River hydraulic for flood risk evaluation

RIVER HYDRAULICS FOR FLOOD
RISK EVALUATION
(River serio project)
Prof. Alessio Radice
Prof. Gianluca Crotti
Group Members :
Kasra Majdanishabestari 872111
Nikola Rakonjac 874094

General presentation of the case-study 2
Introduction of the Area
The serio river is a river located entirely
within the region Lombardy in the
north of Italy. This river is also crossing
the provinces of Bergamo and Cremona
and flows into the Adda River at Bocca
di Serio to the south of Crema.
Picture 1.Full view of the riverPicture 1.Full view of the river
Picture 2.Close view of the river Picture 3.Close view of the river

Properties of the area :
• Length: 125 km
• Area of basin: 1250 km2
• Average discharge: around 25 m3/s
• Water used for hydropower (famous falls
are activated some times every year) and
irrigation.
Our project area is the last 15 km of the river,Our project area is the last 15 km of the river,
from Crema to the intersection with the
Adda.
Data provided:
• Cross sections (map and survey data)
• Flood hydrograph
• Geometry data incorporated into a project
of Hec‐Ras
• Pictures of the reach
Picture 4. General view of the reach

Figure 1. Longitudinal profile of the river Serio

1-D modelling 5
Steps:
• Cross section data: choosing suitable values of roughness (Manning
coefficient) for main channel and floodplains
• Geometry data: defining bridge in section 6.1
• Choosing discharge and BC.s (boundary conditions)
• Putting levees in the correct nodes (for avoiding error of Hec-Ras)
• Running models
• Steady model with ordinary flow: benchmark solution,• Steady model with ordinary flow: benchmark solution,
sensitivity analysis (manning value and Boundary Conditions)
and comparing the results
• Steady model with peak flow: benchmark solution, sensitivity
analysis (geometry, levees, manning value, Boundary
Conditions) and comparing the results
• Unsteady model for 200-year hydrograph: benchmark solution,
sensitivity analysis and comparing the results

1-D modelling 6
Theoretical Background
HEC-RAS as an 1-D modelling software is based on the Saint Venant Equations.
These equations are obtained based on the following assumptions, generally satisfied
in hydraulic processes:
1.
2.
flow is one-dimensional.
All the quantities can be described as continuous and derivable functions
longitudinal position (s) and time (t).
Fluid is uncompressible.
Flow is gradually varied, and the pressure is distributed hydrostatically.
of
3.
4. Flow is gradually varied, and the pressure is distributed hydrostatically.
Bed slope is small enough to consider cross sections as vertical.
Channel is prismatic in shape.
Flow is fully turbulent.
4.
5.
6.
7.
Continuity equation
Momentum equation

1-D modelling 7
For special cases, these equations can be simplified as follows:
Steady flow with no temporal variation:
Steady flow with no spatial and temporal variability )Uniform flow:(
In case of steady flow, modelling is simple: a constant discharge should be assign to the
entire reach, and a boundary condition for water level which would be at upstream for
supercritical flows or at downstream for subcritical flows.

1-D modelling 8
In case of unsteady flow, an initial condition is necessary together with an upstream
boundary condition (usually a discharge hydrograph) and a second boundary condition
which must be upstream for supercritical flows or downstream for subcritical flow.
Characteristic depths
Critical Depth dc:
The depth for which the specific energy is
minimum is called the critical depth.
Figure 2. dc with respect to specific energy
and hydrodynamic force
Figure 3. Representation
of normal depth
Normal Depth d0:
If no quantity varies with the longitudinal direction, the
flow is called uniform, and the momentum equation
representing the process is S0= Sf. The depth for
which this happens is called the normal depth
For a given discharge, Sf is a decreasing
function of water depth, therefore:
d >
d <
d0 ⇒
d0 ⇒
S0 > S f
S0 < Sf

1-D modelling – Steady – Ordinary Flow 9
Steady model for the ordinary flow
Length: 125 km
Average discharge: 25 m3/s
S0= 0.15%
The manning values for main
Manning Coefficient:
The manning values for main
channel and floodplains are
selected according to the G o o g l e -
e a r t h a n d t h e given pictures
of the sections. It can be selected
according to vegetation areas and
physical considerations. The values
are obtained from the table which
is available in the HEC-RAS program
manual. (Version 5.03)
Figure 4. View of the river
with it’s sections in Hec-
Ras

