WRE 404 Lab - Lec1 to Lec6

WRE 404: Computer Applications in WRE

Dr. Md. Mostafa Ali, Associate. Prof., WRE Dept, BUET, Dhaka


Department of Water Resources Engineering

BUET, Dhaka-1000




Course Credit Hour: 1.5

Course Teacher:

1) Dr. Md. Mostafa Ali, Associate Professor, Dept. of WRE, BUET; Room: 748 (CE);

email: [email protected] ; mobile: 01682308323; and

2) Mr. Sarfaraz Alam, Lecturer, Dept. of WRE, BUET

Marks distribution:

1) Attendance: 10%

2) Assignments and Daily performance: 30%

3) Midterm quiz: 20%

4) Final quiz: 20%

5) Term project: 20%

Reference Books:

1) HEC-RAS Users Manual (2010)

2) HEC-RAS: Hydraulic Reference Manual (2010)

3) HEC-RAS: Applications Guide (2010)

Lecture distribution:

1) Lab # 1: Introduction to Modeling and HEC-RAS: Modeling uniform flow

2) Lab # 2: Steady Flow Modeling: Modeling three slopes

3) Lab # 3: Steady Flow Modeling: Modeling sinusoidal bed

4) Lab # 4: Steady Flow Modeling: Modeling Broad crested weir

5) Lab # 5: Steady Flow Modeling: Modeling Venturi Flume

6) Lab # 6: Steady Flow Modeling: Modeling Natural River with Junction

7) Midterm Quiz Lab # 1 to 6

8) Lab # 7: Steady Flow Modeling: Modeling Afflux due to Bridges

9) Lab # 8: Steady Flow Modeling: Modeling Local scour due to Bridges

10) Lab # 9: Unsteady Flow Modeling: Flood routing with a dam/sluice gate

11) Lab # 10: Water quality Modeling: Modeling Triangular Distribution

12) Lab # 11: Morphological Modeling: Modeling knick point migration

13) Lab # 12: 2D Flow Modeling with River2D: Modeling Groin

14) Final Quiz Lab # 7 to 12 /Term Paper Submission

Course Ethics:

1) Copying Assignments from someone else will be considered as a copying in an

exam and will be handled as per university ordinance.



Lab # 1: Introduction to Mathematical Modeling and HEC-RAS: Modeling Uniform Flow Depth

Mathematical Modeling:

A model is a simplified representation of a complex process or phenomenon. Since

studying the real world processes could be extremely time consuming, expensive and

even dangerous, models are constructed to study pertinent system responses. Models

are broadly classified into two major groups: scale models and mathematical models. In

a scale model, the actual system is reproduced in a reduced scale with the same

essential features to be studied. The scaled down model of a dam spillway is an

example of a physical model.

When a model uses quantitative or mathematical expressions to describe the system

behavior, it is called a mathematical model. A mathematical model always contains

three important components: variables, governing equations and parameters. A variable

is an entity which has no fixed value. It may change with both time and space, and may

be dependent or independent. A governing equation (also called the state equation) is a

mathematical description of the physical process being modeled. This equation is

formulated on the basis of conceptualization of the physical process based on actual

observation and existing proposed theories. A parameter, which usually appears in the

governing equation, is a constant. However, it may assume different values if the

circumstances change.

In water resources engineering, the governing or state equation of a system may be

empirical or hydrodynamic. Empirical equations are usually based on field observations,

experiments, and statistical analysis of the relationship between inputs and outputs.

Hydrodynamic equations are derived from the conservation laws of physics such as the

conservation of mass, momentum, and energy. Typically hydrologic models (e.g., a

rainfall-runoff model) have empirical state equations and hydraulic models (e.g., a flood

routing model) have hydrodynamic state equations. Some model known as composite

or hybrid models may have both the empirical and hydrodynamic elements.

Governing equations of Open Channel Flow:

The flow in an open channel or in a closed conduit with a free surface is referred to as

free-surface or open channel flow. Some examples of open channel flow are the flow in



natural streams and rivers, and the flow in man-made channels, including irrigation and

navigation canals, drainage pipes, culverts, and spillways. The study of the flow

behavior in open channels is known as open channel hydraulics and this knowledge is

essential in many water resources problems. For example, flood forecasting, hydraulic

structures designing, morphological modeling, fish habitat modeling, ice process

modeling, and contaminant transport modeling all require knowledge of the velocity and

depth of an open channel flow. The numerical solution of an open channel flow problem

is known as Computational Hydraulics and has become an important subfield of Open

Channel Hydraulics.

