Joseph Lawson Dissertation

University of Brighton Joseph Lawson 10808671
1
Faculty of Science & Engineering
School of Environment & Technology
Final Year Individual Project
in part fulfilment of requirements for the degree of
MEng (Hons) in Civil Engineering
Investigating the use of Converging Ski-Jump Spillways and their effects on the
characteristics of Hydraulic Jump and Energy Dissipation.
By: Joseph Lawson
10808671
Supervised by: Dr. Heidi Burgess
7th
May 2014

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Declaration
I Joseph Lawson, confirm that this work submitted for assessment is my own and is
expressed in my own words. Any uses made within it of the works of other authors in
any form (e.g. ideas, equations, figures, text, tables, programmes) are properly
acknowledged at the point of their use.
I also confirm that I have fully acknowledged by name all of those individuals and
organisations that have contributed to the research for this dissertation.
A full list of the references employed has been included.
Signed: …………………………….
Date: ……………………………….

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Acknowledgements
Throughout the course of this dissertation, I have gained help and guidance from
many University of Brighton lecturers, help from my friends, and continued support
from family.
I would like to express my utmost gratitude in particular, to my dissertation
supervisor, Dr. Heidi Burgess, for all her help, guidance, patience and enthusiasm
throughout this project. I would also like to express my gratitude to all the laboratory
technicians, in particular, Dominic Ryan, who continually supported me though all
laboratory experiments.

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1.0 Abstract
A spillway is a structure constructed on the face of a dam. Ski-jump spillways are the
only hydraulic structures which can efficiently dissipate energy where take-off
velocities exceed 15-20m/s. The design of the ski-jump spillways forms a jet which
causes large amounts of scour around the point of impact, which can be avoided by
converging jets. This research project aims to investigate the use of converging ski-
jump spillways. Modelling both horizontal and vertical converging spillways, across
a range of discharges of flood capacity and analysing the data recorded. Based on the
experiments conducted, the following parameters were analysed: (1) the energy
dissipation in phases two and three; (2) the energy dissipation in phases four and
five; (3) the length of hydraulic jump and length of spilling basin; (4) the
downstream water depth; (5) the characteristics of jet disintegration and air
entrainment; and (6) the effects of cavitation . The majority of the results presented
larger amounts of energy dissipation in phases two and three, and therefore less
scour/erosion would occur on the stilling basin and downstream. The results also
showed that the stilling basin length could be reduced. Although cavitation was
observed on the models with higher energy dissipation.

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Table of Contents
Acknowledgements...................................................................................................... 3
1.0 Abstract .................................................................................................................. 4
2.0 Introduction............................................................................................................ 6
3.0 Literature review .................................................................................................... 8
3.1 Energy Dissipation............................................................................................. 8
3.2 Hydraulic Jump and Froude Number............................................................... 11
3.3 Measurement of the Length of Hydraulic Jump .............................................. 14
3.4 Cavitation......................................................................................................... 15
4.0 Methodology and Design..................................................................................... 20
5.0 Results.................................................................................................................. 28
6.0 Analysis of Results and Discussion ..................................................................... 41
7.0 Conclusions and Future Work.............................................................................. 51
8.0 References............................................................................................................ 53
9.0 Appendices........................................................................................................... 57

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2.0 Introduction
This research project is focused within the area of hydraulics. In particular, this
project aims to analyse hydraulic structures and the variation of energy dissipation
across spillways and stilling basins.
A spillway is a structure which is constructed on the face of a dam. It facilitates the
control of downstream water flow, including removing the risk of flood waters
exceeding reservoir capacities. The most common types of spillways are; the ogee,
overfall and breast-wall (Azmathullah & Deo, 2005), however, for energy dissipation
purposes these are relatively in-efficient; therefore trajectory, or ski-jump spillways
tend to be used. A ski-jump spillway is the only type of structure which can
efficiently dissipate water energy from a dam, where take-off velocities exceed 15-
20m/s (Heller, Hager & Minor, 2005). Ski-jump spillways are widely used,
particularly in areas which experience high levels of flood water. This is due to the
design of the hydraulic structure, in which water can be transferred in a hydraulically
safe manor, and it’s energy dissipated, without affecting the integrity of the structure
(Heller, Hager & Minor, 2005). A ski-jump spillway transfers water by throwing a
water jet away from the spillway edge, through the air, and into a plunge pool or
stilling basin, downstream and dissipating energy as it’s released, (Azmatullah &
Deo, 2005). The design of a ski-jump spillway encourages a high-velocity water jet
to impact on the stilling basin below. This causes a large amount of scour, both
upstream and downstream of the site of impact of that jet (Schmocker et al., 2008).
The impinging water jet produces a breaking hydrodynamic pressure fluctuation on
the downstream rock bed. This can trigger a hydraulic jacking action, in which small
pieces of rock mass can be broken apart and swept downstream, (Azmathullah &
Deo, 2005). This process is known as erosion and can have significant
geomorphological implications to the river basin over long periods of time, (Kehew,
1982).
‘After a full analysis of the current literature that has been published on spillways
and hydraulic structures to date, it is apparent that there is a need to design a more
efficient structure that is less disruptive to the surrounding habitats. In this
investigation, it is necessary to design and test a number of new structures that may
provide a more successful solution than is currently available.’

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This research project aims to investigate the use of converging ski-jump spillways.
More specifically, this project will test both horizontal and vertical converging
designs and analyse their effects on water energy dissipation compared with non-
converging structures. The convergence of two or more jets of water, from ski-jump
spillways, reduces the embodied energy within the jets of water, to the atmosphere,
therefore reducing the effects of erosion to the stilling basin where the water is
transferred, (Steiner et al., 2008). Studies have shown that energy losses that take
place in the period immediately after the ski-jump, when the water is travelling
through the air, directly affect the amount of erosion that takes place within the
plunge pool area, (Nov k & C belka, 1981).Thus having less environmental and
ecological disruptions to the habitats below, (Graff, 2006).
This research project included practical experimental testing of converging and non-
converging ski-jump spillways, within a controlled flume. A hydraulic jump is
formed and energy dissipations were calculated from the raw data collected. The
Hydraulic jump phenomenon occurs during the flow transition from a supercritical
flow to subcritical flow. Large energy losses occur during a hydraulic jump due to
the high turbulent intensity (Chadwick & Morfett, 2013). The energy dissipations of
each spillway were modelled and the results were tabulated. Analytical testing was
carried out and a full examination of the information has been concluded to compare
for a range of hydraulic discharges.

8
3.0 Literature review
3.1 Energy Dissipation
The classic overflow spillway, i.e ogee or overfall are smooth and have a streamlined
surface and overflow transitional section into the stilling basin. Therefore
comparatively, only a small percentage of energy can be dissipated on the spillway
surface, where an accelerated movement of water passes. Consequently the majority
of the energy dissipation will take place in the hydraulic jump. This high localised
energy dissipation produces large forces on the stilling basin and requires one with
significantly large dimensions, and high construction and upkeep cost.
To lessen these forces, alterations to the spillway, and different overflow design
solutions have been investigated, providing energy dissipation at various phases
during the passage of discharge ov bel a, . For example baffles can
be used on the spillway surface and a ski-jump to the end of the spillway. These
produce an intensive energy dissipation in the phases during and before the impact
with the stilling basin. As a result the forces acting upon the stilling basin, are now
just residual energy which can be dissipated in a much smaller and inexpensive
stilling basin. ov and bel a (1981) had produced research and concluded that
if a ski-jump spillway was designed where the overflow jet was projected far enough
away from the edge of the jump, aided by a particular spillway surface, and the jet
falls upon a firm rock bed, then it could be possible to not have a stilling basin at all.
The Froude law of similarity (Avery & Novak, 1978) can be used to most efficiently
model the energy dissipation over a spillway for the most economical and
technological designs. The Froude law is explained in more detail in section 3.2.
Formalised by ov and bel a (1981), there are different phases of the passage
of discharge over a spillway and stilling basin, which incorporate a ski-jump and
baffles. The five phases are:
1. The phase where the water flows down the spillway, from the crest down
to the edge of the spillway.
2. The phase where the water takes off from the edge of the spillway, travels
through the air and hits the surface of downstream water.
3. The phase of impact with the stilling basin pool.