River Station Left Bank Main Channel Right Bank
20 0.04 0.04 0.04
19 0.04 0.04 0.04
18 0.035 0.041 0.037
17 0.035 0.04 0.035
16 0.035 0.042 0.035
15.1 0.035 0.04 0.05
15 0.038 0.042 0.05
14 0.038 0.041 0.065
13 0.038 0.04 0.042
12.1 0.035 0.04 0.035
12 0.035 0.04 0.038
11 0.04 0.04 0.037
10 0.037 0.04 0.037
9 0.037 0.041 0.04
Table 1. Manning Coefficients
9 0.037 0.041 0.04
8.2 0.04 0.041 0.046
8.1 0.042 0.043 0.048
8 0.07 0.041 0.038
7 0.035 0.04 0.035
6.15 0.04 0.04 0.04
6.1 Bridge Bridge Bridge
6.05 0.04 0.04 0.04
6 0.036 0.039 0.036
5 0.045 0.04 0.048
4 0.08 0.048 0.07
3 0.08 0.045 0.08
2.1 0.08 0.045 0.036
2 0.085 0.04 0.07
1 0.048 0.05 0.075

In section 8.1, a levee should be added to the right of the main channel. Since Hec-Ras is a
1-D modelling software, it cannot consider whether water can move across the main
channel to the floodplains or not. Therefore, if the bed elevation at floodplain is lower
than water surface, Hec-Ras will consider water flows into the banks.
To prevent this error, in these sections like section 8.1 in our model, a levee has to be
added.
Figure 5. Example of solving Hec-
Ras problem, by adding levee

Bridge:
A Bridge in section 6.1 needs to be added. To do this, we need to add one section to
the upstream, one section to downstream and one section at the place where the
structure is located.
The distance between this three sections is 10m from the middle section of the
bridge, and the total width of the bridge is 10m.
Figure 6. Cross section of the bridge Table 2. Bridge Data

Picture 5. Top view of the bridge
Picture 6. Upstream view of the bridge Picture 7. Downstream view of the bridge

Discharge and boundary conditions:
The discharge for the ordinary flow is 25 m3/s.
The boundary conditions for the river depend on the nature of the flow. In the case of
subcritical flow, we have to input just downstream condition and for supercritical flows, just
upstream condition is needed.
By running the model with some assumed boundary conditions (critical flow at upstreamBy running the model with some assumed boundary conditions (critical flow at upstream
and normal flow at downstream), it was noted that the Froud Number along the channel is
lower than 1. Therefore, the flow is subcritical and just downstream boundary condition has
to be set. To do so, a sensitivity analysis of the boundary condition need to be done.
Sensitivity Analysis for the Ordinary Flow
In this case we have to do sensitivity analysis of boundary conditions and the
Manning values for the main channel, left and right bank to compare the influence
on the water surface elevation and velocity.

SensitivityAnalysis for different Boundary Conditions for the Ordinary Flow
To check the sensitivity of the results with respect to the boundary
boundary conditions are considered and their results are compared:
• Downstream critical depth
• Downstream normal depth (S=0.0015)
• Upstream critical depth & downstream normal depth (S=0.0015)
conditions, 3 sets of
65 Figure 7.Water elevation for different B.Cs
Downstream normal
45
50
55
60
0 2000 4000 6000 8000 10000 12000 14000
Elevation(m)
Station(m)
Downstream normal
depth(S=0.0015)
Upstream crtitical depth
and downstream normal
depth(S=0.0015)
downstream critical
depth
Ground level

0.5
1
1.5
2
2.5Velocity(m/s) Figure 8. Velocity for different B.Cs
Downstream normal
depth(S=0.0015)
Downstream critical depth
Upstream critical depth and
downstream normal
depth(S=0.0015)
It is clear that having different boundary conditions for the ordinary flow case does not
affect the results, except for a few sections close to the downstream which is due to
depth we have chosen there.
0
0 2000 4000 6000 8000 10000 12000 14000 16000
Station(m)

Running the Model for Steady-Ordinary Flow :
Elevation(m)Elevation(m)
Main Channel Distance (m)
Figure 9. Longitudinal Profile of river Serio in Hec-Ras

Roughness SensitivityAnalysis
To perform the sensitivity analysis of the roughness of the river, a control state is
considered as the model in which the manning coefficients are those which were assigned
to different sections based on the ground condition and vegetation. To study the roughness
sensitivity, the manning coefficients are once increased and once decreased for 0.01
The roughness sensitivity is evaluated regarding two aspects
Water surface elevation
Velocity

49
51
53
55
57
59
61
63
Elevation(m)
Figure 10. Water elevation with different Manning coefficient
Manning coeff
without changening
Ground level
Manning coeff+0.01
Manning coeff -0.01
Roughness sensitivity analysis on water surface elevation
What is clearly observed in the plot is that by changing the value of manning coefficient, the changes
occurred in the water surface elevation is negligible compared to the total dimensions of the problem.
However, generally it is seen that increasing the manning coefficient leads to an increase in the water
surface elevation. This conclusion cannot be stated with certainty and further analyzing is required
45
47
49
0 2000 4000 6000 8000 10000 12000 14000 16000
Stations(m)

1
1.5
2
2.5
Velocity(m/s)
Figure 11. Velocity for different values of Manning coeff
Manning
without
changing
Manning -0.01
Roughness sensitivity analysis on velocity along the river
As it is shown, manning coefficient has a considerable effect on velocity values. Regardless of the
velocity changes along the river, it is clear that the model with the lowest manning coefficient has the
highest velocity and vice versa.
0
0.5
0 2000 4000 6000 8000 10000 12000 14000 16000
Velocity(m/s)
Stations(m)
Manning +0.01