Saint-Venant equations: The Saint-Venant equations provide the fundamental

mathematical description governing the depth and average velocity in one-dimensional

(1D) and two-dimensional (2D) open channel flows. The Saint-Venant equations for

unsteady flow in an 1D open channel flow are given by

Continuity equation:

and

Momentum equation:

Where x and t are the special and time variables, A= cross-sectional area, Q=

discharge, u = cross-sectional average velocity, g = gravitational acceleration, S0 = bed

slope, and Sf= friction slope.

For a steady state case:

and

, therefore:

and

;

This equation is also known as gradually varied flow equation



Numerical solution of steady state gradually varied flow equation:

Using a simple forward finite difference formula, the above equation can be

discretized as follows

Figure 1: A general descritization of a channel

Introduction to HEC-RAS:

HEC-RAS is an acronym for Hydrologic Engineering Centers River Analysis

System. HEC-RAS, developed by US Army Corps of Engineers (USACE), is an

integrated system of software, designed for interactive use in a multi-tasking

environment. The system is comprised of a graphical user interface (GUI), separate

analysis components, data storage and management capabilities, graphics and

reporting facilities (HEC-RAS, 2010).

Capabilities of HEC-RAS:

The HEC-RAS System contains four one-dimensional river analysis components (HEC-

RAS, 2010):

1. Steady flow water surface profile computations

j J+1



2. Unsteady flow simulation

3. Movable boundary sediment transport computations

4. Water quality analysis.

A key element is that all four components use a common geometric data representation

and common geometric and hydraulic computation routines. In addition to the above

four river analysis components, the system contains several hydraulic design features,

such as channel modification, flood inundation mapping, hydraulic design functions etc

(HEC-RAS, 2010).

Tools and Components of HEC-RAS:

The HEC-RAS has the following different tools and components (HEC-RAS, 2010):

Pre-processing tool:

o Geometry editor

o Flow data editor

o Sediment data editor

o Water quality data editor

River Analysis Components:

o Steady Flow Module

o Unsteady Flow Module

o Sediment Analysis Module

o Water Quality Analysis Module

o Hydraulic design module

Post-Processing tool:

o Cross-section viewer

o longitudinal profile viewer

o General variable profile viewer

o 3D plot viewer

o Stage and flow hydrograph viewer

o Table viewer

General steps to build a model in HEC-RAS:

Creating a schematic of a river

Assigning all the geometric variables and parameters

Assigning all the initial conditions and boundary conditions

Performing an analysis

Viewing the results



Objectives of This Lab:

In this lab, our objective is to understand the basic concepts of mathematical modeling

and to be familiar with different components of HEC-RAS. In this lab we will model

uniform depth for a given flow and slope and we will compare it with a uniform flow

formula, such as Manning's uniform flow equation. Manning's uniform flow equation is

given as follows:

(1)

Where Q = Discharge (m3/s), A= Area (m2), R= Hydraulic radius (m), Sf = Frictional

Slope and n = Manning's roughness parameter (s/m1/3).

Specific Tasks:

1. Create a new project

2. Draw a schematic of a hypothetical channel

3. Assign cross-section data

4. Assign boundary data

5. Perform a steady flow analysis

6. View the results

Following information will be needed for this project.

The channel is rectangular

The channel length is 1000 m.

The channel width is 100 m.

Manning's n can be assumed as 0.025 s/m1/3.

The discharge in the channel is 200 m3/s.

The channel slope is (Last two digits of your student number + 50)/10,000.

Downstream depth is = normal depth.

Submissions:

1. Calculate uniform depth for your case using Manning's equation and compare it

with your model result.

2. Take a print of longitudinal profile of water surface for your model result.

3. Take a print of longitudinal profile of Froude number for your model result.

4. Derive 1D Saint-Venant equations and write down its assumptions.

5. What would be a reasonable value of Manning's n for flood plains with dense

grasses.

6. What will happen if downstream depth is higher than the normal depth? Explain.

7. Discussions.



Lab # 2: Steady Flow Modeling: Modeling Backwater and Drawdown Curves using Three Slopes

Introduction:

Open channel flow is characterised by two major non-dimensional numbers. The first

one is the Reynolds number (Re). The Reynolds number is defined by the ratio of

viscous and inertial force (Chaudhry, 1994). If the viscous forces dominate the flow

is laminar and if the inertial forces dominate, the flow is turbulent. The transition from

laminar to turbulent in the open channel flows occur for Re of about 600.

Mathematically, Reynolds number is calculated as

Where U=mean velocity, R = hydraulic radius, and = kinematic viscosity of water.