9
4. The phase of the hydraulic jump in the stilling basin pool.
5. The phase of transition from hydraulic jump and into conventional river
flow.
Energy Dissipation in the Second Phase
During the second phase where the water takes off from the edge of the spillway,
travels through the air and hits the surface of downstream water, there are three main
types of energy dissipation. These are air resistance, internal friction and in
particular, the collision of different separated overflow jets and the water particles
within.
The ski-jump spillway together with a combination of the three main types of energy
dissipation, disperses and aerates the overflow jet in supercritical flow. The
effectiveness of this energy dissipation is increased by the compression of entrained
air bubbles as part of a colliding jet mixture, ( ov bel a, . hese ets
apply much less stress on the stilling basin then an unaerated compact jet.
However the dispersed and aerated overflow jet does not substantially increase the
energy dissipation during phase two (the fall); the energy dissipation is around 12%,
as discovered by Horeni (1956). Although the dispersed and aerated overflow jet
does contribute greatly to energy dissipation upon impact with the stilling basin pool,
phase three. What does produce the high energy dissipation in phase two are the
multiple colliding jets themselves.
The collision of these jets is a highly complicated hydraulic problem, but by treating
it as a vertical sum of momentum problem, with the two jets being symbolised as
solid colliding bodies, on a two-dimensional plane, an approximation of the specific
energy loss can be calculated. Faktorovich (1952) derived such an equation, which is
expressed in equation 3.1.1 below:
(eq. 3.1.1)
Where k2 is the specific energy loss, qI and qII are specific discharges relating to jets
I and II, and vI and vII are the jets mean velocities during collision.

10
The above equation has been used for many years, by such people as Komora (1969)
and has proven to produce an adequate approximation for specific energy loss.
However the actual energy loss for this hydraulic jet collision problem is actually
larger than Faktorovich's equation estimates. This is due to volumetric alterations in
the entrained air bubbles of the aerated jets. The rapid compression when the jets
collide contributes an additional energy loss ov and bel a, .
Many engineers such as Faktorovich (1952) and Roberts (1980) have produced a
variety of overflow spillway designs involving the jet collision principle to dissipate
energy intensively. Some of Faktorovich's (1952) designs incorporated the use of
bottom outlets combining with the spillway flow. Whereas many of Roberts (1980)
designs incorporated a few baffles along the spillway surface and a ski-jump beneath.
In 1934 Roberts design was used to construct the Vaalbank and Loscop dams in
South Africa. Figure 3.1.1 below depicts two of Skoupy's designs, figure 3.1.1a
shows a design using deflectors and figure 3.1.1b shows a design combining
deflectors and baffles at various locations on the spillway. This design in figure
3.1.1b can significantly increase the energy dissipated in phase 1 and 2.
Figures 3.1.1 - Spillways with baffles and deflectors (Horsky, 1961)
Energy Dissipation in the Third Phase
During the third phase the water impacts with the stilling basin pool. The energy
dissipation in this phase is due to the water mass colliding with the downstream
stilling basin pool. It is also due to the compression of entrained air bubbles within
the overflow jet undergoing rapid pressure increase at the point of impact. The
energy dissipation increases with greater aeration and dispersion of the overflow jet.
It is therefore logical to aim to achieve an overflow jet which maximises the aeration

11
and dispersion during phase two. However in phase three these energy losses can
only be achieved if the downstream pool is sufficiently deep at point of impact.
3.2 Hydraulic Jump and Froude Number
The Hydraulic jump phenomenon occurs during the flow transition from a
supercritical flow to subcritical flow. Large energy losses occur during a hydraulic
jump due to the high turbulent intensity. It is not possible to use the specific energy
method for this phenomenon, therefore the momentum and continuity equations are
used to establish a relationship between upstream depth y1 and downstream depth y2,
which also incorporates the Froude Number, Fr (Chadwick & Morfett, 2013). A
Reference diagram for the momentum and continuity equations is shown in figure
3.2.1 below:
Figure 3.2.1 - Reference diagram for the momentum and continuity equations (Nalluri and
Featherstone, 2001).
The Froude Number in its simplest form is shown in equation 3.2.1 below:
√
(eq. 3.2.1)
Where V is the flow velocity, g is the acceleration due to gravity and L is a
characteristic dimension. For the experiments carried out in this investigation the
characteristic dimension was expressed as yi which was the depth at a location i in
the channel. This produced the equation 3.2.2 below:
√
(eq. 3.2.2)
The basic principle of the Froude Number was that it classifies the regime of flow.
The Froude Number has become one of the most important figures in Hydraulic
Jump and many other hydraulic structure analyses (Mahmodinia et al., 2012). The
main reason for the Froude Number being so important is it can directly classify the

12
regime of flow, and can produce a link between upstream and downstream
dimensional properties. There are three classifications of the Froude Number which
are Subcritical flow, Critical flow and Supercritical flow.
 Subcritical flow is when the flow velocity V is less than the critical flow
velocity Vc. This is when Fr < 1, and downstream control effects upstream
water level.
 Critical flow is when the flow velocity V is equal to the critical flow
velocity Vc. This is when Fr = 1, and undular standing waves are created by
unstable flow.
 Supercritical flow is when the flow velocity V is greater than the critical
flow velocity Vc. This is when Fr > 1, and downstream control do not effect
upstream water level, since flow disturbances travel downstream only, due
to the water velocity being greater than the wave velocity. This is different
to subcritical flow, where flow disturbances travel downstream and
upstream.
The United States Bureau of Reclamation (USBR), produced a table which clearly
classifies the type of hydraulic jump, in respect to its upstream Froude Number and
presents approximate energy dissipations for each type. This table is shown in figure
3.2.2:
Hydraulic Jump Classification (USBR, 1955)
Type of Jump Froude Number, Fr Energy Dissipation
Undular Jump 1.0 - 1.7 < 5%
Week Jump 1.7 - 2.5 5 - 15%
Oscillating Jump 2.5 - 4.5 15 - 45%
Steady Jump 4.5 - 9.0 45 - 70%
Strong Jump > 9.0 70 - 85%
Figure 3.2.2 - Hydraulic Jump Classification and Energy Dissipations (USBR, 1955)
As stated above a relationship can be established between upstream depth y1 and
downstream depth y2, using the momentum equation. The resulting equation for y2 in
terms of y1 is shown in the equation 3.2.3 below (Streeter and Wylie, 1981):
( ) (√ ) (eq. 3.2.3)

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and y1 can also be found in terms of y2 as shown in the equation 3.2.4 below:
( ) (√ ) (eq. 3.2.4)
The equations 3.2.3 and 3.2.4 above are true for rectangular horizontal channels with
constant channel width and assuming all wall and bed friction are negligible
(Chanson,1995).
The energy loss through the hydraulic jump can be determined by evaluating
equation 3.2.3 in terms of y1. Therefore an equation for the change in energy or
energy dissipation is shown in equation 3.2.5 below:
( ) ( ) (eq. 3.2.5)
By substituting in discharge, , an energy dissipation equation can be found in
terms of q and y, shown in equation 3.2.6 below:
( ) (eq. 3.2.6)
Equation 3.2.3 can be rewritten with Fr1
2
as the subject, shown in equation 3.2.7
below:
( ) (eq. 3.2.7)
and equation 3.2.7 can be found in terms of q and y, shown in equation 3.2.8 below:
(eq. 3.2.8)
By substituting in equation 3.2.7 and equation 3.2.8, an energy dissipation equation
can be found in terms of y1 and y2 only, shown in equation 3.2.9 below:
(eq. 3.2.9)
For investigation and experimental purposes it is very useful to have equation 3.2.9
to calculate the energy dissipation purely in terms of the flow depth parameters. It
can be seen in equation 3.2.9 that the relative height of the jump, y2-y1 cubed, that
with increased relative height of the jump, the energy dissipation is sharply
increased. Therefore if the aim in an investigation is to produce a large energy
dissipation, it is also an aim to achieve an increased relative height of the jump.