1-D modelling – Steady – Peak Flow 21
Steady model for the peak flow
Length: 125 km
Peak discharge: 561.12 m3/s
S0= 0.15%
The geometry of the model is the same as the ordinary
flow, except for 2 sections that are deleted .
Figure 12. View of the river
with it’s sections in Hec-Ras

Sections 15.1 and 8.2 are deleted.
In the case of sections 15.1 and 8.2, the general
direction of
down. Since
located after
the flood would be vertically
the sections are too narrow and
a bend in the main river, all the
sections will be flooded, so we can delete them.
Picture 8. Deleted cross sections

After running the peak flow simulation , in sections:
20, 18, 17, 16, 15, 14, 12, 11, 10, 9, 8, 5, 4, 2.1, 2 and 1
We can observe water in some parts of the sections where it is not supposed to be. This
problem can lead us into wrong conclusion about judging the real situation of the river.
The reason for this error has been explained on page 11.
As an example of the above mentioned situations is section(17) ,which is shown below :
section 17
In all cross sections which are mentioned above, levees should be added in the similar way
as in section(17).
Figure 13. Example of solving Hec-Ras problem, by adding levees

Running the Steady-Peak flow model:
Figure 14. Longitudinal Profile of river Serio, for Peak flow

25
SensitivityAnalysis of the different Boundary Conditions for the Peak Flow
To check the sensitivity of the results with respect to the boundary
boundary conditions are considered and their results are compared:
• Downstream critical depth
• Downstream normal depth
• Upstream critical depth and downstream normal depth (S=0.015)
conditions, 3 sets of
1-D modelling – Steady – Peak Flow
In this case we have to do sensitivity analysis of boundary conditions, geometry of peak
flow and the Manning values for the main channel, left and right bank to compare the
influence on the water surface elevation and velocity.
Sensitivity Analysis for the peak Flow
45
50
55
60
65
70
0 2000 4000 6000 8000 10000 12000 14000
Elevation(m)
Station(m)
Figure 15. Water elevation for different B.Cs Downstream normal
depth(S=0.0015)
Upstream crtitical depth
and downstream normal
depth(S=0.0015)
downstream critical
depth
Ground level

1
2
3
4
5
6Velocity(m/s)
Figure 16. Velocity for different B.Cs
Downstream normal
depth(S=0.0015)
Downstream critical
depth
Upstream critical
depth and
downstream normal
depth(S=0.0015)
It is clear that having different boundary conditions for the peak flow case does not
affect the results, except for a few sections close to the downstream which is due to
different criteria we have chosen there.
0
0 2000 4000 6000 8000 10000 12000 14000 16000
Station(m)
depth(S=0.0015)

SensitivityAnalysis of the geometry for the Peak Flow
In order to check the sensitivity of the results with respect to the geometry of the data
we can delete some sections with respect to the water direction in peak flow , which
passes from some sections.
In this case we delete sections 8.2 and 15.1, because they are in position which in peak
flow condition they might have small influence on water direction .
Since the flow is subcritical, and subcritical flows need downstream boundary conditions,
the effect of changing the geometry would be on the upper sections.
70
45
50
55
60
65
70
0 2000 4000 6000 8000 10000 12000 14000
Elevation(m)
Station(m)
Figure 17. Water elevation with some deleted cross sections Without deleting
cross sections
Ground level
deleted cross
section 15.1
Deleted cross
sections 15.1, 8.2

0
0.5
1
1.5
2
2.5
3
3.5
4
0 2000 4000 6000 8000 10000 12000 14000 16000
Velocity(m/s)
Station(m)
Figure 18. Velocity with some cross sections deleted
Without deleting
cross sections
Deleted cross
section 15.1
Deleted cross
sections 15.1, 8.2
Station(m)
Results:
• The changes, for water surface elevation and velocity around deleted sections
are more obvious in velocity.
• The differences in water surface elevation along the river because of elimination
of two sections are small.
• The effect on velocity is remarkable, while elimination of sections has an
insignificant effect on water surface elevation.

51
53
55
57
59
61
63
65
67
69
Elevation(m)
Figure 19. Water elevation with different Manning coefficient
Manning coeff without
changening
Ground level
Manning coeff+0.01
Roughness sensitivity analysis on water surface elevation
In the same manner as the previous case, the lower the manning coefficient is, the lower is the water
surface elevation and vice versa. A clear difference between this plot with the one corresponding to the
ordinary flow is that, the peak flow condition is more sensitive to manning variation when
compared to the ordinary flow.
45
47
49
51
0 2000 4000 6000 8000 10000 12000 14000 16000
Stations(m)
Manning coeff -0.01

1
1.5
2
2.5
3
3.5
4
4.5
Velocity(m/s)
Figure 20. Velocity for different values of Manning coeff
Manning without
changing
Manning -0.01
Manning +0.01
0
0.5
0 2000 4000 6000 8000 10000 12000 14000 16000
Stations(m)
Results :
According to graph it is obvious that the effect of modification of the Manning
values is remarkable on velocity magnitude, which means if the roughness
increases the magnitude of velocity will decrease and vice versa.

