hydraulic characteristics of flow and energy dissipation over stepped spillway

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

68

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

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 (α=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,

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69

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



70

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

Dimension of

steps in (cm) Number

of steps

(NS)

Downstream

slope (α)

(V:H)

Run

No.

Model

No.

Series

No.

Crest

Height

P(cm)

Spillway

type

Group

No.

L h

Without step

1:0.75 1-6 1

1 30 Traditional

spillway 1 1:1 7-12 2

1:1.25 13-18 3

4.48 6 3

1:0.75

19-24 1

1 30

Stepped

spillway 2

2.98 4 5 25-30 2

2.24 3 7 31-36 3

6 6 3

1:1

37-42 4

2 30 4 4 5 43-48 5

3 3 7 49-54 6

7.5 6 3

55-60 7

3 30 5 4 5 1:1.25 61-66 8

3.75 3 7 67-72 9



71

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



72


with d/s slope [V: H = 1:0.75] and Ns =7


with d/s slope [V: H = 1:1] and Ns =3


with d/s slope [V: H = 1:1] and Ns =5


with d/s slope [V: H = 1:1] and Ns=7



73

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


[V: H = 1:1.25] and Ns=5


[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

dimensions (h/l=53.13ο, 45

ο and 38.66

ο) 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 (α=h/l=53.13ο and 45

ο). 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 (α=h/l=38.66ο). In this

flow, the jet does not fully impinge on the whole surface of step. It is characterized by water



74

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 (α=h/l=53.13ο). 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 (α=h/l=45ο and

38.66ο). 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.

Α Type 1 Limits of flow

Ns=3 Ns=5 Ns=7

53.13 ο

Jet flow

�� ⁄ � �. ��) ��. � � � � ��⁄ ��. ��)

��. �� ⁄ � �. ��)

45 ο

��. �� ⁄ ��. ��)

��. �� ⁄ � �. � ) -

36.66 ο ��. � � � ��⁄ � �. ��) - -

53.13 ο

partially

nappe

flow

- �. �� ⁄ �1.456 ) �. �� ⁄ �1.109)

45 ο

- �. �� ⁄ � 2.25 ) ��. �� ⁄ ��. �� ) 36.66

ο - ��. �� ⁄ � �. �� ) ��. � � � ��⁄ � �. ��)

53.13 ο

nappe

flow

- - -

45 ο

- - �. �� ⁄ � �. �� )36.66

ο - ��. �� ⁄ � 2.81 ) �. �� ⁄ � 2.23 )

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]),



75

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

(α=36.66 ο

). 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]).

Type3-Skimming flow

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.

α Type 3 Limits of flow

Ns=3 Ns=5 Ns=7

53.13 ο

Skimming

flow

� � ��⁄ � 0.861) � � ��⁄ � 0.632) � � ��⁄ � 0.451)

45 ο

� � ��⁄ � 1.353) � � ��⁄ � 0.926) � � ��⁄ � 0.608)

36.66 ο � � ��⁄ � 1.28) � � ��⁄ � 1.19) � � ��⁄ � 0.86)

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

Table 3: Details of type2 of flow and limitation.

α Type 2 Limits of flow

Ns=3 Ns=5 Ns=7

53.13 ο

Transition

flow

�. �� ⁄ �) �. �� ⁄ . ��)

�. � � �� ⁄ . �� )

45 ο

�. �� ⁄ �. ��)

�. �� ⁄ �. ��)

�. � �� ⁄ �. ��)

36.66 ο �� ⁄ �. � ) �. �� ⁄ �. ��) �. �� ⁄ �. � )



76

the discharge over all stepped models and the model that have steep slope (α=53.13о) is dissipated

more energy than other models that have flat slope; such as (α=45о

and 38.66 о

). 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 (α=53.13о)

dissipated energy of flow more than the other models that have flat slope such as(α=45о

and 38.66 о

).

Discharge Q L/sec

Fig. 11: Relation between Relative dissipation and Discharge for stepped

spillway (models No.1, 2 and3) with d/s slope (α=V: H=1:075)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

Discharge Q L/sec


spillway (models No.7, 8 and9) with d/s slope (α=V: H=1:1.25)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

Discharge Q L/sec


spillway (models No.4, 5 and6) with d/s slope (α=V: H=1:1)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)



77

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.

X (cm)

Fig. 14: Piezometric head distribution over horizontal face for Stepped spillway

model (No.1) with d/s slope (1:0.75) and NS=3

hp

=(z

+P

/γ)

in (

cm)

Pseudo-bottom



78

X (cm)

Fig. 17: Piezometric head distribution over vertical face for stepped spillway


hp

=(z

+P

/γ)

in (

cm)

X (cm)



hp

=(z

+P

/γ)

in (

cm)

X (cm) Fig. 16: Piezometric head distribution over horizontal face for stepped spillway


hp

=(z

+P

/γ)

in (

cm)

X (cm)

Fig. 15: Piezometric head distribution over horizontal face for stepped spillway


hp

=(z

+P

/γ)

in (

cm)



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:

#�� % $ ,� -�� , 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:

#�� % $ ,� -�� , 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)



hp

=(z

+P

/γ)

in (

cm)



80

g = acceleration due to gravity (m/s2),

α1= kinetic correction coefficient, for turbulent flow, generally equal to 1.1, [Chow[16]],

%ο

E

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),

υ= kinematics viscosity of water (m2/sec),

α = Spillway slope,

F٭= Friction Froude number defined as [:+ $ ;/�=> + sin B + CDE&F,

Ks= Roughness height (m) and step dimension normal to the flow: ks=h*cosα,

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 (α) 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).



81

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).

d0 /dc

Fig. 20: Dimensionless relation between Relative dissipation and

(d0/dc) for stepped spillway (series No.1) with (α=V: H=1:075)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

d0 /dc


(d0/dc) for stepped spillway (series No.2) with (α=V: H=1:1)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

d0 /dc


(d0/dc) for stepped spillway (series No.3) with (α=V: H=1:1.25)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)



82

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


(L/dc) for stepped spillway (series No.1) with (α=V: H=1:075)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

L /dc


(L/dc) for stepped spillway (series No.2) with (α=V: H=1:1)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

L /dc


(L/dc) for stepped spillway (series No.3) with (α=V: H=1:1.25)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)



83

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).

F٭

Fig. 26: Dimensionless relation between Relative dissipation and roughness

Froude number (F*) for stepped spillway, (series No.1) with (α=V: H=1:075)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

F٭


Froude number (F*) for stepped spillway, (series No.2) with (α=V: H=1:1)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

F٭


Froude number (F*) for stepped spillway, (series No.3) with (α=V: H=1:1.25)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)



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 (α=V: H=1:1)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

Number of step (Ns)


number of steps for stepped spillway, (series No.1) with (α=V: H=1:075)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)

Number of step (Ns)

Fig. 31: Dimensionless relation between Relative dissipation and number

of steps for stepped spillway, (series No.3) with (α=V: H=1:1.25)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)



85

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(α=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.

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

� .��+( 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 (α=V: H=1:0.75)

Rel

ati

ve

dis

sip

ati

on

(▲E

/E0%

)



86

Fig. 33: Variation of predicted value of (∆E/E0) % with the observed once for all stepped model

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/P>3 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).



87

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.

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hydraulic characteristics of flow and energy dissipation over stepped spillway

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