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The efficiency of the hydraulic jump can be calculated using the energy upstream, E1
(calculated using equation 3.2.11) and the energy downstream, E2 (calculated using
equation 3.2.11). The efficiency of the hydraulic jump, η is shown in equation 3.2.10
below:
(eq. 3.2.10)
(eq. 3.2.11)
(eq. 3.2.12)
3.3 Measurement of the Length of Hydraulic Jump
The length of the hydraulic jump has typically been difficult to measure. The
definition of this length is the horizontal distance Lj from the start of the roller
upstream, in supercritical flow, to the downstream section where the mean surface
water achieves an approximate maximum flow depth, and is reasonably level, in
subcritical flow (Ead & Rajaratnam, 2002). Consequently a sizable human error is
usually introduced with the determination of this measurement, since investigating
engineers determine the end of the jump in different locations. To normalise the
length of hydraulic jump, equations have been produced to match the values from
experimentation. Chaudhry (2008) produced such an equation to approximate the
length of jump, shown in equation 3.3.1 below:
[ ] (eq. 3.3.1)
Due to the difficulties in determining the length of jump, involving residual
turbulence and surface waves at the end of the hydraulic jump, studies have been
produced to find an improved and easier parameter to determine a hydraulic jump
length characteristic measurement. Many studies including Carollo and Ferro (2007),
Ead and Rajaratnam (2002) and Rutschmann and Hager (1990) support this need for
an improved measurement and all state that the 'length of roller' would be easier to
measure. This is due to the end of the roller being easy to observe, particularly in
steady flow conditions. The definition of the length of roller is the horizontal
distance Lrj from the start of the roller upstream, in supercritical flow, to the

15
downstream point of surface stagnation (Carollo & Ferro, 2012). This is represented
graphically in figure 3.3.1 below:
Figure 3.3.1 - Graphical depiction of Jump Length and Roller Length (Ead & Rajaratnam, 2002).
The length of roller Lrj can be calculated by equations 3.3.2, 3.3.3 and 3.3.4. The
applicability of the relationships are verified by Carollo (2007).
( ) (eq. 3.3.2)
( )
(eq. 3.3.3)
( ) (eq. 3.3.4)
Where is a coefficient equal to 4.616, 0 is a coefficient equal to 2.244, and b0
depends on the ratio between surface roughness ks and h1. The coefficients and 0
were found through experimentation by Carollo (2007). In this research project a
negligible surface roughness ks was assumed in all experiments, therefore these
equations were not valid in this project.
3.4 Cavitation
Cavitation Background
Many hydraulic structures including spillways are affected by cavitation, involving
several mechanisms of damage. The process of cavitation is where a void or bubble
forms within a liquid. Falvey (1990) explained cavitation as the change of state from
a liquid to a vapour, by reducing the local pressure, whilst keeping a constant
temperature. The reduction in local pressure can be from vortices or turbulence in
flowing water.

16
Within a hydraulic structure, the water flow can contain impurities and air bubbles of
various types and sizes, ranging from microscopic to a few centimetres. These
microscopic impurities and air bubbles are essential to initiate cavitation, and are part
of what causes the damage to hydraulic structures.
The occurrence is a property which can also be used to describe cavitation. For
instance, increases in the flow velocity, decrease the flowing water pressure. A
critical condition is achieved here, at the point where cavitation begins, which is
called incipient cavitation. Likewise if flowing water pressure increases and flow
velocity decreases then another critical condition is achieved called desinent
cavitation, (Falvey, 1990). In practical purposes the distinction between these two
conditions is not relevant; however in laboratory investigations it becomes more
significant. There is also a third critical condition known as supercavitation,
developed flow or cavity flow, which is when individual cavitation bubbles rapidly
transition into large cavitation voids.
Due to the critical nature of cavitation and the occurrence of cavitation to occur and
to supercavitate, a parameter was defined to explain the cavitation in a system,
known as the cavitation index, σ. The Bernoulli equation for steady flow between
two points is used to derive the equation for the cavitation index, and the full
derivation can be found in the ‘ avitation of hutes and Spillways’ Falvey, 0 .
Therefore the cavitation index is given in equation 3.4.1 below:
(eq. 3.4.1)
Where E0 is the potential energy at a reference point, Z is the elevation vertical, ρ is
the fluid density, g is the acceleration due to gravity, Pv is the fluid vapour pressure
and V0 is the fluid velocity at a reference point. If Z is equal to Z0 then the equation
above can be refined as the following equation below:
(eq. 3.4.2)
Where P0 is the pressure at a reference point.
Evaluation of both equations 3.4.1 and 3.4.2 show that with an increase in fluid
vapour pressure Pv, the cavitation index decreases, therefore increasing the changes
of cavitation and supercavitation.

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For streamline smooth bodies, the peak negative pressure materialises at the
boundary, and pressure measurements made at the surface can be used to estimate
the cavitation index. However for non-streamlined bodies, the peak negative pressure
will materialise within the flow, due to the flow separating from the body (Falvey,
1990).
Figure 3.4.1 depicts the development of cavitation, and their respective cavitation
indexes. The figure therefore shows that cavitation will not occur for a cavitation
index of larger than 1.8, and supercavitation will only occur for a cavitation index of
less than 0.3.
Figure 3.4.1 - Development stages of cavitation (Falvey, 1990).

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Damage from Cavitation
Cavitation can cause a large amount of damage to hydraulic structures, including
spillways. An example of damage to a spillway would be where cavitation forms on
an irregular surface. The damage will occur on the downstream end of the collapsing
cavitation bubble cloud. After some time, a crack or hole will form on the surface of
the concrete and over more time this will increase in size due to the increased
pressure and flow velocity impinging on the downstream edge of the hole. Therefore
bits of aggregate or small chunks will likely start to erode away (Falvey, 1990). The
damage can be substantially increased if the spillway includes reinforcement bars.
This is due to, if the erosion exposed the bars to the high flow velocity, the bars
could start to vibrate; leading to what could be significant breach in the dam
structure, or a catastrophic mechanical failure. In 1983 the Bureau's Glen Canyon
Dam had this happen to its spillways, causing a substantial amount of damage.
It is important to know the factors which effect cavitation damage in order to be able
to design against them. Falvey (1990) outlined some of the main factors as follows:
 Cause of cavitation
 Location of cavitation damage
 Intensity of cavitation
 Flow velocity magnitude
 Flow air content
 Surface resistance to damage
 Time of exposure to the cavitation
Damage from cavitation can occur in different locations depending on the shape of
the hydraulic structure surface and its roughness properties. The surface roughness
can be categorised into two main categories, singular roughness and uniformly
distributed roughness. A singular roughness involves a surface which has protruding
irregularities which are smaller than the singular roughness irregularities itself.
Whereas a uniformly distributed roughness does not have singular roughness’s
(Falvey, 1990).
Singular roughness’s are sometimes known as local asperities, of which some
hydraulic structure examples include:
 Offset into the flow (figure 3.4.2a)

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 Offset away from the flow (figure 3.4.2b)
 Abrupt curvature away from flow (figure 3.4.2c)
 Voids and transverse grooves (figure 3.4.2e)
 Protruding joints(figure 3.4.2g)
The figure below shows graphically some isolated roughness elements:
Figure 3.4.2 - Typical Isolated roughness elements located on hydraulic structures (Falvey, 1990)
The spillways in this investigation are based around dissipating high amounts of
energy. When utilising converging jets in ski-jump spillway design, high amounts of
aeration occurs (see section 3.1). It is known that aerated flows prevent cavitation
damage to some degree, where used with hydraulic structures (Bradley, 1945).

20
4.0 Methodology and Design
Methodology
For this research project, experiments were conducted within a scaled flume located
at the University of Brighton. The parameters of the flume were; length (L) equal to
5m, width (b) equal to 300mm, and height (h) equal to 475mm. The discharge
pumped though the flume was part of a hydraulic circuit to provide a steady
discharge recirculation. The flume had a maximum discharge, Qmax equal to 118.8
m3
/h, or 0.033 m3
/s, and was measured by an electro-magnetic flow meter, with a
maximum error to the order of 0.2%.
The flow depths (yi) were measured using manometers, with a zero reference at the
base of the flume. The accuracy of the manometers was to the order of 0.5mm and
the pressure heads were read taken to the closest millimetre, due to a fluctuation
turbulent flow. The longitudinal distance i.e. to measure the length of jump/roller,
was measured using a scale along the base of the flume, with a zero reference at the
take-off edge of the ski-jump spillway. The accuracy of this scale was to the order of
1mm. The experiments were all conducted for classic hydraulic jumps, therefore the
inclination angle (α) was equal to 0o
.
In the experiment a pre-fabricated ski-jump spillway was utilised, and tested on its
own, to achieve a base energy dissipation result which would act as a comparator for
alternative designs. The dimensions of the spillway are; height of the peak (P) equal
to 310mm and width 300mm, with a flip-bucket with deﬂection angle (β) and of
radius (R). Deflectors were added to the pre-fabricated ski-jump spillway, to achieve
predicted increased energy dissipation. One model aimed to vertically collide the
overflow jets, and another to horizontally collide the overflow jets.
The flow approaching the spillways was non-aerated, known as "black water". The
jet cavity was naturally aerated to atmospheric pressure. These experiments were
restricted to a horizontal flow channel approach, which kept in unison with bottom
outlet investigations, as such avoiding complications with steeply sloping chute
ﬂows. herefore the data is not li ely to give a true representation of all field
applications with high bed slope angles, although does give a good estimation and
comparative data to other laboratory investigations (Juon & Hager, 2000). Heller,