1-D modelling – Unsteady – Peak Flow 31
Unsteady model for 200-year Hydrograph
In unsteady modeling, all the parameters from previous
levees.
models are used, except for the
1. Model conditions
Boundary condition
Upstream: 200-year hydrograph
Downstream: normal depth with slope of 0.0015
Initial conditionInitial condition
Initial discharge
Trial running and detecting possible problems2.
3. Running the model and defining benchmark solution

Unsteady flow data
The original dataset is interpolated with 1 hour time interval (using Matlab software).
This time interval is small enough with respect to the whole event history.
Figure 21. Flow Hydrograph

Comparison: Unsteady and steady flow
Boundary condition in steady flow for downstream is normal depth with slope 0.0015
and discharge is 561.12 m3/s.
Boundary condition in unsteady flow for the upstream is hydrograph and for the
downstream is normal depth with slope 0.0015.
50
55
60
65
70
Elevation(m)
Figure 22.Water elevation for different B.Cs
Steady flow
Ground level
45
50
0 2000 4000 6000 8000 10000 12000 14000
Elevation(m)
Station(m)
Unsteady
flow
0
0.5
1
1.5
2
2.5
3
3.5
4
0 2000 4000 6000 8000 10000 12000 14000 16000
Velocity(m/s)
Station(m)
Figure 23. Velocity for different B.Cs
Steady flow
Unsteady
flow

342-D modelling
Theoretical concept
The numerical formulation of 2D river
modelling was originated from the analysis
of shallow water. The main outputs of the
2D model are two water velocity
components and a vertical water depth for
each defined node. Generally, the results of
the program has been generated by the
solution of the mass conservation equation
and the two momentum conservationand the two momentum conservation
equations.
Momentum
conservation
Mass
conservation
Lateral stresses
Figure24. River 2D interface

2-D modelling 35
The 2D model depth averaged, mass and momentum conservation equations are:
The bed shear stress are computed by: and
The turbulent normal and shear stresses are computed according to the
Boussinesq’s assumption as:
Disadvantages:
• Modeling complexity and precision are not a substitute for clear and fast
engineering judgment.
• Results are limited by the accuracy of the assumptions, input data and the
computing power of the computer program.
Advantages:
• Ability to model more complex flows including floodplain and underground
flows.
• No need to force the geometry to be appropriate for modelling.
• Ability to consider impact of obstructions.

362-D modelling
Comparing the results of 2-D with 1-D modelling
Since River 2D results 2 values for velocity along the X and Y axis, and computes the
water depth at each node, it is not possible to have single longitudinal profile for
velocity and water surface for the river. Therefore, the results are compared section by
section.
In order to compare the results, all sections have been compared and some of them,
randomly, have been chosen to show in the report. Moreover, comparing the results
at the beginning and the end of the river are not necessary due to less accuracy of the
results in these sections.
Water Surface Elevation
The comparisons for the first and last sections
are neglected due to less accuracy of results in
these sections.
For our comparisons also one of the important
parameter is water depth.
Figure 25. Water depth in 2D

Comparing water surface elevation in 1-D & 2-D model (sections 10,12,13 & 15) 37
53
58
63
68
73
0 200 400 600 800 1000
Elevation(m)
Stations(m)
Figure 26. Water elevation(section 10)
Bed
elevation
2D
1D, peak
flow,
steady
53
58
63
68
73
0 200 400 600 800 1000
Elevation(m)
Stations(m)
Bed
elevation
2D
1D,peak
flow,
steady
53
58
63
68
73
0 200 400 600 800 1000 1200
Elevation(m)
Stations(m)
Bed
elevation
2D
1D,peak
flow,
steady
55
60
65
70
0 500 1000 1500
Elevation(m)
Stations(m)
Bed
elevation
2D
1D,peak
flow,
steady

Comparing water surface elevation in 1-D & 2-D model (sections 17 & 18) 38
57
62
67
Elevation(m)
Bed
elevation
2D
1D,peak
flow,
steady
53
58
63
68
73
78
0 200 400 600 800
Elevation(m)
Bed
elevation
2D
1D,peak
flow,
steady
0 200 400 600 800 1000
Stations(m)
0 200 400 600 800
Stations(m)
Results of water surface:
• In most of the plotted figures we can observe that in River 2D higher water surface
elevation has been obtained along the river, which is caused by activation of more
floodplains. For the sections near to the upstream side of the river, we decided to neglect
the results, due to the less accuracy.
• According to graphs it is obvious, the water surface elevations resulted from River 2D are
more accurate than Hec-Ras in which a single value is reported for each section.

