Hydraulics Structure II Lecture Note

1. I
ADDIS ABABA SCIENCE AND TECHNOLOGY UNIVERSITY
COLLEGE OF ARCHITECTURE AND CIVIL ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
Lecture Materials
Hydraulic Structure-II
(CENG-4162)

2. 1
CHAPTER ONE
1. Introduction to River Engineering and Hydraulics
River engineering is the process of planned human intervention in the course, characteristics or flow of a
river with the intention of producing some defined benefit to community.
River engineering is a practice in which a river is modified with the goal of creating a change, which can
vary from protecting wetlands to providing navigable water for boats. In fact, Rivers are the natural
channels which carry a huge quantity of water drained by the catchment as runoff. Many river systems
have been seriously affected by the construction and operation of major engineering works. (i.e water
supply, agricultural, municipal, industrial, domestics, power generation, navigation and water
transportation, recreation, waste disposal land drainages etc… Natural streams are essentially open
hydraulic systems in equilibrium. The variables are those that govern discharge and are: -
 Channel Width
 Boundary Roughness
 Size and Concentration of Sediment Load
 Depth and Slope
A change in any one of these interdependent variables must be compensated for by a change in the others.
The main reason for the complexity of river engineering is that river flow in alluvium has no really fixed
boundaries and geometry compared with, say, pipe flow or open-channel flow in rigid canals.
The first step in river engineering is to identify why a river needs to be engineered. For example, engineers
may be called in to divert a river so that seasonal flooding becomes less dangerous for people who live in
the area.
The scope of river engineering includes the following
• River training works
• Channel design works
• Flood control works
• Water supply
• Navigation improvement
• Hydraulics structures design
• Hazard mitigation
• Environmental enhancement
1.1 River Characteristics
The primary function of a river channel is the conveyance of water and sediment. The most obvious aspect
of a river channel, apart from its size, is the amount of water it carries. This is best shown in a hydrograph.
Periodically flooded land is called the flood plain. Whilst in the upper reaches the flood plains are usually
narrow or even non-existent, in the lower reaches of a river the flood plains could be tens of kilometers
wide.
1.2 Rivers and their Behaviors

3. 2
Rivers are important arrangements of the hydrological cycle.
Types of Rivers
Rivers can be classified according to various criteria.
I. Classification based on variation of discharge
a) Perennial Rivers: These rivers have adequate discharge throughout the year. These rivers obtain their
supply from melting of snow and from precipitation. flow is available continuously during both wet and
dry times. Baseflow is dependably generated from the movement of ground water into the channel.
b) Non perennial Rivers: are those that are snow fed. These rivers obtain the supply from rain and the
flow is high during and after raining season, but they carry little flow in non-rainy season.
C) Flashy Rivers: The rivers in which there is a sudden increase in discharge. The river stage rises and
then falls in a very short period. However, a small flow in a flashy river may continue after the flood.
d) Virgin Rivers: are those rivers which get completely dried up due to large evaporation and percolation
losses
II. Classification based on on the location of Reach
a) Mountainous rivers: These rivers flow in hilly and mountainous regions. These rivers are further
divided in to rocky rivers. (Rocky stage and boulder stages).
b) Rivers in Flooded Plains: After the boulder stage, a river enters a flooded plains having alluvial
soil.The bed and banks of rivers in flood plains are made up of sand and silt.
C) Delta Rivers: When a river enters in to a deltaic plain, it sprits up in to a number of small branches due
to very flat slopes. There is a shoal formation and braiding of the channel in the delta rivers.
d) Tidal Rivers: Just before joining the sea or an ocean, the river becomes as tidal river.In a tidal river
there are periodic changes in water levels due to tides. The river receives the sea water during flood tides,
but during ebb tides it delivers in to the sea.
III. Classification based on plan form
a) Straight rivers: These rivers are straight in plan and have cross sectional shape of a trough. The
maximum velocity of flow usually occurs in the middle of the section. The river may be easiest in the
mountainous regions but they are rare in flood plains.
b) Meandering Rivers: These rivers follow a winding, crooked course, they consist of a series of bends of
alternate curvature in the plan. The successive curves are connected by small straight reaches of the river
called cross rivers or crossings.
c) Braided rivers: A braided river flows in to two or more channels around alluvial islands developed due
to deposition of silt.
1.3 Behaviors of rivers in alluvial stages