21
Hager & Minor, (2005) considered this sufficient in their studies of ski-jump
spillway hydraulic parameters.
Part of the limitations of using a flume in this project is that sidewall effects may
occur. These sidewall effects may have a negative influence on the results within this
research project. This is due to the narrow flume width, where the water is deflected
by the edges of the flume, causing manufactured results (Chiang et al., 2000). The
impact of this has been ignored for the purposes of this dissertation research project,
however, the impacts of the sidewalls remained constant throughout the experiments,
thus keeping consistency in the data analysed. The effects of the sidewalls were
minimised by the manometers being arranged centrally in the flume width. It was
also noted that the surface roughness was not a variable in this investigation, due to
the bed roughness not being a variable parameter in the hydraulic flume.
The experiments were tested for a scaled design discharge (Q) of 33m3
/h
(0.00917m3
/s) which was approximately similar to the 1:50 scaled discharge of a
large dam spillway under high flood conditions. The experiments were therefore
tested for 15 discharge increments ranging between 26-40m3
/h (0.00722-
0.01111m3
/s).
The raw data measured in the experiments were; upstream depth (y0), supercritical
depth (y1) and downstream depth (y2), (see figure 4.1). The downstream gate height
(Hg) was measured for reference purposes to understand the downstream flow depth
required for a hydraulic jump to occur in the required location. The length of jump
(Lj) and length of roller (Lr) were also recorded in order to compare between the
calculated and measured jump/roller lengths.
Figure 4.1 - Depiction of the dimensions y0, y1 and y2 measured by manometers.

22
Design
There are two main types of shapes of bucket deflectors in current use worldwide;
the circular-shaped buc et deﬂector and the triangular-shaped buc et deﬂector,
(Steiner et al., 2008). The triangular deflector usually produces greater throwing
distances, which can be advantageous in many applications. However for this
investigation it was preferable to have shorter throwing distances, therefore the
circular-shaped deflector design was used. In a full scale model, these shorted
throwing distances usually decrease the dimensions of the stilling basin, which likely
reduces construction costs. A circular-shaped deflector design was also preferable
due to the easier construction when testing, and therefore more reliable data as the
equipment is more robust.
As stated in the methodology a pre-fabricated ski-jump spillway was used as the non-
converging spillway, with moulded plasticine being secured to the pre-fabricated
spillway to form the horizontal and vertical converging aspects of the second and
third spillway models. Figure 4.2 depicts 3D illustrations of the three spillway
models. The models in figure 4.2 were initial designs, which were altered after
preliminary testing of each model at a design discharge (Q) of 33m3
/h (0.00917m3
/s).
Alterations were quick and cost effective to model due to the ductility of the
plasticine. However in the full scale model these would be constructed from
concrete. The vertical converging spillway design took aspects from those produced
by ov and bel a , and aimed to achieve 50% of the water flow over the
main bucket deflector, and 50% of the water flow over the additional deflectors.
From the literature reviewed for this project, the horizontal converging spillway
design is new concept. The three different models were tested against each other to
determine the most efficient design for water dissipation.

23
Figure 4.2 – 3D illustrations of the three spillway models; Non-Converging, Horizontal Converging
and Vertical Converging respectfully.
This research project was split into two phases. The first phase consisted of the
testing of three different types of spillways.
1. Non-converging spillway – pre-fabricated spillway
2. Horizontally-converging spillways – concept created as an alternative to
current designs from previous literature
3. Vertically-converging spillways – designed from the use of previous studies
ov k & bel a,
The second phase of this research project, was to use a calculated method to design
an efficient model for water dissipation. The calculation chosen for this project is the
‘vertical sum of momentum problem’ formula. his can be found in equation 3. . .
After initial testing of the three different designs, the vertically-converging model
produced the most efficient water dissipation results. herefore, the ‘vertical sum of
momentum problem’ equation was applied to produce a final model for the
vertically-converging spillway concept. This fourth design is known as the modified
vertically-converging spillway for the purposes of this dissertation.
Final technical-design, or as-built, drawings of the three spillway models are shown
in figures 4.3, 4.4 and 4.5 respectfully. The fourth model, and as-built technical-
design drawing, created using the ‘vertical sum of momentum problem’ formula, can
be found in figure 4.6. All dimensions shown are in millimetres (mm).

24
Figure 4.3 – Non-Converging Ski-Jump Spillway Design, Technical drawing; Side view and front
view (dimensions in mm)

25
Figure 4.4 – Horizontal Converging Ski-Jump Spillway Design, Technical drawing; Side view and
front view (dimensions in mm)

26
Figure 4.5 –Vertical Converging Ski-Jump Spillway Design, Technical drawing; Side view and front
view (dimensions in mm)

27
Figure 4.6 – Modified Vertical Converging Ski-Jump Spillway Design, Technical drawing; Side view
and front view (dimensions in mm)

28
5.0 Results
The experiments of this investigation were undertaken in three laboratory sessions. The three spillway models, the non-converging, horizontally-
converging and vertically-converging ski-jump spillways were all tested in a flume with a discharge (Q) ranging between 26-40m3
/h (0.00722-
0.01111m3
/s) passing over them, which the raw data for each are summarized respectively in figures 5.1, 5.2 and 5.3.
The raw data which was measured from experiments are upstream depth (y0), supercritical depth (y1) and downstream depth (y2), which can be
seen in figure 4.1. The downstream gate height (Hg) Length of jump (Lj) and length of roller (Lr) were also recorded. All other data was
calculated from the raw data measured, and using the equations shown in the literature review of this report, section 3.0.
Figure 5.1 - Experimental results for the Non-Converging Ski-Jump Spillway

29
Figure 5.2 - Experimental results for the Horizontally-Converging Ski-Jump Spillway
Figure 5.3 - Experimental results for the Vertically-Converging Ski-Jump Spillway

30
Figure 5.4 shows all the supercritical Froude numbers (Fr1) of each spillway, with
their relevant hydraulic jump classifications, based upon the United States Bureau of
Reclamation, USBR hydraulic jump classification table is shown in figure 3.2.2.
Discharge
(M3
/s)
Non-Converging Horizontal Converging Vertical Converging
Froude
Number
(Fr1)
Hydraulic
Jump
Classification
Froude
Number
(Fr1)
Hydraulic
Jump
Classification
Froude
Number
(Fr1)
Hydraulic
Jump
Classification
0.00722 3.0801 Oscillating 5.0183 Steady 2.8402 Oscillating
0.00806 2.7263 Oscillating 5.0085 Steady 2.3785 Weak
Figure 5.4 - Classification of Hydraulic Jump (Tabulated)
Figure 5.5 shows a graphical interpretation of the data in figure 5.4. It shows an
increase in sequent depth ratio for increased discharge for the non-converging and
horizontal converging spillways, a decrease in sequent depth ratio for increased
discharge for the vertical converging spillway.
Figure 5.5 - Graphical depiction of the Classification of Hydraulic Jump

31
The following graphs in figures 5.6 - 5.15 show graphical results of the experimental
raw data and subsequent calculated data taken directly from figures 5.1, 5.2 and 5.3.
The energy dissipations in the graphs were all within the hydraulic jump, not in
phases 2 and 3 of the passage of water (unless stated).
Figure 5.6 - Graphical depiction of Supercritical Froude Number (Fr1) against Energy Dissipation
(ΔE)
Figure 5.6 shows that the energy dissipation across the jump increased for all
spillways with an increase in supercritical Froude number. Figure 5.7 shows that the
energy dissipation increases for the non-converging and horizontal converging
spillways as discharge increases, and energy dissipation decreases for increased
discharge for the vertical converging spillway.
Figure 5.7 - Graphical depiction of Energy Dissipation (ΔE) against Discharge (Q)

32
Figure 5.8 - Graphical depiction of Relative energy loss against Supercritical Froude number (Fr1)
Figure 5.8 shows that the relative energy loss increased for all spillways with an
increase in supercritical Froude number. Figure 5.9 shows that the supercritical
Froude number increased for the non-converging and horizontal converging
spillways as discharge increased. Thus supercritical Froude number decreased for
increased discharge for the vertical converging spillway.
Figure 5.9 - Graphical depiction of Supercritical Froude number (Fr1) against Discharge (Q)

