended upon the discharge, downstream slope and number of step of stepped spillway as
concluded.by(Chanson[3]);(Boes and Hager[10])and (Ohtsuet al. [11]}. The observations on the
physical model built in the Laboratory shown that the above regime of flow for discharges under the
limits shown in Table (2).
Table 2: Details of type1of flow and limitation.
Type 1
Limits of flow
Ns=3 Ns=5 Ns=7
53.13
Jet flow

8. )
)

9. )
45
)
) -
36.66

10. ) - -
53.13
partially
nappe
flow
-
)
)
45 -
)
)
36.66 - )
)
53.13
nappe
flow
- - -
45 - -
)
36.66 - )
)
Type2: Transition flow
Transition flow occurred as the discharge increasing greater than those which limit nappe
flow and continue until the onset of skimming flow was considered to have occurred, the recent
works studied by (Pinheiroand Fael[12]),(Amador et al[13]),(Chanson [3]), agree that a transition
flow is developed, until the onset of skimming flow was considered to have occurred (Chanson[14]),

11. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
as can be seen in Table 3. Transition flow depended to the size and number of steps of spillway to
developed; where, it is observed over the spillway with (Ns=3) at discharge (Q4=22.22 L/sec) and
dc/h=0.977; while; it is observed at less discharge(Q3=13.49 and 14.16 L/sec) with dc/h=1.05 and
1.45 as increases the number of steps to Ns=5 and 7 for the same spillway and downstream slope
(=36.66 ). These values not coincide with the estimated threshold of the onset of skimming flow
that had been established by Rajaratnam[5], by using the expression dc/h= 0.80, which had in turn
been obtained from experimental data from (Essery and Horner [15]).
Table 3: Details of type2 of flow and limitation.
Ns=3 Ns=5 Ns=7
36.66

12. )
)
)
75
Type 2
53.13
Transition
flow
45
Type3-Skimming flow
Limits of flow

13. )
)

14. )
)
)
)
Skimming flow occurs at moderate to high discharges. No nappe is visible and the spillway
is submerged beneath a strong, relatively smooth current. The water flows down the stepped face as a
coherent stream, skimming over the steps and cushioned by the recirculation fluid trapped by the
momentum transfer to the recirculation fluid.
From Figures.(2 to 10), it can be seen that onset of skimming flow was considered to have
occurred when the air-filled cells trapped beneath the upper main flow and the vertical face of the
step filled with an air–water mesh along the entire length of the spillway. The last criterion fits quite
well with (Chanson [14]). The observations on the physical model built in the laboratory show the
skimming flow for discharges under the limits in the Table (4).
Table 4: Details of type3 of flow and
limitation.
Type 3
Limits of flow
Ns=3 Ns=5 Ns=7
53.13
Skimming
flow
) ) )
45 ) ) )
36.66 ) ) )
IV. RELATIVE ENERGY DISSIPATION RATIOAND DISCHARGE RELATION
The relative energy dissipation ratio of flow over stepped spillway model with different
downstream slope and number of steps, were plotted as a function of discharge as shown in Figures
(11 to 13). From these figures it can be seen the relative energy dissipation decreases by increasing

15. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
the discharge over all stepped models and the model that have steep slope (=53.13
76
) is dissipated
more energy than other models that have flat slope; such as (=45
and 38.66
). Also; observed that
model with less number of steps (Ns=3) dissipate energy more than higher number of steps (Ns=5
and 7) for the same stepped spillway. At the range of discharge from (5 to 30L/sec) the relative
energy dissipation decreases from (84% to 60%) for model (No.1), from (79% to 55%) for model
(No.4) and from (78%to44%) for model (No.7). The model that have steep slope (=53.13
)
dissipated energy of flow more than the other models that have flat slope such as(=45
and 38.66
).
Discharge Q L/sec
Fig. 11: Relation between Relative dissipation and Discharge for stepped
spillway (models No.1, 2 and3) with d/s slope (=V: H=1:075)
Relative dissipation
(E/E0%)
Discharge Q L/sec
Fig. 13: Relation between Relative dissipation and Discharge for stepped
spillway (models No.7, 8 and9) with d/s slope (=V: H=1:1.25)
Relative dissipation
(E/E0%)
Discharge Q L/sec
Fig. 12: Relation between Relative dissipation and Discharge for stepped
spillway (models No.4, 5 and6) with d/s slope (=V: H=1:1)
Relative dissipation
(E/E0%)

16. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
V. PRESSURE DISRIBUTIONOVER STEPPED SPILLWAY
The experimental measurements and results of piezometric head profiles along the center line
of the crest and steps of stepped spillway with different downstream slope were found in Figures (15
to 17) show Piezometric head for various discharges over stepped spillway with downstream slope
(V: H=1:0.75), it becomes clear from these figures that the regions of negative readings at the crest
when the discharge is high and number of steps Ns=3. When increases the number of steps to Ns=5,
the negative readings observed near the end of sloping straight line and before the first step of
spillway. This agree as Was mentioned by (Chow[16]),as the spillway must be operated under heads
other than the design head, the pressure on the crest of spillway will increase under the lower heads
and decrease under the higher heads.
When flow rate increased over stepped spillway, this lead to development skimming flow, the
lower area beneath the pseudo-bottom, formed by almost triangular cells, contains maximum
turbulence. The pressure field in these cells is generating exhibit intense pressure fluctuations and
therefore, it is important to know whether fluctuating pressure depressions can cause intermittent
cavitations inception. This is particularly important in the region between the crest and the point of
inception, because this region does not contain air to mitigate cavitations damage. Far below, in the
region of uniform flow, air has reached the bottom layer hence; this reach is well protected against
cavitations damage [17].
Figures (14to16) show minimum piezometric head distribution for various discharges over
horizontal face for stepped spillway. It was found that, the piezometric head on the crest of spillway
will increase under the lower heads and decrease until accrue negative readings under the higher
heads. Also, the negative readings observed on the horizontal face of step number four under the
lower heads and increases under the higher heads for model (No.3).
Figures (17 to 19) show minimum piezometric head distribution for various discharges over
vertical face of stepped spillway. It was found that, the vertical face of all the steps of spillway
mostly was subjected to negative pressure in two cases firstly at low discharge,
resultingjetadherencecausesthestreamlinestobecomemore curvedandtheflowvelocitytobecomehigher
and secondly at higher number of steps; this resulting to converted jet flow to partially nappe flow
and then to nappe flow generating triangular cells, contains maximum turbulence. The pressure field
in these cells is generating exhibit intense pressure fluctuations, these negative pressure converted to
positive pressure when increase the discharge. Matos et al. [18] and Shu-Xun et al. [19] have also
reached the same conclusion.
)
P/z+hp=(X (cm)
model (No.1) with d/s slope (1:0.75) and NS=3 Fig. 14: Piezometric head distribution over horizontal face for Stepped spillway
77
in (cm)
Pseudo-bottom

17. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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X (cm)
Fig. 17: Piezometric head distribution over vertical face for stepped spillway
model (No.1) with d/s slope (1:0.75) and NS=3
78
hp=(z+P/)
in (cm)
X (cm)
Fig. 18: Piezometric head distribution over vertical face for stepped spillway
model (No.2) with d/s slope (1:0.75) and NS=5
hp=(z+P/)
in (cm)
X (cm)
Fig. 16: Piezometric head distribution over horizontal face for stepped spillway
model (No.3) with d/s slope (1:0.75) and NS=7
hp=(z+P/)
in (cm)
X (cm)
Fig. 15: Piezometric head distribution over horizontal face for stepped spillway
model (No.2) with d/s slope (1:0.75) and NS=5
hp=(z+P/)
in (cm)

18. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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79
VI. DIMENSIONAL ANALYSIS
Based on energy relationships, the general relationship for the flow energy dissipation can be
verified. Applying energy equations between U/S and D/S of stepped spillway, one can get:
!
………………………………………………………………………..………….. (1)
!
………………………………………………………………………..………….. (2)
# $
% ……………………………………………………………………..………… (3)
#
' $ (
)
* +
' ………………………………………………………………….…… (4)
The functional relationship for (E/E0%) with the main flow parameters for stepped spillway
may be expressed as follows:
, -#
'. /.
. 0..12.!. 3.425=0 ………………………………………………………….. (5)
Then equation (5) becomes as:
#
' $ ,

19. -
. 6
. 7+. 89.425 ……………………………………………………………….... (6)
Reynolds number (Re) which has very large values and hence its effect on (E/E0%) will be
very little, therefore, Re will be neglected in this study then equation (7) can be rewritten as:
#
' $ ,

20. -
. 6
. 7+. 89.425………………………………………………………………..…(7)
Where:
E0= U/S energy (m),
E1=D/S energy (m),
V0= velocity at sec. 0 (m/sec),
V1= velocity at sec.1 (m/sec),
X (cm)
Fig. 19: Piezometric head distribution over vertical face for stepped spillway
model (No.3) with d/s slope (1:0.75) and NS=7
hp=(z+P/)
in (cm)

21. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
g = acceleration due to gravity (m/s2),
1= kinetic correction coefficient, for turbulent flow, generally equal to 1.1, [Chow[16]],
80
%
DE
o E
= Relative energy dissipation between U/S and D/S of stepped and traditional spillway,
q = discharge over the spillway per unit width (m2/s/m),
dc= critical depth over spillway (m),
d1= D/S depth of water at toe of stepped and traditional spillway (m),
d0= U/S depth of water (m),
= kinematics viscosity of water (m2/sec),
= Spillway slope,
F
EF.
= Friction Froude number defined as [:+ $ ;= + ?@A B + CD
Ks= Roughness height (m) and step dimension normal to the flow: ks=h*cos,
L=Horizontal step (m),
h=Vertical step (m),
Ns = Number of steps.
VII. RESULTS AND DISCUSSION
For each model tested in this study, the energy dissipation investigated. One of the main
objectives of this study is to determine the influence of dimensionless parameter on the energy
dissipation ratio (E/E0) % forstepped spillway with semicircular crest with different downstream
slope () and number of steps Ns.
Effect of U/S water depth to critical depth ratio (d0 /dc)
Variations of (E/E0)% with (d0/dc) for stepped spillway with semicircular crest are shown in
Figures (20 to 22). From these figures one may observed that for all shapes of spillway an increase in
(d0/dc) value causes an increases in (E/E0)%,also; for all three series of stepped spillway the model
with less number of steps Ns=3 dissipated energy more than the models with number of steps (Ns=5
and 7). When the ratio of (d0/dc) increases from (6 to 20) causes an increase in(E/E0)% from (62%
to 91.5%) for model No.1 with (V:H=1:0.75), from (56% to 84%) for model No.4 with (V:H=1:1)
and from (46% to 81.5%) for model No.7 with (V:H=1:1.25). More over; at the same value of
(d0/dc=20) for series No.1 the value of (E/E0)% increases from (67%) for model No.3 to (80%) for
model No.2 to (91%) for model No.1.
This could be attributed to the reason that; as the head above crest of high spillway increases
the overflowing process becomes easier and developing suctionpressureatthecrest and first
stepresultingnappeadherencecausesthestreamlinestobecomemore
curvedandtheflowvelocitytobecomehigher, this lead to developing jet flow over semicircular stepped
spillway after hit it at first step, trying to speed the jet and consequently increase the flow rate
passing over it and increasing the energy dissipation. These results agree very well with previously
published results by Chanson [14]. As well as these figures show that spillway model (No.1) gives
higher energy dissipation than spillways models (No.4 and No.7).

22. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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d0 /dc
Fig. 20: Dimensionless relation between Relative dissipation and
(d0/dc) for stepped spillway (series No.1) with (=V: H=1:075)
Effect of horizontal length of step to critical depth ratio (L /dc)
Variations of (E/E0) % with (L/dc) for stepped spillway are shown in Figures (23 to 25),
these figures show that the values of (E/E0)% increases with increasing the ratio of (L/dc) for all
series of stepped models. When the value of (L/dc) will vary from (0.7to2), the value of (E/E0)%
increases from (61% to 84%) for model No.1, (51% to 72%) for model (No.4) and (34% to 62) for
model (No.7).
81
Relative dissipation
(E/E0%)
d0 /dc
Fig. 21: Dimensionless relation between Relative dissipation and
(d0/dc) for stepped spillway (series No.2) with (=V: H=1:1)
Relative dissipation
(E/E0%)
d0 /dc
Fig. 22: Dimensionless relation between Relative dissipation and
(d0/dc) for stepped spillway (series No.3) with (=V: H=1:1.25)
Relative dissipation
(E/E0%)

23. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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In order to show the effect of horizontal length of step size on energy dissipation Figure (24)
shows a comparison between three configurations of model, model No.3 with (Ns=7), model No.2
with (Ns=5) and model (No.1) with (Ns=3). At the value of (L/dc=1) the values of (E/E0)% are
increases from (60%) for model No.3 to (65%) for model No.2 and (70%) for model (No.1).
moreover; It is clear that as the step size increases with less number of step the energy dissipation
over the spillway increases, more than spillway with small size and higher number of steps for the
same d/s slope of stepped spillway, therefore; the spillway model (No.1) give higher energy
dissipation than spillway models (No.2 and No.3).
L /dc
Fig. 23: Dimensionless relation between Relative dissipation and
(L/dc) for stepped spillway (series No.1) with (=V: H=1:075)
82
Relative dissipation
(E/E0%)
L /dc
Fig. 24: Dimensionless relation between Relative dissipation and
(L/dc) for stepped spillway (series No.2) with (=V: H=1:1)
Relative dissipation
(E/E0%)
L /dc
Fig. 25: Dimensionless relation between Relative dissipation and
(L/dc) for stepped spillway (series No.3) with (=V: H=1:1.25)
Relative dissipation
(E/E0%)

24. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
Effect of Friction Froude number on energy dissipation
As illustrated in Figures (26 to 28) for all three series of experiments of stepped spillway, the
relative dissipation(E/E0)% value decreased with increasing the roughness Froude number (F*). In
order to show the effect of height of step size on energy dissipation Figure (27) shows a comparison
between three configurations of model, model No.6 with( Ns=7), model No.5 with (Ns=5) and model
(No.4) with (Ns=3). At (F*=2) the values of (E/E0) % are increase from (47%) for model No.6 to
(52%) for model No.5 and (58%) for model (No.4). moreover; for the same d/s slope of spillway, it
is clear that as the height of steps increases with less number of steps the energy dissipation is more
than the spillway with small height of steps and more number of steps, therefore; the spillway model
(No.4) dissipates more energy than models (No.5 and No.6).
83
F
Fig. 26: Dimensionless relation between Relative dissipation and roughness
Froude number (F*) for stepped spillway, (series No.1) with (=V: H=1:075)
Relative dissipation
(E/E0%)
F
Fig. 27: Dimensionless relation between Relative dissipation and roughness
Froude number (F*) for stepped spillway, (series No.2) with (=V: H=1:1)
Relative dissipation
(E/E0%)
F
Fig. 28: Dimensionless relation between Relative dissipation and roughness
Froude number (F*) for stepped spillway, (series No.3) with (=V: H=1:1.25)
Relative dissipation
(E/E0%)

25. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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84
Effect of number of step (Ns)
Figures from (29 to 31) show that the relation between relative energy dissipation with
number of steps (Ns) for stepped spillway at different discharge, from these figure it can be shown
that the relative energy dissipation decreases when the number of steps increases for all series and
models at the same discharge,For example, at (Q=9 L/sec) the relative energy dissipation(E/E0)%
value are equal to (76%, 60% and 45%) for series(No.1) of stepped spillway with (Ns=3,5 and 7).
Therefore, stepped spillway with large size and less number of steps (L=4.48cm, h=6cm and Ns=3)
dissipated energy more than smaller size and higher number of steps (L=2.98 and 2.24cm, h=4 and
3cm, Ns=5 and 7) as shown in Figure (29). Also, it is observed from the same figure that stepped
spillway dissipated energy at low discharge higher than at high discharges.
Number of step (Ns)
Fig. 30: Dimensionless relation between Relative dissipation and number
of steps for stepped spillway, (series No.2) with (=V: H=1:1)
Relative dissipation
(E/E0%)
Number of step (Ns)
Fig. 29: Dimensionless relation between Relative dissipation and
number of steps for stepped spillway, (series No.1) with (=V: H=1:075)
Relative dissipation
(E/E0%)
Number of step (Ns)
Fig. 31: Dimensionless relation between Relative dissipation and number
of steps for stepped spillway, (series No.3) with (=V: H=1:1.25)
Relative dissipation
(E/E0%)

26. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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VIII. COMPARISON BETWEEN TRADITIONAL AND STEPPED SPILLWAY
In order to show the effect of stepped on energy dissipation Figure (32) shows a comparison
between four configurations of model with the same height p=30cm and d/s slope(=V: H=1:0.75).
Three models are stepped in series No.1, model No.1 with (Ns =3), model No.2 with (Ns=5) and
model (No.3) with (Ns=7) and one model is traditional with fully smooth in series No.1. In general
view this figure showed a decending trend in energy dissipation with increasing the flow rate for all
types of spillway, this can be attributed to the fact that as flow increases skimming flow dominates
over nappe flow.
It is clear that the energy dissipation over stepped spillway is more than over traditional
spillway with fully smooth. Also; for stepped spillway when the number of stepped increases, the
energy dissipation over the spillway decreases. This means that the small steps have little significant
effect and they are like a smooth surface, this conclusion is agreed with (Amanj [20]).
At the value of discharge increases from (Q=5 to 30 L/sec) the values of (E/E0)% are
decrease from (84% to 61%) for stepped model No.1, while the values of (E/E0)% are decrease
from (45% to14%) for traditional model No.1, moreover; at constant discharge (Q=25 L/sec) the
energy dissipation over the spillway increases from 17% for traditional model No.1 to 34% for
stepped model No.3 to 50% for stepped model No.2 to 63% for stepped model No.1.
85
IX. EMPIRICAL RELATION
Based on equation (7), nonlinear regression analysis in(IBM SPSS Statistics 20) was used to
correlate (E/E0)%with (d0/dc), (L/dc), (F*) and (Ns) in an empirical relation for stepped spillway as
following:
(#
*' $
G