4. 3
The behaviors of alluvial rivers depend to a large extent on the sediment carried by it. The sediment carried
by the river poses numerous problems, such as:
 Increasing of flood levels
 Silting of reservoirs
 Silting of irrigation and navigation channels
 Splitting of a river into a number of interacted channels
 Meandering of rivers
Specially the meandering causes the river to leave its original course and adopt a new course.
An alluvial river usually has the following three stages:
 Flow in a straight reach:
 The river cross section is in the shape of a ditch, with high velocity flow in the middle of the
section.
 Since the velocity is higher in the middle, the water surface level will be lower in the middle and
higher at the edges.
 Due to the existence of this transverse gradient from sides towards the center, transverse rotary
currents get developed.
 However, straight reaches are very few in alluvial channels.
 Does not follow a sinuous course.
 The stretch of the river which has sinuosity less than 1.5 (sinuosity is the ratio of channel length to
valley length.)
 Sinuosity varies from a value of unity for a straight reach to a value of three or more.
 A sinuosity of 1.5 is usually taken as the dividing line between meandering and straight channels.
 Flow at bends:
 every alluvial river tends to develop bends, which are characterized by scouring on the concave side
and silting on the convex side.
 The silting and scouring in bends may continue due to the action of centrifugal force.
 These rotary currents cause the erosion of concave edge and deposition on the convex edge forming
shoal on this edge.
 When once the bend forms, it tends to make the curvature large and larger.
 Development of meanders:
Various stages of River
As a river flows from its orginal in a mountain to a sea, it passes through various stages.A river
generally has the following four stages namely Rocky stage, boulder stage, trough and alluvial stage,
delta stage.
i. Rocky stage
The rocky stage is also called hilly or mountainous stage or the incised stage and this is the first stage
of a river, after it takes off from a mountain and flows through the hilly region. The flow channels are
formed in the rocky by degradation, and cutting and the cross section of river usually made up of
rock.In rocky stage, the river has very steep slopes and velocity of water is quick high. As the bed and
banks are are rocky they are less susceptible to erosion and the river is therefore quite stable. The rock
stage is ideal for construction of dams.

5. 4
ii) Boulder stage (Sub mountainous stage)
It is the second stage of the river and the river passes from the rocky stage to the boulder stage as it
flows down the mountains. In this stage, the bed and banks are usually composed of large boulders,
gravels, shingles. The river cross section is well defined and the river generally confined between non
submersible high banks on either side. In this stage bed slope is quite steep, and the velocity is high, but
less than rocky stage.
iii) Trough and Alluvial stage
In this stage, a river flows in a zigzag manner known as the meandering and the river meanders freely
in the alluvial soil from one bank to the other. In plan the river seems to more like a snake and the cross
sec tion of the river is made up of alluvial sand and silt. The behavior of river in this stage depends up
on the silt charge and flood discharge. The river training works (groynes, spurs) are required in the
alluvial stage of floods.
iv) Deltaic stage
This stage is the last stage of the river just before it discharges in to the sea.in this stage the river
gets divided in to a number of small branches and forms a delta ( shaped formation).The bed slope
and river is unable to carry its sediment load and consequently it drops its sediments and gets
divided in to channels on either side of the deposited sediment and frames the delta.
Fig Stages of a River