33
Figure 5.10 - Graphical depiction of Downstream depth (y2) against Discharge (Q)
Figure 5.10 shows that the downstream depth (y2) increased for all spillways with an
increase in discharge. Figure 5.11 shows that the length of jump ratio increased for
all spillways with an increase in supercritical Froude number.
Figure 5.11 - Graphical depiction of Length of jump ratio (Lj/y1) against Supercritical Froude number
(Fr1)

34
Figure 5.12 - Graphical depiction of Discharge (Q) against Length of jump (Lj)
Figure 5.12 shows that the length of jump increased for the non-converging and
horizontal converging spillways as discharge increased. For the vertical converging
spillway the length of jump decreased slightly, and then increased back to the same
value for increasing discharge.
Figure 5.13 - Graphical depiction of Discharge (Q) against Length of Jump/Roller for Non-
Converging Spillways

35
Figure 5.14 - Graphical depiction of Discharge (Q) against Length of Jump/Roller for Horizontal
Figures 5.13, 5.14 and 5.15 show a more detailed graphical interpretation of figure
5.12. They all show that the measured jump/roller length for each was greater than
the calculated equivalent length, and that the length of jump was greater than the
length of roller.
Figure 5.15 - Graphical depiction of Discharge (Q) against Length of Jump/Roller for Vertical

36
Figure 5.16 - Graphical depiction of Discharge (Q) against Energy Dissipation (Phases 2 and 3 only)
Figures 5.16 and 5.17 show the energy dissipation against discharge for phases 2 and
3 (phases from take-off from the spillway edge to the impact with the downstream
pool), and the same for phases 4 and 5 (phase of hydraulic jump and transition to
conventional river flow) respectfully.

37
The experiments show raw data relating to three scale models of spillway designs.
To assess how this raw data would compare to a full scale dam spillway under flood
conditions, dimensional analysis was necessary. A 1:50 scale was chosen to represent
an average full scale model. The derived scale factors are:
; √ and (eq. 5.1)
The following graphs in figures 5.18, 5.19, 5.20 and 5.21 are scaled up models of the
raw data produced from the experiments.
Figure 5.18 - Graphical depiction of Discharge (Q) against Length of jump (Lj) (Full Scale)
Figure 5.18 shows the length of jump against discharge for a full scale model. This
shows that the length of jump ranged between 16-19m for the vertical converging
spillway, and the non-converging spillway ranged between 20-35m.

38
(Full Scale)
Figures 5.19 and 5.20 show the energy dissipation against discharge for phases 2 and
3, and the same for phases 4 and 5 respectfully for a full scale model, scaled up by a
factor of 50.
(Full Scale)

39
Figure 5.21 - Graphical depiction of Downstream depth (y2) against Discharge (Q) (Full Scale)
Figure 5.21 shows the downstream depth against discharge for a full scale model.
This shows that the downstream depths ranged between 3.1-3.7m for the vertical
converging spillway, and the non-converging spillway ranged between 3.4-5.0m.
A modified vertical converging ski-jump spillway was tested in the same flume,
under the same conditions. The raw data for this experiment is summarized in figure
5.22.
Figure 5.22 - Experimental results for the Modified Vertically-Converging Ski-Jump Spillway
The supercritical depth of the modified vertically-converging spillway could not be
recorded in this experiment, due to the hydraulic jump occurring immediately at the
toe of the spillway, therefore limited graphs and conclusions could be drawn from
this data. Figures 5.23 and 5.24 show graphs of the data recorded.

40
Figure 5.23 - Graphical depiction of Discharge (Q) against Total Energy Dissipation (Full Scale)
Figure 5.23 shows the total energy dissipation across the length of the whole system
against discharge for a full scale model. It was noted that the modified vertical
converging spillway produced the largest energy dissipations across all discharges
tested. Figure 5.24 shows the downstream depth against discharge for a full scale
model. This shows that the downstream depths ranged between 2.4-3.3m for the
modified vertical converging spillway (shorter than the other two spillways).
Figure 5.24 - Graphical depiction of Downstream depth (y2) against Discharge (Q) (Full Scale)

41
6.0 Analysis of Results and Discussion
The results in section 5.0 show that altering the spillway structure has the potential to
increase energy dissipation and reduce subsequent erosion downstream. This will be
discussed in more detail.
Analysis of Results
The main objective of this research project was to investigate, through practical
experimentation, if larger energy dissipation could be achieved by converging jets as
part of a ski-jump spillway. The experiments show that the horizontal converging
ski-jump spillway decreased the energy dissipation in phases 2 and 3 (see section
3.1) of the passage of discharge over a spillway and stilling basin, compared to a
non-converging ski-jump spillway. However the vertical converging ski-jump
spillway substantially increased the energy dissipation in phases 2 and 3.
The classifications of the jumps ranged between steady and weak (see section 3.2).
Reviewing the non-converging and vertically-converging spillways, the vertically-
converging spillway decreased from an oscillating to weak jump at around a sequent
depth ratio of 3.00, whereas the non-converging spillway remained as an oscillating
jump, increasing slightly.
The vertically-converging spillway dissipated the least energy in the hydraulic jump
(phases 4 and 5) and therefore dissipated the most energy in phases 2 and 3. Figures
5.6 and 5.7 shows this in terms of energy dissipation against supercritical Froude
number and against discharge respectfully. Figures 5.16 and 5.17 also show the
energy dissipation against discharge, for phases 2 and 3, and also for phases 4 and 5
separately.
The downstream water depth is lowest for the vertically-converging spillway, where
the non-converging and horizontally-converging spillways were considerably higher
(see figure 5.10).
The length of jump ratio increased for increasing supercritical Froude number for all
spillways, with the non-converging spillway having a larger length of jump ratio than
the vertically-converging spillway.

42
The length of jump for the non-converging spillway increased noticeably with
increased discharge and was much larger than that of the vertically-converging
spillway, which remained at a reasonably constant length across all discharges tested.
The experimentally measured hydraulic length of jump/roller was, for all spillways,
overestimated compared to the calculated values of each. All related measured and
calculated length of hydraulic jumps and rollers demonstrated a similar correlation,
(the hydraulic length of jump/roller are explained in more detail in section 3.3).
Cavitation was observed for all three spillways, particularly for the converging
spillways, with moderate to severe cavitation occurring on the jump edge of the
vertically-converging spillway.
Discussion
As previously stated, the horizontally-converging ski-jump spillway does not present
increased energy dissipation in phases 2 and 3, compared to the non-converging ski-
jump spillway, this could be due to a number of factors. The most rational reason
would be that the angle of colliding jets was not large enough; therefore the act of
colliding the jets together was not achieving the air entrainment and dispersion
required for energy dissipation in these earlier phases (discussed in more detail in
section 3.1).
Figure 6.1 – Experimental testing of the horizontal converging spillway

43
In fact the jets were converging smoothly enough to form a uniform single jet with
increased velocity and throwing the jet further from the spillway edge (which can be
seen in figure 6.1), therefore decreasing the energy dissipation in phases 2 and 3, and
increasing the classification of the hydraulic jump to a steady jump (see figures 5.4
and 5.5). This can also be seen in figures 5.6, and 5.7, which show the relationships
between energy dissipation and supercritical Froude number and with discharge
respectfully, and figure 5.8 shows the relationship between relative energy loss and
supercritical Froude number. All three figures show that the horizontally-converging
ski-jump spillway increased energy dissipation the most within the hydraulic jump,
therefore the least in phases 2 and 3. The horizontally-converging spillway did not
achieve the level of energy dissipation anticipated in the early phases, therefore
further investigation could be undertaken to design a model which converged the
horizontal jets at a larger angle. The collisions at larger angles are likely to achieve
the collision forces required for air entrainment and dispersion, therefore high energy
dissipation (see section 3.1).
This compares to the vertically-converging spillway, in which a large proportion of
the energy was dissipated within phases 2 and 3. This can be seen in figure 5.5,
where the classification of the jump decreased from an oscillating jump to a weak
jump at around a sequent depth ratio of 3.00. Figure 5.16, shows the energy
dissipation during phases 2 and 3 are higher for the vertically-converging spillway,
than the non-converging spillway. As discussed in section 3.1, the energy dissipation
in phases 2 and 3 were greatly increased by achieving a dispersed and highly air
entrained jet, ov & bel a, 1981). Since more energy is dissipated in the
earlier phases, less energy is required to be lost in the hydraulic jump to achieve
subcritical conventional river flow (see figures 5.16 and 5.17).
The energy dissipation also stays relatively constant for the vertically-converging
spillway compared to the non-converging spillway (see figure 5.16). This is more
desirable as a design solution for a large dam spillway under a fluctuating flood
discharge. Therefore the downstream river channel will be less affected by a more
constant flood river flow. The non-converging spillway varies significantly in energy
dissipation between different discharges and phases, therefore has a greater effect on
downstream river flow.