The second non-dimensional number is the Froude number (Fr). The Froude number

is defined as the ratio of inertial force and gravitational forces. A flow is said to be

critical if the flow velocity is equal to the velocity of a gravity wave having small

amplitude. A gravity wave may be produced by a change in the flow depth. If the

flow velocity is less the critical velocity, then the flow is called subcritical flow. If the

flow velocity is greater than the critical velocity, then the flow is called supercritical

flow. Therefore, if Fr < 1, flow is subcritical and if Fr > 1, flow is supercritical.

Mathematically, Froude number is calculated as

Where g = gravitational acceleration and h = mean depth.

In natural river flow is normally turbulent and subcritical. Supercritical flow occurs if

the slope is steep and if flow past a hydraulic structure. Flow in natural river is also

non-uniform and unsteady. However, if flow changes slowly, for simplicity flow can

be assumed as steady and uniform flow. Uniform flow depth can be calculated using

any uniform flow formula as we did in Lab # 1. Non-uniform flow is occurred due to

changes in bed elevation or width. Moreover, presence of any hydraulic structure

also generates non-uniform flow. If the rates of changes are not rapid, the flow is

considered as Gradually Varied Flow.



Gradually Varied flow is described mathematically by the following ordinary

differential equation:

Where S0 = bed slope, Sf = frictional slope, Fr = Froude number.

The above ordinary differential equation can be derived from the 1D Saint-Venant

equation (assignment # 4). A numerical method is needed to solve this equation.

The equation describes the depth profile due to the differences in S0 and Sf, which

produces different water surface profiles. For example, if Sf < S0, a positive gradient

will occur and that will produce a backwater curve which is also known as M1 curve.

Again, if Sf > S0, a negative gradient will occur and that will produce a drawdown

curve which is also known as M2 curve. Similarly, due to different transition of slopes

(e.g., mild to steep, steep to mild, steep to steeper, mild to horizontal etc.) different

water surface profiles are generated in open channel flow. For other water surface

profiles, please see your open channel flow text book.

Objective of this lab:

In this lab, our main objectives are to understand the fundamentals of gradually

varied flow and to be familiar with different components of HEC-RAS. Therefore, in

this lab we will simulate two water surface profiles (backwater and drawdown) for a

subcritical flow by using two transitions of slope. This problem is also known as a

three-slope problem. A Typical profile for a three-slope problem is shown in figure 1.

0 2000 4000 6000 8000 10000

97.5

98.0

98.5

99.0

99.5

100.0

100.5

101.0

ThreeSlope_Subcritical Plan: Plan 01 28/01/2015

Main Channel Distance (ft)

Ele

vation

(ft)

Legend

WS PF 1

Ground

ThreeSlope Test1



Figure 1: A Typical water surface profile for a three-slope test case

Specific Objectives:

1. Create a new project.

2. Draw a schematic of a straight river.

3. Assign cross section data.

4. Assign boundary condition data.

5. Perform the analysis

6. View and present the results.

Following information are needed for this lab:

The channel is rectangular.





The channel slope for the first and last third parts of the channel is = (Last two

digits of your student number + 50)/10,000.

The channel slope for the middle part is = twice the slope of the first or last

part of the channel.

Downstream boundary condition is = (normal depth+0.3) m

Submissions:

1. Calculation of your downstream boundary condition.

2. Printing of longitudinal profile of water surface elevation.

3. Printing of longitudinal profile of velocity magnitude.

4. Derivation of Gradually Varied Flow equation from 1D Saint-Venant equation.

5. Do you expect to see a hydraulic jump for this simulation? Justify your

answer.

6. What is the Reynolds number in your case? State whether the flow is laminar

or turbulent.

7. Discussions.



Lab # 3: Steady Flow Modeling: Modeling Water Surface Profile with a Sinusoidal Bed

Introduction:

Because of continuous sediment movement in river beds, bed levels are changed

and formed into different shapes depending on the flow states. These are known as

bed forms. Typical bed forms are: a) Ripples b) Dunes c) Plane bed d) Anti dunes

and e) Chutes and Pools. These bed forms are shown in figure 1.

Ripples (figure 1a) are the bed forms of having small amplitudes and wavelengths.

They are nearly sinusoidal and have gentle upstream slope with a relatively higher

downstream slope. Dunes (figure 1c) are larger than ripples but smaller than bar or

island. Water surface profile is out of phase with the bed level profile. Both ripples

and dunes are developed during low flow regime, i.e, subcritical flow.

Figure 1: Different bed forms in alluvial channels (after Simons et al., 1966)



As the flow moves towards higher flow regime, bed forms are washed out and

formed plane bed (figure 1e). As flow increases and sediment transport continues,

antidune bed forms are formed. For this bed form, water surface profile is in phase

with bed elevation profile (figure 1f). For rivers with steep slope, such as mountain

rivers, alternate deep pool and steep chutes are observed (figure 1h).