6. 5
1.4 Development Process of alluvial Streams
The behavior of alluvial rivers depends up on to a large extent on the sediment carried by it. Every alluvial
river tends to develop bends, which are characterized by scouring on the concave side and silting on the
convex side.
Types of Alluvial Rivers
Rivers in flood plains (alluvial stage) may be broadly classified in to three categories:
1. Aggrading (accreting) type: For a river collecting sediment and building up its bed called an aggrading
type. It is a silting river and builds up its slope.
The silting is mainly due to various reasons, such as: heavy sediment load, construction of an obstruction
across a river, sudden intrusion of sediment from a tributary, etc.
2. Degrading type: If the bed is getting scoured year to year, it is called degrading.
If the river bed is constantly getting scoured, to reduce and dissipate available excess land slope.
3. Stable river: If there is no silting or scouring, it is called a stable river. A river that does not change its
alignment, slope and its regime significant.
4. Deltaic: Is the last stage of the river just before it discharge into the sea. The river is unable to carry its
sediment load. As a result, It drops its sediments and gets divided into channels on either side of the
deposited sediment and form the delta.
1.5 River Morphology
The terms river morphology and its synonym stream morphology are used to describe the shapes of river
channels and how they change in shape and direction over time. The morphology of a river channel is a
function of a number of processes and environmental conditions, including the composition and erodibility
of the bed and banks (e.g., sand, clay, bedrock);
The morphology of a river can be viewed conveniently by considering its longitudinal profile and cross-
sectional profile. The geology, tectonics, topography, climate, land use, and human activity
determine the geomorphic and hydrologic characteristics of the basin in the hill catchments
(Horton, 1932). The basin characteristics, in turn, influences the hydrological response and
river morphology downstream. The river morphology basically determined by the valley
topography and the characteristics of the river basin (geology, soil, mechanical properties).
Longitudinal profile is the section or line, which can be obtained by plotting the axial line of the channel
from the source to the mouth. Such a section will indicate the slopes in different reaches of the channel.
The upper surface of the stream or river water in case of perennial rivers will also reflect the general
character of the longitudinal profile.
The other characteristics of the river morphology can be seen through the cross sectional profiles in
different sections of the river. Such profile will show the characteristics of the banks, the natural levees, the
meanders, width and depth of the channel, the slopes of the channel, the slopes of the banks or valley
flanks, braiding of the streams, river terraces, alluvial cones, cones, fans and nature of the channel floor.

7. 6
The various features of river morphology mentioned above are associated with certain physical process.
 Longitudinal profile of a river
 Water falls
 Falls due to earth movement
 Lithology an important cause
 Falls due to hanging valleys
1.6 Meandering and Braided Stream
Once a bend in the river has been developed, either due to its own characteristics or due to the impressed
external forces, the process continues furthest downstream. The successive bends of the reverse order are
formed. It ultimately leads to the development of a complete S-curve called a meander. When a large
number of such consecutive curves of reverse order connected by short straight reaches called crossings
have been developed, the river is called a meander river.
Mechanism of meander development
The development of meander is a highly complex phenomenon. Various investigators studied the problem
in the past and gave their own theories.
a) Inglis theory
when there is heavy load of bed material in movement during floods, excess turbulent energy is developed
due to unevenness of bed and in such condition symmetrical axial flow is not maintained and flow tends to
concentrate towards one of the banks.
b) Friedkins theory
Meandering occurs because of local bank erosion and consequent overloading and deposition by the river
of the heavier sediments which move along the bed.

8. 7
C) Joglekars theory
The primary cause of meandering is excess of sediments in river during floods.This sediment load being in
excess of the load carrying capacity of the river is deposited on the bed.
Braided channels
Braiding is a feature of channels with steeper slopes, where flows have high energy. Braided channels are
subdivided at normal flows by midstream bars of sand or gravel. At high water, many or all bars are
submerged. A single meandering channel may convert to braiding where one or more bars are formed,
where for example, downstream of a tight bend material is brought up from the pool bottom. Each of the
subdivided channels is less efficient, being smaller than the original single channel and this is often
compensated for by an increase in slope (i.e., by down cutting).
Fig . Braided Channel
Meander parameters and their relation ships
Meanders can be classified as regular or irregular. If there is a series of bends approximately to some
curvature and frequency the meander is said to be regular.
If the radius of curvature is uniform, it is said to be simple meandering.
If the radius of curvature is not uniform, it is said to be compound meandering.
Geometry of Meander
The geometry of meander is usually described by the meander length and meander width.
Meander length (ML): the tangential distance between the consecutive corresponding points of a meander.
Meander width (MB): The distance between outer edges of one clock wise loop and the adjacent
anticlockwise loop of the meander.
Meander Ratio (MR): the ratio of of meander width to meander length.
Khadris: The permanent banks between which a river meanders.
ISLANDS