Comparing Velocity in 1-D & 2-D model (sections 10,12,13 & 15) 39
0
0.5
1
1.5
2
2.5
0 200 400 600
Velocity(m/s)
Figure 32. Velocity(section 10)
Velocity
-2D
Velocity
-1D
0
0.5
1
1.5
2
2.5
0 100 200 300 400 500
Velocity(m/s)
Velocity
-2D
Velocity
-1D
0 200 400 600
Stations(m)
0 100 200 300 400 500
Stations(m)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 200 400 600
Velocity(m/s)
Stations(m)
Velocity-
2D
Velocity-
1D
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 200 400 600
Velocity(m/s)
Stations(m)
Velocit
y-2D
Velocit
y-1D

40
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Velocity(m/s)
Velocity-
2D
Velocity-
1D
Results of velocity:
As it was mentioned before HEC-RAS
considers only velocity for each section
along the river, but River2D considers two
parameters for velocity, in X and Y
directions.
In the case of 1D modeling just friction
losses are considered while in the case of
2D modeling, lateral stresses are
Comparing Velocity in 1-D & 2-D model (sections 17 & 18)
0
0 50 100 150 200 250 300 350 400 450
Stations(m)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 50 100 150 200 250 300 350 400 450
Velocity(m/s)
Stations(m)
Velocity-
2D
Velocity-
1D
2D modeling, lateral stresses are
considered as well.
Due to these reasons two different results
are obtained in the case of velocity.

2-D modelling - Velocity 41
Conclusions:
The differences in the values of velocity obtained
by the two software are because:
As it was mentioned, software River 2D
considers two components for velocity (in
X direction and Y direction), so we evaluated
unique value of velocity for each section, by
combining data from water depth and discharges
unique value of velocity for each section, by
combining data from water depth and discharges
in X and Y directions.
In 2D modelling, lateral stresses are also
considered while in the 1D modelling only
friction losses are considered.
Figure 38. Velocity representation in 2-D
On the other hand Hec-Ras considers only one
velocity for each section along the channel (so
perpendicular to the cross sections)

Sediment Transport 42
0.015m
)

0.05 is
W0=V*/0.3

0
0.02
0.04
0.06
0.08
0.1
0.12
0 2000 4000 6000 8000 10000 12000 14000
Length of the river (m)
Figure 39. Shields number in the river(ordinary flow)
tau*
tau*,
critical
0
0.05
0.1
0.15
0.2
0 2000 4000 6000 8000 10000 12000 14000
Figure 40. Shields number in the river(peak flow)
tau*
tau*,
critical

0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 2000 4000 6000 8000 10000 12000 14000
d(m)
Figure 41. Ordinary flow
ds,critical,suspended
ds,critical ( Tau*,critical=0.05)
d50
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 2000 4000 6000 8000 10000 12000 14000
d(m)
Figure 42. Peak flow
ds,critical,suspended
ds,critical ( Tau*,critical=0.05)
d50

Distance Q Total
Hydraulic
Radius Channel
Vel channel S (f,skin) Τ* τ* Critical
0 25 1.14 0.66 0.000162 0.008225 0.05
550 25 0.42 2.03 0.005814 0.108534 0.05
1097 25 1.64 0.43 4.24E-05 0.003093 0.05
1501 25 1.09 0.8 0.000253 0.012266 0.05
2297 25 0.62 0.78 0.000511 0.014073 0.05
3532 25 1.2 0.75 0.000196 0.01044 0.05
4033 25 0.89 1.05 0.000572 0.022607 0.05
4875 25 0.78 0.95 0.000558 0.019338 0.05
4929.21 25 1.16 0.43 6.73E-05 0.003471 0.05
5524.21 25 1.8 0.52 5.48E-05 0.004384 0.05
Table 3. Ordinary flow data for Sediment Transport
5524.21 25 1.8 0.52 5.48E-05 0.004384 0.05
6505.21 25 1.1 1.15 0.000517 0.025269 0.05
7174.21 25 1.22 0.63 0.000135 0.007326 0.05
7580.21 25 1.34 0.55 9.09E-05 0.005412 0.05
7927.21 25 0.46 1.19 0.00177 0.036183 0.05
8829.21 25 1.5 0.32 2.65E-05 0.001764 0.05
9253.21 25 0.59 1.14 0.001166 0.030562 0.05
9828.21 25 1.22 0.61 0.000127 0.006869 0.05
10129.21 25 1.09 0.66 0.000172 0.008348 0.05
10537.21 25 0.6 0.98 0.000842 0.022459 0.05
10537.21 25 Bridge Bridge Bridge Bridge Bridge
10933.21 25 0.37 1.93 0.006223 0.102339 0.05
11419.21 25 1.43 0.58 9.27E-05 0.005889 0.05
11811.21 25 1.29 0.52 8.55E-05 0.004899 0.05
12492.21 25 1.49 0.91 0.000216 0.0143 0.05
12979.21 25 1.01 0.84 0.000309 0.013871 0.05
13515.21 25 0.81 0.83 0.000405 0.014576 0.05
13894.21 25 1.29 0.64 0.000129 0.007421 0.05
14363.21 25 0.81 0.67 0.000264 0.009498 0.05