44
The experiments in this investigation showed raw data relating to four scale models
of spillway designs. To assess how this raw data compared to a full scale dam
spillway under flood conditions, dimensional analysis was necessary. A 1:50 scale
was chosen to represent an average full scale model. The results of which can be
seen in figures 5.18, 5.19, 5.20 and 5.21.
Figures 5.19 and 5.20 show full scale interpretations of figures 5.16 and 5.17, these
demonstrate the relationship between energy dissipation and discharge, for phases 2
and 3, and also for phases 4 and 5 separately. The energy dissipations of the full
scale models are a factor of 50 larger than the scaled models due to the units of
energy dissipation being in metres head. Although the discharge is a factor of 17678
larger, due to scale effects. It is important to note that the energy dissipation of the
vertically-converging spillway has a much smaller full scale range of 13.0-14.5m
head compared to the non-converging spillway which has a full scale range of 10.0-
13.5m head. Therefore the energy dissipation is not only much larger in the phases 2
and 3, but the range of energy dissipation is also 2.33 times smaller than the non-
converging spillway. The results indicate that the dimensions of the stilling basin
could be reduced, potentially leading to cost savings in the construction process
(Toso & Bowers, 1988).
The downstream water depth was lowest for the vertically-converging spillway,
where the non-converging spillway is considerably higher (see figure 5.10). Figure
5.21 shows a full scale interpretation of figure 5.10, which demonstrates the
relationship between downstream water depths and discharge. The downstream water
depths range between 3.1-3.7m for the vertically-converging spillway, and the non-
converging spillway range between 3.4-5.0m. Therefore the downstream depths are
not only much shallower for the vertically-converging spillway, but the range of
depths was also around 2.67 times smaller. The relevance of this does depend on
what is required downstream of the spillway, due to the habitats and biological
communities within a river varies with water depth, distance from the coastline and
with environmental seasonal changes, (Wetzel, 2001). For many river systems a
varied flow depth is favourable to mimic a natural ecosystem, if designed correctly,
(Gehrke et al., 1995).

45
To show the relationship between the length of hydraulic jump and discharge, the
measured length of jump was used in its graphical representation, rather than the
measured length of roller, or calculated versions of each. This length was used due to
it being more common in similar previous studies, and allows an easier comparison
between this and other studies (Li et al., 2012; Wu et al., 2012).
The length of jump is lowest for the vertically-converging spillway, where the non-
converging spillway is considerably higher (see figure 5.12). Figure 5.18 shows a full
scale interpretation of figure 5.12, which shows the relationship between the length
of jump and discharge. This shows that the length of jump ranged between 16-19m
for the vertically-converging spillway, and the non-converging spillway ranged
between 20-35m. Therefore the lengths of jumps are not only much shorter for the
vertically-converging spillway, but the range of lengths are also around 5.00 times
shorter. With the length of jump range vastly smaller, this allows for the construction
of a stilling basin, in which the hydraulic jump occurs over the majority of it across
most discharges. This compared to the non-converging spillway, in which the full
usage of the stilling basin would only be used for the highest of discharges. A much
shorter stilling basin could also be constructed, due to the length of jump having
decreased, therefore the area of erosion is smaller. The shorted stilling basin length is
likely to lower construction costs.
It is useful to evaluate the length of jump/roller relative to supercritical depth; this is
common practice in many other studies (Gupta et al., 2013; Hager, 1989). Therefore
the relative length of the jump Lj/Y1 is plotted against the supercritical Froude
number, providing a relative comparison between the three spillway models tested.
The relative length of jump/roller is a dimensionless measurement; hence clearer
conclusions can be derived using data from a larger discharge range, and
comparisons with previous and future work can be made without using the same
discharges or scaling.
The resulting graph in figure 5.11 shows that the non-converging spillway has a
larger relative length of jump and supercritical Froude number than the vertically-
converging jump, for supercritical Froude numbers ranging between 1.9 and 3.9
(weak and oscillating jumps). For the experiments carried out on spillways (above)
the figure shows an increase in relative length of jump, with increased supercritical

46
Froude number. The data for the non-converging spillway shows a sizable deviation
in data points, which may be due to the inaccuracy in determination of the correct
location of the start and end of the length of jump. To correct this inaccuracy
duplicates of the experiments could have been undertaken, therefore an average of
the readings could be taken, providing a more accurate measurement.
The measured and calculated lengths of jump/roller of all three spillways are
presented in figures 5.13, 5.14 and 5.15 respectfully. These results present a good
correlation between different methods of producing the measurements. They
demonstrate a similarity between what was measured experimentally and what was
calculated from the raw data (Carollo & Ferro, 2012). The measured lengths appear
to be larger than the calculated results for almost all data points, resulting in an
average discrepancy of 21%, 8% and 14% respectfully. To achieve a higher accuracy
experimental repeats could be undertaken. The variation in the experimental results
shows that it is good practice to take measured and calculated parameters. This helps
to clarify that both measured and calculated results may not be the most accurate
measurement in scale modelling, and a new method may be required. Furthermore
the figures also show a correlation between length of jump and length of roller. This
is clarified by Hager (1989), who also establishes an equivalent relationship in his
study, and large scattering of measured data for the length of jump/roller. This
demonstrates that other authors have found discrepancies in measuring the lengths of
jump/roller.
Following analysis of the three models tested, it became apparent that the vertically-
converging spillway was the most efficient and dispersing energy. This lead to the
vertically-converging design being selected and further modelling was carried out
using the ‘vertical sum of momentum problem’ formula this can be found in
equation 3.1.1). The results from the equation showed an increase in energy
dissipation and therefore the design was constructed and tested. This further testing
was carried out in order to confirm if further efficiencies could be reached. The
modifications, identified from the calculations from the formula, included an
increase in the height of the two small ski-jumps further up the pre-fabricated
spillway. This was done with the aim of altering the angle of collision to something
closer to 90o
, therefore increasing the collision forces between the water jets and
increasing air entrainment and dispersion ov & bel a’s, 1981).

47
The experiments for this model presented results which behaved differently to the
other three models. The hydraulic jump for the modified vertically-converging
spillway occurred immediately at the toe of the spillway and therefore the
supercritical depth and length of jump/roller could not be measured, (using either
calculation or standard measurement). It is normal practice to measure a supercritical
depth for the calculation, which wasn't evident for this model. However the upstream
and downstream depths could be measured and therefore graphs of the total energy
dissipation could be plotted and compared. Figure 5.23 shows a graph of the total
energy dissipation against discharge. The figure demonstrates that the modified
vertically-converging spillway has the greatest total energy dissipation of all the
models tested. A calculated hydraulic jump classification was not possible to be
calculated for this model, however through observation it can be seen that the
hydraulic jump was undulating (see figure 6.2) and therefore was dissipating less
than 5% of the total energy in the hydraulic jump according to USBR (1955), shown
in figure 3.2.2. Therefore, a large proportion of energy is lost, during phases 2 and 3,
to achieve an undulating jump at such high discharges.
Figure 6.2 - Undular hydraulic jump, downstream of the modified vertical converging spillway
The full scale downstream water depth was lowest for the modified vertically-
converging spillway, where the non-converging spillway is considerably higher (see
figure 5.24). The downstream water depths ranged between 2.4-3.3m for the
modified vertically-converging spillway. However, the vertically-converging and
non-converging spillways ranged between 3.1-3.7m and 3.4-5.0m respectively.