Presence of bed forms effect the flow resistance, i.e., roughness. Moreover, water

surface profile is also affected by the types of bed forms. For example, in subcritical

flow regime, water surface elevation becomes out of phase with bed elevation

profile. If flow becomes supercritical, hydraulic jump is formed. These phenomenons

can be simulated with the Gradually Varied Flow equation as described in the Lab #

2.


In this lab, our main objectives are to understand the effects of bed forms on flow

and to be familiar with different components of HEC-RAS. Therefore, in this lab we

will simulate water surface profiles due to a sinusoidal bed for a subcritical flow.


1. Generate a sinusoidal bed profile using the given information.











Use 50 m interval



Bed profile = Amplitude*Cos(PI*distance/625)

Amplitude is = (Last two digits of your student number + 50)/100.

Downstream boundary condition is = (Amplitude+0.3) m



Submissions:

1. Calculation of your longitudinal bed profile.

2. Calculation of your downstream boundary condition.


4. Printing of longitudinal profile of Froude number.

5. Does your water surface elevation is out of phase with bed elevation profile?

Justify your answer.

6. What is a bar/island? How does a bar/island different than other bed forms?

7. Discussions.



Lab # 4: Steady Flow Modeling: Modeling Water Surface Profile with a Broad Crested Weir

Introduction:

Broad crested weir, a hydraulic structure, is widely used in open channel flow as a

discharge measuring structure. Flow is obstructed by the structure and a critical

depth is attained on the structure. Based on the upstream depth above the crest

level, flow over a broad crested weir can be calculated based on the following

formula:

(1)

Where Q = discharge, B = channel width, g = gravitational acceleration, and H =

upstream flow depth above the crest.

Depending on the downstream depth, a hydraulic jump may form at a downstream

section of the channel. A typical water surface profile for a broad crested weir is

shown in figure 1. When both subcritical and supercritical flows occur in a channel,

the flow is known as a mixed flow or transcritical flow.

Figure 1: A typical water surface profile for flow over a broad crested weir

0 2 4 6 8 10 120.0

0.1

0.2

0.3

0.4

0.5

broad crested wier Plan: Plan 01 28/01/2015

Main Channel Distance (m)

Ele

vation

(m

)

Legend

WS PF 1

Ground

x c



To simulate a mixed flow is a challenging task in the Computational Hydraulics.

Many popular numerical schemes cannot handle sharp discontinuity during the

simulation. Special techniques or measures are needed to capture shock or jump in

a numerical simulation. HEC-RAS uses popular Box Finite Difference Scheme which

alone cannot handle mixed flow. Special codes are employed to handle hydraulic

jumps. Therefore, if there is any possibility to form any jump, mixed flow module

should be turned on. Otherwise model will give erroneous result or model will face

stability problem.


In this lab, our main objectives are to understand the effect of transcritical flow and

to be familiar with different components of HEC-RAS. Therefore, in this lab we will

simulate water surface profile with a broad crested weir.


8. Generate a broad crested bed profile in excel using the given information.











Use 0.1 m interval


The discharge in the channel is 0.2 m3/s.

Hump height = (Last two digits of your student number + 10)/100

Downstream boundary condition is = (Hump height +0.05) m

Upstream boundary condition is = (Hump height +0.05) m



Submissions:

8. Calculate upstream depth using the equation 1 and compare it with your

model result.

9. Calculate the analytical critical depth for your case and compare it with your

model result.



12. What will happen if downstream depth is increased? Explain with model

simulation results.

13. Discussions.



Lab # 5: Steady Flow Modeling: Modeling Water Surface Profile with a Venturi Flume

Introduction:

Venturi flume, a hydraulic structure, is also commonly used in open channel flow as a

discharge measuring structure. In Venturi flume width of the channel is reduced

gradually and then width is increased gradually again. A typical plan view of a Venturi

flume is shown in figure 1. Flow is obstructed by the reduced width and critical depth is

attained on the minimum width section. Based on the upstream depth, flow over a

Venturi flume can be calculated based on the following formula:

(1)

Where Q = discharge, B = Width of the flume at throat section, g = gravitational

acceleration, and H = upstream flow depth above the crest.

Depending on the downstream depth, a hydraulic jump may form downstream of the

Venturi flume. A typical water surface profile for a Venturi flume is shown in figure 2.

Like Broad crested weir flow case, transcritical or mixed flow also occurs for Venturi

flume flow case. To simulate mixed flow case, one must use mixed flow module in HEC-

RAS.