Table 4. Peak flow data for Sediment Transport
4
Distance Q Total
Hydraulic
Radius Channel
Vel channel S (f,skin) Τ* τ* Critical
0 561.12 3.18 2.47 0.000579 0.08183 0.05
550 561.12 3.07 2.54 0.000642 0.087555 0.05
1097 561.12 1.44 1.35 0.000497 0.031833 0.05
1501 561.12 1.58 2.74 0.001811 0.127138 0.05
2297 561.12 1.5 0.59 9E-05 0.005998 0.05
3532 561.12 1.8 2.12 0.000911 0.072874 0.05
4033 561.12 2.16 2.37 0.000893 0.085705 0.05
4875 561.12 0.97 1 0.000462 0.019925 0.05
4929.21 561.12 1.45 0.63 0.000107 0.006916 0.05
5524.21 561.12 1.2 2.67 0.002481 0.132319 0.055524.21 561.12 1.2 2.67 0.002481 0.132319 0.05
6505.21 561.12 1.62 0.79 0.000146 0.010481 0.05
7174.21 561.12 1.6 1.84 0.000803 0.057094 0.05
7580.21 561.12 1.25 1.6 0.000844 0.046874 0.05
7927.21 561.12 1.48 0.57 8.55E-05 0.005623 0.05
8829.21 561.12 3.28 1.68 0.000257 0.037467 0.05
9253.21 561.12 1.81 0.85 0.000145 0.011693 0.05
9828.21 561.12 2.64 2.34 0.000666 0.078143 0.05
10129.21 561.12 1.65 0.7 0.000112 0.008179 0.05
10537.21 561.12 3.55 2.22 0.000404 0.063722 0.05
10537.21 561.12 Bridge Bridge Bridge Bridge Bridge
10933.21 561.12 3.49 2.27 0.000432 0.067004 0.05
11419.21 561.12 3.42 2.04 0.000358 0.054481 0.05
11811.21 561.12 1.09 1.16 0.000532 0.025789 0.05
12492.21 561.12 2.14 1.4 0.000315 0.029999 0.05
12979.21 561.12 2.7 2.44 0.000703 0.08433 0.05
13515.21 561.12 1.55 1.78 0.000784 0.053999 0.05
13894.21 561.12 1.56 0.71 0.000124 0.008573 0.05
14363.21 561.12 2.52 1.63 0.000344 0.038509 0.05

Calculating Sediment Transport (Different formulas)
In this stage sediment transport rate has been calculated by these four different
formulas: Einstein(1942) , Peter-Meyer(1951) , Nielsen(1992) , Van Rijn (1982-1993) .
Calculating Sediment Transport (Using Different Equations)Calculating Sediment Transport (Using Different Equations)

0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0 2000 4000 6000 8000 10000 12000 14000 16000
qs
Length of the river(m)
Figure 43. Ordinary flow
qs ( Einstein )
qs ( Nielsen )
qs( Meyer)
qs( Van Rijn)
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0 2000 4000 6000 8000 10000 12000 14000 16000
qs
Length of the river(m)
Figure 44. Peak flow
qs ( Einstein
)
qs ( Nielsen )
qs( Meyer)
qs( Van Rijn)

Hazard evaluation 50
For evaluation of the hazard in the flooded area, there are several important parameters,
which can be taken into consideration from our previous analysis. Some of them are:
-water surface level at affected area
-flood duration
Our hazard evaluation is also affected with our input hydrograph, and with return period
of the flood. Also one of the important things is to clearly understand what is exposed to
the flood ( people, houses…)
Comparing all observed parameters , and combining it with our understanding of
exposed things in this case, we made a conclusion that there are only a few farms which
are really exposed and that can be truly damaged with calculated flood.
There are different measurements which can be done to reduce the risk in the areas that
can be potentially damaged. Some of them are structural(levees…), some of them are
not structural(emergency planning..).

Final Discussion 51
Advantage and disadvantages of different models:
Steady flow 1-D model:
Considers only water elevation and velocity in space but not in time. To take different
velocities into account, main channels and banks have to be seperated.
Unsteady flow 1-D model:
More realistic and accurate than steady flow model, since it represents the longitudinal
decrease of peak discharge and depth.
It requires flow hydrograph as an input
Steady flow 2-D model
More complex modelling than 1D model, thus more accurate results.
Takes into account floodplains, lateral stresses, roughness, geometry, boundary
conditions…
Velocity is calculated in two different directions (x and y). Also, the inclusion of the
lateral stresses makes the velocity distribution more accurate. While 1-D model
considers only the axial direction of the flow without lateral stresses.