9. 8
Crossings: The short straight reaches of a river connecting two consecutive clock wise and anti clock wise
loops.
Sinuosity: the ratio of talwege length to valley length. The talwege length is the length of the river along
the line of maximum depth.
 Sinuosity varies from a value of unity for a straight reach to a value of three or more.
 A sinuosity of 1.5 is usually taken as the dividing line between meandering and straight channels.
Tortuosity: the ratio of the length of the channel measured along the curve to meander length.
𝐓𝐨𝐫𝐭𝐮𝐨𝐬𝐢𝐭𝐲 =
(𝐓𝐚𝐥𝐰𝐞𝐠𝐞 𝐥𝐞𝐧𝐠𝐭𝐡 − 𝐕𝐚𝐥𝐥𝐞𝐲 𝐥𝐞𝐧𝐠𝐭𝐡)
𝐕𝐚𝐥𝐥𝐞𝐲 𝐥𝐞𝐧𝐠𝐭𝐡
Meandering channels are single channels that are sinuous in plan. Meandering channels are efficient
equilibrium features that represent the channel plan geometry, where single channels deviate from
straightness. This deviation is related in part to the cohesiveness of channel banks and the abundance and
bulk of midstream bars.
Fig . Meandering channel
L
a
Thalweg
Pool
Riffle

10. 9
Incised rivers: The rivers which flow in cross sections cut below the natural ground surface on
either side which is not liable to submergence.
Riffles and pools
Straight rivers are rare in nature. This is in part linked to the fact that velocity at a river cross section is
unevenly distributed. As a consequence, convergent and divergent patterns of downstream flow result in
the development of a longitudinal sequence of pools and riffles. The bed of a meandering stream includes
pools at (or slightly downstream of) the bends and riffles between the bends.
Fig . Pool (scour) & Riffle (fill)
Meander wavelength
Meanders may be characterised by their length, L, and amplitude, a, (See fig 4). Meander wavelength, the
distance between two successive bends has been the subject of much research. Measurements of
meandering watercourses show that there is a pattern to the shape of the meanders. Approximate
wavelengths of one full meander may be summarised as follows:
 Approximately 10 to 14 times the bank full width of the watercourse.
 Concentrated between 8 and 10 bedwidths.
 7<L/B<11
Because bed width is related to discharge, meander wavelength is also related to discharge. There are a
number of equations showing this relationship, for example:
 L = 46Q0.39
POOL: Convergent
RIFFLE: Divergent

11. 10
Relation Rivers in flood plain Incised rivers
Relations depending on Q
1. Meander length
2. Meander width
3. River width
ML=53.61*Q1/2
ML=6.06*W
MB =153.42*Q1/2
MB =17.4*W
MB =2.86*ML
W=8.84*Q1/2
ML=46.01*Q1/2
ML=11.45*W
MB =102.16*Q1/2
MB =27.3*W
MB =2.20*ML
W=8.84*Q1/2
Note: Q= 1.5 to 2 times Qd, where Qd= dominant discharge which determines the meandering
pattern.
1.7 River Hydraulics
Rivers are complex and dynamic. It is often said that a river adjusts its roughness, velocity, slope, depth,
width, and planform in response to human activities and (perhaps associated) changing climatic, geologic,
and hydrologic regimes.
The phenomena in rivers may vary considerably in magnitude both in time and space. The flow in a river
can be classified as uniform/non- uniform, steady/ unsteady, laminar/ turbulent, Tranquil/rapid in three
dimensional. In natural low land rivers, the flow is non-uniform, unsteady, turbulent and tranquil. The rapid
flow occurs in the vicinity of drop structures and also the mountainous rivers.