Figure 1: A typical plan view of cross sections for flow through a venture flume



Figure 2: A typical water surface profile for flow through a venture flume


In this lab, our main objectives are to understand the effect of transcritical flow and

to be familiar with different components of HEC-RAS. Therefore, in this lab we will

simulate water surface profile with a Venturi Flume.


15. Generate a Venturi flume cross section profile in excel using the given

information.









The channel width is 1 m except in the flume.

The channel width is 0.5 in the constricted zone.


Use 0.1 m interval


0 2 4 6 8 10 120.0

0.1

0.2

0.3

0.4

venturi flume Plan: Plan 01 28/01/2015

Main Channel Distance (m)

Ele

vation

(m

)

Legend

WS PF 1

Ground

x c



The discharge in the channel is 0.2 m3/s.

Downstream boundary condition is = 0.3 m

Upstream boundary condition is = 0.4 m

Submissions:

14. Calculate upstream depth using the equation 1 and compare it with your

model result.

15. Calculate the analytical critical depth for your case and compare it with your

model result.



18. What is a shock capturing scheme? Give examples of three shock capturing

schemes.

19. Why do we need shock capturing scheme to model Transcritical flow?

Explain.

20. Discussions.



Lab # 6: Steady Flow Modeling: Modeling Water Surface Profiles for Natural Rivers with a Junction

Introduction:

In previous five labs, five hypothetical test cases (i.e., constant slope, three-slope,

sinusoidal bed, broad crested weir and venture flume) have been modeled. By modeling

hypothetical test cases, basics of steady flow modeling using Gradually Varied Flow

equation have been described. Moreover, Different components of HEC-RAS also have

been covered. We will use these understandings now for Natural Rivers.

Natural rivers have variations in bed elevation as well as in cross-sections. These

variations produce variations in water surface elevation and depending on the

magnitudes of variation a jump or vertical fall may form. In addition, natural rivers have

tributaries, branches, confluences and bifurcations which produce a network of rivers

with one or more junctions. A typical river network has been shown in figure 1.

A confluence is a junction where two or more rivers are met at one point, and a

bifurcation point is a junction where one river is divided into two or more rivers. To

simulate a junction, one needs two extra boundary conditions. The first condition comes

from the continuity equation. For a confluence, the continuity equation becomes:

Q1+Q2=Q3 where Q1 and Q2 are the discharges of two upstream rivers meeting at a

junction and Q3 is the total downstream discharge. For a bifurcation junction, the

continuity equation becomes: Q1=Q2+Q3 where Q1 is the upstream discharge and Q2

and Q3 are the discharges of two bifurcated rivers. Distribution of Q2 and Q3 depends on

the conveyance of those bifurcated rivers. The second condition at a junction comes

from the momentum or energy condition. This states that energy levels or water surface

elevations for all rivers meeting at a junction should be equal. Therefore,

mathematically, WSE1= WSE2 =WSE3.

In previous labs, model results are verified and compared with the analytical uniform or

critical depths. Verification of a model result is an important part of mathematical

modeling. Without verification, any model result is ineffectual. Similar to the modeling of

hypothetical test cases, simulation with natural rivers must need to be verified. In natural

rivers, this verification is done with the observed or measured data at one/more

locations those are located within the model boundaries.



Verification of model results is done in two parts: Calibration and Validation. Calibration

means tuning of model parameters with one set of data and Validation means further

verification of calibrated model results using another set of data. In both processes,

comparisons are done using visual inspection normally. Beside visual inspection,

different statistical parameters, such as correlation parameter, NSE () etc. can be

calculated.

Figure 1: A plan view of a river network


In this lab, our main objectives are to understand the hydraulics of natural river and

to understand the calibration and validation processes in mathematical modeling.

Therefore, in this lab we will simulate water surface profiles with a natural river

network.

Tributary

0.2

0.1

0.0

Butt e

Cr

.

Upper Reach

10

9.9

9.8

Fa

ll R

i v er

Lower Reach

9.79

9.7

9.6

9.5

Fa

ll R

i v

e r

Sutter





23. Draw a schematic of a river network using the given data.





28. Calibrate and Validate the model.


The channel is irregular. Cross section data will be given in an excel file

The channel length data will be given in an excel file.

Manning's n needs to be adjusted.

The discharge data will be given in the class.

Boundary condition will be given in the class.

Submissions:

21. Adjust Mannings n to calibrate the model results with the observed data.


23. What is calibration and validation? Why these two processes are important in

mathematical modeling?

24. What is a junction? How a junction is handled in HEC-RAS?

25. Discussions.

Documents

WRE 404 Lab - Lec1 to Lec6