LaboratoryProject 52
For our laboratory project we have 2 different Profiles.
In first case we considered a steep channel because all over the channel
our d0 is lower than dc, and in the second we considered a mild channel
because all over the channel our d0 is higher than dc.
For every case firstly we have read laser values which later will be used
for calculating the slope of the channel.for calculating the slope of the channel.
Then we inserted some obstacles inside of the channel with considering
their dimensions and position from upstream.
After that we read the discharge values from flow-meter and measured
depth by piezometric probes.
INITIAL GIVEN DATA
Tilting flume with rectangular cross section
Length of the flume : 5.2 (m)
Width of the flume : 0.3 (m)
Height of the flume : 0.45 (m)

Laboratory 53
Formulas and relations used for calculation of slope by laser reading and
calculation of water depth by piezometric probes :

LaboratoryProject(steep) 54
First Profile (Steep) :
In this case we inserted 2 obstacles.
First obstacle has been positioned on 1.01 (m) from upstream which affect the channel
as a step with height of 0.02 (m), same width as our channel and length of a 0.25 (m).
Second obstacle has been positioned on 2.785 (m) from upstream which affect our
channel as abrupt contraction which has length of a 0.25 (m) and reduces width of the
channel for 0.065 (m).
Bed sills (step)
Flow constrictions
(contraction)
Calibration of the Manning coefficient :
We made our analyses with manning coefficient 0.01 and 0.02 , But for the manning
coefficient 0.01 our obtained values were more coincide in comparison to the measured
one.
This was also matched with our research about manning coefficient of the material from
which flume is made (glass).

Piozometer
Distance
[m]
Measured
values
[m]
Measured
water depth
[m]
normalized
depth
[m]
normalised
bed-elev
[m]
Q
Measured
[m3/s]
1 0.16 0.559 0.0438 1.2495 1.2057 0.01045
2 0.5 0.583 0.0752 1.2726 1.1974 0.01043
3 1.14 0.54 0.0481 1.2299 1.1818 0.01051
4 1.79 0.51 0.0328 1.1987 1.1660 0.01044
5 2.44 0.492 0.0304 1.1806 1.1502 0.01037
6 3.09 0.479 0.0342 1.1686 1.1344 0.01571
7 3.74 0.459 0.0296 1.1482 1.1185 0.01043
8 4.39 0.442 0.0277 1.1304 1.1027 0.01054
9 5.04 0.424 0.0267 1.1136 1.0869 0.01061
S0(Slope) =
0.024
n(manning coeff)=
0.01 [(m^1/3)/s]
Q-average=
0.0105 [m3/s]
Table for measured profile by piezometric probes (steep)
0.424
d1 V1 A1 O1 Rh1 Sf1 E1 d2 V2 A2 O2 Rh2 Sf2 E2 Sf-av deltaS S
0.049
836
0.699
205
0.014
951
0.399
671
0.037
408
0.003
908
0.074
754
0.049
615
0.702
32
0.014
884
0.399
229
0.037
283
0.003
96
0.074
755
0.003
934
7.24735
E-05
7.25E-
05
0.049
615
0.702
32
0.014
884
0.399
229
0.037
283
0.003
96
0.074
755
0.049
394
0.705
462
0.014
818
0.398
787
0.037
158
0.004
014
0.074
759
0.003
987
0.00021
9723
0.000
292
Example of calculation of water depth by energy equation
.
.
.

Table for computed profile
Distance
[m]
computed
depth[m]
normalised
depth
[m]
Bed-elev
[m]
0 0.05 1.260 1.210
0.16 0.041 1.247 1.206
0.5 0.075 1.272 1.197
0.885 0.087 1.275 1.188
1.135 0.056 1.238 1.182
1.14 0.043 1.225 1.182
1.79 0.035 1.201 1.166
2.44 0.032 1.182 1.150
2.66 0.037 1.182 1.145
2.91 0.034 1.173 1.139
2.96 0.025 1.163 1.138
Equations used for computing d0 (normal
depth) and dc (critical depth):
Q=(1/n)*A*R^(2/3)*sqrt(S0) => d0 ;
(A^(3))/B=(Q^(2))/g => dc ;
d0=0.027 m; dc= 0.05m ; -values obtained for the
whole channel, except for the part the with
contraction
2.96 0.025 1.163 1.138
3.09 0.0254 1.160 1.134
3.74 0.0258 1.144 1.119
4.39 0.0263 1.129 1.103
5.04 0.0267 1.114 1.087
d0=0.031; dc=0.059; -values obtained for the
contraction
Example of Energy curve and profile obtained before bed sill (includes hydraulic jump)
0.02
0.04
0.06
0.08
0.1
0.12
0.07 0.08 0.09 0.1 0.11
Energy curve
0
0.01
0.02
0.03
0.04
0.05
0.06
0 2 4 6 8
Profile S2
0
0.02
0.04
0.06
0.08
0.1
0 0.2 0.4 0.6 0.8 1
Profile S1