27. +(
*
)
+H4IF)
+H7+FJ

28. +( K
*
……………………………………….... (8)
With a correlation coefficient = 0.954and percentage standard error=-0.407.
A comparison between(E/E0)%values predicted by equation (8) and observed values
experimentally is shown in Figure (33).
Discharge Q L/sec
Fig. 32: Relation between Relative dissipation and Discharge for
traditional and stepped spillway with d/s slope (=V: H=1:0.75)
Relative dissipation
(E/E0%)

29. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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Fig. 33: Variation of predicted value of (E/E0) % with the observed once for all stepped model
86
X. CONCLUSIONS
Based on the results and analysis of this study, the following main conclusions were
summarized as:
1- The U/S water flow heads can be measured correctly at a location when X/P3 U/S of the
traditional spillway and X/P 2.5 U/S of the stepped spillway.
2- The flow regime on a stepped spillway depends on the discharge, downstream slope and the
step geometry.
3- Minimums piezometric head distribution for various discharges over horizontal face of stepped
spillway was found on the crest of spillway then increases under the lower heads and decrease
until accrue negative readings under the higher heads. Also, minimums piezometric head
distribution measured over vertical face of stepped spillway, mostly the vertical face of all steps
of spillway was subjected to negative pressure in two cases firstly at low dischargeand
secondly at higher number of steps.
4- Stepping spillway will improve and increase the energy dissipation andenergy dissipation
decreases by increasing the flow rate over all models. The dissipated energy of flow over the
model with large size and less number of steps (NS =3) is dissipated energy more than the
traditional form and other sizes and number of steps (NS =5and 7).
5- For all shapes and series of stepped spillway an increase in (d0/dc) value causes an increases
in(E/E0)%,also; the model with less number of steps Ns=3 dissipated energy higher than the
models with greater number of steps Ns=5 and 7. More over; at the same value of (d0/dc=20)
for series No.1 the value of (E/E0) % increases from (67%) for model No.3 to (80%) for
model No.2 to (91%) for model No.1. As well as the results show that spillway model (No.1)
gives higher energy dissipation than spillways models (No.4 and No.7).
6- When the ratio of (L/dc) increases the values of (E/E0) %increases for all series of stepped
models. At the ratio of (L/dc=1) the values of (E/E0) % are increases from (60%) for model
No.3 to (65%) for model No.2 and (70%) for model (No.1). moreover; It is clear that as the
step size increases with less number of step the energy dissipation over the spillway increases,
higher than spillway with small size and higher number of steps for the same d/s slope of
stepped spillway, therefore; the spillway model (No.1) give higher energy dissipation than
spillway models (No.2 and No.3).

30. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 68-88 © IAEME
7- For all three series of stepped spillway, when the roughness Froude number increased (F*) the
relative energy dissipation (E/E0) % value decreased. moreover; It is clear that as the height
of step increases with less number of step the energy dissipation over the spillway increases,
higher than spillway with small height of step and higher number of steps for the same d/s
slope of stepped spillway, therefore; the spillway model (No.1, 4and 7) give higher energy
dissipation than other spillway models such as (No.2, 3, 5, 6, 8 and No.9).
8- The relative energy dissipation decreases when the number of steps increases for all series and
models at the same discharge, the relative energy dissipation(E/E0)% value are equal to
(76%, 60% and 45%) for series No.1 of stepped spillway with (Ns=3,5 and 7) at Q=9 L/sec.
therefore; stepped spillway with large size and less number of step(L=4.48, h=6cm and Ns=3)
dissipated energy more than smaller size and higher number of steps (L=2.98, 2.24, h=4,3cm
and Ns=5, 7). Also, observed that stepped spillway dissipated energy at low discharge higher
than at higher discharges.
9- An empirical relations were obtained to estimate (E/E0)%, the first for traditional spillway
While the second relation for stepped spillway.
87
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