12. 11
In a turbulent flow the fluid element moves along irregular parts and mixing is no longer confined to
molecular interaction between adjacent fluid layers, However it involves a transfer of momentum by eddies
of different sizes.
The equation for shear stress is given by
𝛕 = 𝛍
𝛛𝐮
𝛛𝐙
…………………. (1) Laminar flow
𝝉 = (𝝁 + 𝝐𝑽)
𝒅𝑽
𝒅𝒁
………………(2) Turbulent flow
Where єV= Eddy viscosity depends on state of turbulence
μ = Viscosity depends on type of fluid property
dv/dZ= Velocity gradient
The flow in a river is a three dimensional varying in space and time. The detail knowledge of three
dimensional flow structure in a river is still very limited.
Let U, V, W are the velocity components in x, y, z direction and g = Acceleration due to gravity
The three dimensional equations derived from ideal fluid flow of motion describing conservation of mass
and conservation of momentum as expressed by Newtons second law of motion (Lamb 1963, oscillation
1959).
The three dimensional equations describing the water motion can be written as according to Jansen et al
1979:
Conservation of momentum
𝛛𝐔
𝛛𝐭
+
𝛛𝐔𝟐
𝛛𝐗
+
𝛛𝐔𝐕
𝛛𝐲
+
𝛛𝐔𝐖
𝛛𝐙
+ 𝐠
𝛛𝐙𝐰
𝛛𝐗
= 𝟎 ……………………………………………… (1)
𝛛𝐕
𝛛𝐭
+
𝛛𝐔𝐕
𝛛𝐗
+
𝛛𝐕𝟐
𝛛𝐲
+
𝛛𝐕𝐖
𝛛𝐙
+ 𝐠
𝛛𝐙𝐰
𝛛𝐗
= 𝟎 … ……………………………………………. (2)
Z
y
x
w V
u
Z=y=Zw
Z Z=0=Zb

13. 12
𝛛𝐖
𝛛𝐭
+
𝛛𝐔𝐖
𝛛𝐗
+
𝛛𝐕𝐖
𝛛𝐲
+
𝛛𝐖𝟐
𝛛𝐙
+
𝟏
𝐏
𝛛𝐏
𝛛𝐙
= −𝐠 … ………………………………………… (3)
Continuity equation
𝝏𝑼
𝝏𝑿
+
𝝏𝑽
𝝏𝒚
+
𝝏𝑾
𝝏𝒁
= 𝟎 … … … … … … … … … … … … … … … … … … … … … … … … … … … … . . (𝟒)
The equation of motion (eq-3) is well approximated by hydrostatic equation. The acceleration due to
gravity is balanced by gradient of pressure. i.e
𝛛𝐏
𝛛𝐙
= −𝛒𝐠
Assuming the pressure vanishes at water surface (Zw) the above equation is integrated at both sides:
∫ 𝛛𝐏 = ∫ −𝛒 𝐠 𝛛𝐙
𝐳
𝐙𝐰
P= -ρg (Z-Zw) implies P= ρg (Zw-Z)
Where Zw = Water level above horizontal reference level
Exercise:
The phenomena in rivers may vary considerably both in magnitude both in time and
space. The continuity equation for unsteady, one dimensional flow is given by :
0






t
A
X
Q
a) Derive the following equation that shows wedge storage, prism and rate of rise?
0









t
y
b
x
v
A
x
A
v S bs
Zw
where ,
bs = Top width at Water surface (m) Z
x = longitudinal distance along the centerline of the river
channel (m)
y = depth of flow (m) R.B.L Zb
t = time (seconds)
Zw = Water surface Elevation (m)
Zb = Bottom Elevation (m)
b) If the water surface elevation above R.B.L is + 120m.What is the pressure induced at
+105m above R.B.L? Hint : use  = 1000kg/m3 and g =9.81m/s2