1.0500
1.1000
1.1500
1.2000
1.2500
1.3000
0 1 2 3 4 5 6
Depth(m)
Measured and computed profile (steep) Measured
Bed
Computed
d0
dc
0 1 2 3 4 5 6
Length(m)
Discussion :
We started our calculation of profile from upstream dc , and we obtained profile S2, which will be
changed to profile S1 with a hydraulic jump ( water doesn’t have enough energy to pass the step ).
During the step the profile is S2, and after that with a step down we will have again profile S2, until
contraction . From the beginning until the contraction, d0 and dc are constant, with considering the
step of the Sill, but during contraction d0 and dc will be increased, while after that they will be the
same as before. In the contraction water profile would be S2, while after that water depth will be
bellow d0, and it will continue with profile S3.
As we can notice from the graph, the difference between the measured values and the calculated one
is very small in some parts, until in some parts is more obvious. This difference is due to the
insufficient number of piezometer probes and differences between theory and experiments.

LaboratoryProject(mild) 58
Second Profile (mild) :
In this case we inserted Movable sluice gate, which has the same width as channel and
will stand 0.03 (m) above the bed, positioned at 1.75 (m) from upstream.
Donwstream
boundary condition
Movable sluice gate
Calibration of the Manning coefficient :
As we mentioned before we made our analyses with manning coefficient 0.01 and 0.02 , But
for the manning coefficient 0.01 our obtained values were more coincide in comparison to
the measured one.
This was also matched with our research about manning coefficient of the material from
which flume is made (glass).

Piozometer
Distance
[m]
Measured
values
[m]
Measured
water depth
[m]
normalized
depth
[m]
normalised
bed-elev
[m]
Q
Measured
[m3/s]
1 0.16 0.652 0.130420 1.318622 1.188202 0.011981
2 0.5 0.652 0.131121 1.318297 1.187177 0.012043
3 1.14 0.652 0.131516 1.316762 1.185246 0.012015
4 1.79 0.594 0.074693 1.257979 1.183286 0.012007
5 2.44 0.6 0.082069 1.263394 1.181325 0.012666
6 3.09 0.606 0.090647 1.270011 1.179364 0.012184
7 3.74 0.61 0.097247 1.274651 1.177404 0.012055
8 4.39 0.61 0.099531 1.274975 1.175443 0.011919
9 5.04 0.61 0.102859 1.276342 1.173483 0.012384
S0(Slope) =
0.003
n(manning coeff)=
0.01 [(m^1/3)/s]
Q-average=
0.012[m3/s]
Table for measured profile by piezometric probes (mild)
Table for computed profile
Distance
[m]
computed
depth[m]
normalised
depth
[m]
Bed-elev
[m]
0 0.159 1.347685 1.188685
0.75 0.16 1.346423 1.186423
1.75 0.144 1.327406 1.183406
1.78 0.039 1.222316 1.183316
1.9 0.019516 1.20247 1.182954
2.28 0.043 1.224808 1.181808
2.44 0.06171 1.243035 1.181325
3 0.101516 1.281152 1.179636
3.7 0.109 1.286524 1.177524
4 0.107 1.28362 1.17662
5 0.11 1.283603 1.173603
5.1 0.092 1.265302 1.173302
Equations used for computing d0 (normal depth)
and dc (critical depth):
Q=(1/n)*A*R^(2/3)*sqrt(S0) => d0 ;
(A^(3))/B=(Q^(2))/g => dc ;
d0=0.061 m; dc= 0.055m ; -values obtained for the
whole channel, except at the end of the channel
for boundary condition where we have 4 big and 1
small obstacle for downstream boundary
condition which made our d0 =0.092(m) and
dc=0.075 (m) on that point

1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Depth(m)
Lenght [m]
Measured profile and computed profile(mild) Measured
Bed
d0
dc
dc(BC)
d0(BC)
Computed
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Lenght [m]
Discussion :
We started our calculation from the part with the gate. We used value of da=Cc*a (Cc=0.64), which is
downstream the gate, for obtaining db which is upstream of the gate. ( da=0.019; db=0.244). Then from
db with profile M1 we arrived to the upstream depth 0.239. After this we continued from da which is
bellow dc, with profile M3. Then we computed from boundary condition in mild our dc=0.075 and
d0=0.092 for that BC . After that we started from above the d0 in that BC (d=0.094), and with energy
equation we obtained starting point( d=0.11 ) for our profile which goes from downstream to upstream
by M1. Then with comparison M1 from downstream and M3 from upstream which we had obtained
before, we concluded that a hydraulic jump will be occurred.
As we can notice from the graph, the most noticeable difference is near the gate, which is caused by not
having piezometric probe immediately after the gate. Other differences are because of the insufficient
number of piezometer probes and differences between theory and experiments.

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