48
Therefore the downstream depths of the modified vertically-converging spillway
were even shallower than the other two models, which would be preferable in most
circumstances.
Although the length of the jump/roller could not be accurately measured for the
modified vertically-converging spillway, the length from the spillway toe to the end
of the hydraulic jump/roller was measured. This is the length which is used for
construction purposes of the stilling basin. It was noted that this length for the
modified vertically-converging spillway was around 61% of the average length of the
original vertically-converging spillway. This vastly reduced length, reduces stilling
basin dimensions and is likely to reduce construction costs. Both of the vertically-
converging spillways had an equally small range of spilling basin lengths for the
discharges tested, which was 38% of the non-converging stilling basin length. The
success of the modified vertically-converging ski-jump spillway design, with its
more efficient energy dissipation results, and cost-effective construction, shows that
it has the potential to be a leading design.
Figure 6.3 - Experimental testing of the modified vertical converging spillway
Cavitation appeared to be a large issue with the modified vertically-converging
spillway. When the water jets from the smaller deflectors converged with the main
water jet, a proportion of it collided with the main ski-jump toe. This collision
formed cavitation in the ski-jump bucket, which can be seen in figure 6.3. Through
observation, and detailed in figure 3.4.1, which shows the development stages of
cavitation, it can be seen that the cavitation formed in the bucket is classed as

49
supercavitation, and therefore has a cavitation index σ of 0.3 or less (the highest form
of cavitation). Cavitation was also observed in the bucket of the original vertical
converging spillway, although not at the same high levels as the modified model. The
cavitation in the bucket of the original model was observed at a class of developed
cavitation, bordering on supercavitation, and therefore has a cavitation index σ of 0.3
to 1.8. Cavitation was not observed with the horizontal and non-converging
spillways.
Although the potential construction costs would be less with the vertically-
converging spillways, due to their shorter stilling basin lengths, the high cavitation
levels experienced increases the amount of potential erosion occurrence in the ski-
jump bucket and toe. These cavitation effects would also be greatly increased when
scaled up to full construction size. This will mean that the construction of the ski-
jump will have to be heavily engineered to resist cavitation erosion. The majority of
dam spillways are constructed from concrete; a material which is susceptible to
cavitation erosion. Therefore without prolonged scaled testing using concrete
models, it is unknown exactly how much cavitation would affect the structure of the
spillways.
Limitations
All the spillways were tested in the same hydraulic flume, under the same conditions
and variables; therefore they can be scaled up to an average full size model and
compared. However the scaled laboratory experiments have many limitations, and it
will always be difficult to generalise findings, due to the results not being
ecologically valid (representative of real life) (Le Coarer, 2007). The laboratory
experiments were tested to a very narrow range in terms of many parameters, which
are generally not issues in full scale prototype testing. For example the relatively
narrow width of the channel meant that scale wall effects altered the trajectory of the
water jets, producing an uncharacteristic flow. This would not be the case in a full
scale construction.
Other limitations included bed slope angle, surface roughness and air entrainment.
The bed slope angle was set at zero degrees for all experiments, which kept in unison
with bottom outlet investigations, as such avoiding complications with steeply
sloping chute ﬂows. herefore the data is not likely to give a true representation of

50
all field applications with high bed slope angles, although does give a good
estimation and comparative data to other laboratory investigations (Juon & Hager,
2000). The surface roughness in the experiments was very low due to the metal bed
and glass walls. When compared to the surface roughness of concrete, which would
most likely be used in a full scale prototype model, which is likely to produce an
altered outcome, slowing the water and an anticipated increase in the hydraulic jump.
The air entrainment observed in large quantities in this investigation could only be
commented in terms of the scaled models, due to scaling limitations and the
equipment used for measuring air entrainment not being available (Juon & Hager,
2000).
Human error is a limitation within these experiments. It is impossible to establish an
exact measurement for many parameters within the field of hydraulics, particularly
when it is difficult to accurately determine a parameter such as the length of
hydraulic jump/roller. Downstream of the hydraulic jump undulations were observed,
particularly with lower classification jumps. Therefore the manometer readings of the
downstream depth often fluctuated, resulting in an average reading being recorded.
The duration of time spent undertaking laboratory experiments was limited, therefore
narrowing the range of experiments which could be undertaken within the time-
frame. Additional experiments could have provided opportunities for further
modifications to the designs tested. Repetitions of experiments would have provided
more reliable and resilient data that could further support the analysis of this report.
The supercritical depth could not be recorded for the experiments of the modified
vertically converging spillway, due to the hydraulic jump occurring immediately at
the toe of the spillway, therefore limited graphs and conclusions could be drawn
from this data. Although the data that was recorded presented some very positive
conclustions.

51
7.0 Conclusions and Future Work
The experiments of both of the vertically-colliding spillway produced positive
results, which confirm ov bel a’s (1981) concept of producing a greater
energy dissipation when converging multiple jets as part of a ski-jump spillway.
Further testing using more modifications of the vertically-converging design would
be recommended to produce the potential of further increases in energy dissipation.
The horizontally-converging spillway did not produce an increase in energy
dissipation, due to a small angle of colliding jets. However further testing would be
recommended, with a design with a greater angle of collision and possibly the
combination of both horizontal and vertical colliding jets, adopting the concept by
ov bel a’s (1981), of the greater the number of colliding jets the greater the
capacity of energy dissipation. However, cavitation erosion would need to be taken
into consideration to understand the consequences of increasing jet collision.
There are many benefits to having the energy dissipation occur during the second and
third phases of the passage of water over a spillway, including a reduction in stilling
basin length, less erosion of the stilling basin and downstream river, and a greater
energy dissipation capacity. Cavitation appears to be a key aspect which needs to be
considered with any proposed designs. This is due to the apparent conclusion that the
designs which produce higher energy dissipations also produce higher levels of
cavitation. The modified vertically-colliding spillway produced greatest energy
dissipations, but also the highest levels of cavitation. Further study could be
undertaken to review whether higher cavitation is always an outcome of high energy
dissipations. If so then comprehensive study into cavitation effects to vertically-
converging spillway designs and how different materials degrade with prolonged
cavitation, could prove valuable. Due to the unknown effects of concrete cavitation
erosion, further studies would need to be undertaken, and a full cost exercise
executed, in order to confirm that cost-savings in reduced energy-dissipation designs,
outweigh the potential increases in costs that cavitation may produce.
Furthermore it can be drawn from this study that hydraulic jump energy dissipation
increases with increased supercritical Froude number, as stated by Chadwick &
Morfett (2013). The sequent depth ratio and length of jump are decreased by multiple
converging ets, as stated by ov bel a (1981). Also the spillway designs

52
with high energy dissipations help prevent erosion downstream of the spillway and
aid the preservation of the conventional river environment downstream.
With the continued reporting of flooding, occurring both nationally and
internationally, and the predicted rate of these events set to increase in the future, it
may be prudent to extend on this project, new high energy dissipation designs for
large scale spillways (Driessen & Van Ledden, 2013).

53
8.0 References
Avery, S. T. and Novak, P. (1978) ‘Oxygen transfer at hydraulic structures’, Journal
of the Hydraulics Division, Vol. 104, No. 11, pp. 1521 – 1540.
Azmathullah, H. M., Deo, M. and Deolalikar, P. (2005) ‘Neural networks for
estimation of scour downstream of a ski- ump buc et’, Journal of Hydraulic
Engineering, Vol.131, No. 10, pp. 898 – 908.
Bradley, J., (1945) ‘Study of air in ection into the ﬂow in the Boulder Dam spillway
tunnels, Boulder Canyon Project’, Bureau of Reclamation, Hydraulic
Laboratory Report, 186.
Carollo, F. G., Ferro, V. and Pampalone, V. (2007) ‘Hydraulic jumps on rough
beds’, Journal of Hydraulic Engineering, Vol. 133, No. 9, pp. 989 – 999.
Carollo, F. G., Ferro, V. and Pampalone, V. (2012) ‘New Expression of the
Hydraulic Jump Roller Length’, Journal of Hydraulic Engineering, Vol. 138,
No. 11, pp. 995 – 999.
Chadwick, A., Morfett, J. C. and Borthwick, M. (2013) Hydraulics in civil and
environmental engineering, Boca Raton, Fla. [u.a.]: CRC Press.
Chanson, H. and Montes, J. (1995) ‘ haracteristics of undular hydraulic umps:
Comparison with Near-Critical Flows’, Journal of hydraulic engineering, Vol.
121, No. 2, pp.129 – 144.
Chiang, T., Sheu, . and Wang, S. 2000 ‘Side wall effects on the structure of
laminar flow over a plane-symmetric sudden expansion’, Computers & fluids,
Vol. 29, No. 5, pp.467 – 492.
Driessen, T. and Van Ledden, M., (2013) ‘The large-scale impact of climate change
to Mississippi flood hazard in New Orleans’, Drinking Water Engineering &
Science, Vol. 6, No. 2.
Ead, S. and Rajaratnam, N. (2002) ‘Hydraulic jumps on corrugated beds’, Journal of
Hydraulic Engineering, Vol. 128, No. 7, pp. 656 – 663.
Faktorovick, M. E. (1952) Energy Dissipation at Jet Collision, (in Russian),
Gidrotechnicheskoje strojitelstvo, No. 8, pp. 43 – 44.

54
Falvey, H. T. (1990) ‘Cavitation in chutes and spillways’, A water resources
technical publication. Engineering monograph, No. 42
Gandhi, S. and Yadav, V. (2013) ‘Characteristics of supercritical flow in rectangular
channel’, International Journal of Physical Sciences, Vol. 8, No. 40, pp. 1934 –
1943. Available at:
http://www.academicjournals.org/article/article1384763242_Gandhi%20and%2
0Yadav.pdf [Accessed: 11th Feb 2014].
Gehrke, P., Brown, P., Schiller, C., Moffatt, D. and Bruce, A. 5 ‘River
regulation and fish communities in the Murray-Darling river system,
Australia’, Regulated Rivers: Research & Management, Vol. 11, No. 3-4, pp.363
– 375.
Graff, W. (2006) ‘Downstream hydrologic and geomorphic effects of large dams on
American rivers’, 37th Binghampton Geomorphology Symposium – The Human
Role in Changing Fluval Systems. Vol. 79. No. 3-4. pp. 336 – 360.
Gupta, S., Mehta, R. and Dwivedi, V. (2013) ‘Modeling of relative length and
relative energy loss of free hydraulic jump in horizontal prismatic
channel’, Procedia Engineering, Vol. 51, pp.529 – 537.
Hager, W. (1989) ‘Hydraulic jump in U-shaped channel’, Journal of Hydraulic
Engineering, Vol. 115, No. 5, pp.667 – 675.
Heller, V., Hager, W. and Minor, H. (2005) ‘S i ump hydraulics’, Journal of
Hydraulic Engineering, Vol. 131, No. 5, pp.347 – 355.
Horeni, p. (1956) Disintegration of a Free Jet in Air, (in Czech), Prace a studie No.
93, VUV, Prague
Juon, R. and Hager, W. (2000) ‘Flip buc et without and with deflectors’, Journal of
Hydraulic Engineering, Vol. 126, No. 11, pp.837 – 845.
Kehew, A. (1982) ‘Catastrophic flood hypothesis for the origin of the Souris
spillway, Saskatchewan and North Dakota’, Geological Society of America
Bulletin, Vol. 93, No. 10, pp.1051 – 1058.

55
Komora, Y. (1969) ‘Spillway design using jet collision for energy
dissipation’, Power Technology and Engineering (formerly Hydrotechnical
Construction), Vol. 3, No. 4, pp. 363 – 364.
Le Coarer, Y. (2007) ‘Hydraulic signatures for ecological modelling at different
scales’, Aquatic ecology, Vol. 41, No. 3, pp.451 – 459.
Li, N., Liu, C., Deng, J. and Zhang, X., (2012) ‘Theoretical and experimental studies
of the flaring gate pier on the surface spillway in a high-arch dam’, Journal of
Hydrodynamics, Ser. B, Vol. 24, No. 4, pp.496 – 505.
Mahmodinia, S., Javan, M. and Eghbalzadeh, A. (2012) ‘The Effects of the Upstream
Froude Number on the Free Surface Flow over the Side Weirs’, Procedia
Engineering, Vol. 28, pp.644 – 647.
Nalluri, C. and Featherstone, R. E. (2001) Civil Engineering Hydraulics. 4th ed.
Oxford: Wiley-Blackwell.
ov , . and bel a, J. (1981) Models in hydraulic engineering. Boston: Pitman.
Roberts, C. (1980) ‘Hydraulic Design of Dams’, RSA Department of Water
Affairs,Forestry and Environmental Conservation, Division of Special Tasks,
July.
Rutschmann, P. and Hager, W. H. (1990) ‘Air entrainment by spillway
aerators’, Journal of Hydraulic Engineering, Vol. 116, No. 6, pp. 765 – 782.
Schmocker, L., Pfister, M., Hager, W. and Minor, H. (2008) ‘Aeration characteristics
of ski jump jets’, Journal of Hydraulic Engineering, Vol. 134, No. 1, pp.90 – 97.
Steiner, R., Heller, V., Hager, W. and Minor, H., (2008) ‘Deflector ski jump
hydraulics’, Journal of Hydraulic Engineering, Vol. 134, No. 5, pp.562 – 571.
Streeter, V. L. and Wylie, E. B. (1981) Fluid mechanics. 2nd ed. New York:
McGraw-Hill.
Toso, J. and Bowers, C. (1988) ‘Extreme pressures in hydraulic-jump stilling
basins’, Journal of Hydraulic Engineering, Vol. 114, No. 8, pp.829 – 843.
Wetzel, R. (2001) Limnology. 3rd ed. London: Academic Press.

56
Wu, J., Ma, F. and Yao, L., (2012) ‘Hydraulic characteristics of slit-type energy
dissipaters’, Journal of Hydrodynamics, Ser. B, Vol. 24, No. 6, pp.883 – 887.

57
9.0 Appendices
Ethics Checklist
Name of student: Joseph Lawson
Name of supervisor: Heidi Burgess
Title of project (no more than 20 words):
Investigating the use of Converging Ski-Jump Spillways and their effects on the
characteristics of Hydraulic Jump and Energy Dissipation.
Outline of the research (1-2 sentences):
This research aims to determine the differences in energy dissipation between
converging ski-jump spillways and the effect this has on the characteristics of a
hydraulic jump.
Timescale and date of completion: 7th
May 2014
Location of research: University of Brighton, Hydraulics Laboratory
Course module code for which research is undertaken: CNM30
Email address: jl297@uni.brighton.ac.uk
Contact address: 30 Newmarket rd, Brighton, East Sussex, BN2 3QF
Telephone number: 07949822829
Please tick the appropriate box Yes No
1. Is this research likely to have significant negative impacts on
the environment? (For example, the release of dangerous
substances or damaging intrusions into protected habitats.)
x
2. Does the study involve participants who might be considered
vulnerable due to age or
to a social, psychological or medical condition? (Examples include
children, people with learning disabilities or mental health
problems, but participants who may be considered vulnerable are
not confined to these groups.)
x
3. Does the study require the co-operation of an individual to gain
access to the
participants? (e.g. a teacher at a school or a manager of sheltered
housing)
x
4. Will the participants be asked to discuss what might be perceived as
sensitive topics?
(e.g. sexual behaviour, drug use, religious belief, detailed financial
matters)
x
5. Will individual participants be involved in repetitive or prolonged
testing?
x

58
6. Could participants experience psychological stress, anxiety or other
negative
consequences (beyond what would be expected to be encountered in
normal life)?
x
7. Will any participants be likely to undergo vigorous physical
activity, pain, or exposure
to dangerous situations, environments or materials as part of the
research?
x
8. Will photographic or video recordings of research participants
be collected as part of the research?
x
9. Will any participants receive financial reimbursement for
their time? (excluding reasonable expenses to cover travel
and other costs)
x
10. Will members of the public be indirectly involved in the research
without their
knowledge at the time? (e.g. covert observation of people in non-
public places, the use of methods that will affect privacy)
x
11. Does this research include secondary data that may carry
personal or sensitive organisational information? (Secondary data
refers to any data you plan to use that you
did not collect yourself. Examples of sensitive secondary data
include datasets held by organisations, patient records,
confidential minutes of meetings, personal diary entries.
These are only examples and not an exhaustive list).
x
12. Are there any other ethical concerns associated with the research
that are not covered
in the questions above?
x
All Undergraduate and Masters level projects or dissertations in the School of
Environment and Technology must adhere to the following procedures on data
storage and confidentiality:
Once a mark for the project or dissertation has been published, all data must be
removed from personal computers, and original questionnaires and consent forms
should be destroyed unless the research is likely to be published or data re-used.
Please sign below to confirm that you have completed the Ethics Checklist and will
adhere to these procedures on data storage and confidentiality. Then give this form
to your supervisor to complete their checklist.
Signed (Student):
Date: 11/02/2014

59
Risk Assessment
School / Department: Environment & Technology Date of assessment: 11/02/2014
Activity / area: Hydraulics Laboratory Next review date:
Assessed by: Dominic Ryan RA Ref No:
No.
What are
the
hazards?
Who
might be
harmed
and how?
What controls do you
already have in place?
Risk
(H/M/L)
What further
action is
necessary to
reduce the risk
to Low?
Action by
whom?
Action by
when? Done
1 Working at Heights User Hold the hand rail of step
ladder when working at
height
L N/A User Before start
of work
Yes
2 Lone Working User Notify a technician of all
works
of work
Yes
3 Slips, trips and falls User Be aware of all obstacles,
clean up water spillages
immediately. Where correct
clothing and PPE
of work
Yes
Assessor signature/date: Head of School signature/date:

Joseph Lawson Dissertation

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