CIV 420: Hydraulics – Fall 2021
Tuesday & Thursday 1:15 – 2:35 pm
Instructor: Ali Farhadzadeh, Ph.D., P.E.
Email: ali.farhadzadeh@stonybrook.edu
Office Hours: TBD
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Course Description
• This course covers principles of flow in open channels, conservation laws, critical flow,
uniform flow, gradually varied flow, flow through hydraulic structures, pipe flow.
• Analytical and numerical techniques will be discussed
• Limited programming assignments may be carried out using (preferably) MATLAB.
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Course Learning Objectives
• Student will be enabled to understand the fundamental principles governing open channel
hydraulics to the design of engineering systems.
• The course is intended to assist students in developing the skills needed for systematic
decomposition and solution of real-‐world problems.
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Textbook
• Chaundhry, M.H. 2008. Open Channel Flow, 2nd Ed., Springer; ISBN: 9 78-‐0-‐387-‐ 30174-‐7
• Henderson, F. M. 1966. Open Channel Flow, Macmillan Publishing Co., Inc. New York
• Nalluri And Featherstone's Civil Engineering Hydraulics: Essential Theory with Worked
Examples, by Martin Marriott (2016)
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Exams and Grading
Calculators and one side of a sheet of paper including only formulas, equations and graphs
(you must turn in with exam). Exams will consist of two sections:
1) Short answer, true false, multiple choice to see if you get the general concepts
(probably only 20% of exam).
2) Several problems to check if you can apply those concepts.
Grades are based on a standard 90-80-70, etc. scale (So you will always know where you
stand with respect to your grade.).
I do reserve the right to push an individual’s grade upward slightly (never downward) if I
see positive trends of progress over the course.
Please note that participation in in-class activities will have positive impact on your grades.
≥ 95
90-94.99 87-89.99 83-86.99 80-82.99 77-79.99 73-76.99 70-72.99 67-69.99 60-66.99 <60
A
A-
B+
B
B-
C+
C
C-
D+
D
F
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Homework
• Homework will be assigned regularly and is due at the beginning of class on the due date.
Late homework will be accepted for reduced credit, at the discretion of the instructor (e.g.,
10% per day).
• Please use one only side of the paper, although you may use recycled paper.
• You need to explain what you are doing because I cannot guess what you were thinking
when solving the problems.
• If you can’t make class, you should have a friend bring it in for you or let me know
(beforehand) to arrange something.
• Assignments should be submitted via Blackboard.
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Course Policies
a. Environment: Questions and discussion are encouraged. That is how you
learn. Real-life examples are often used.
b. Attendance: Attendance is required. You will do poorly in this class if you do
not attend. Make every effort to attend. If, for whatever reason, you are
unable to attend you must communicate with the instructor in advance. See
Absence Policy in the following for more information on attendance.
c. Classroom Procedures: Please come to class on time. Late arrivals disrupt
the class and are not tolerated.
d. Neatness: Anything you turn in is a reflection of you. Please make sure it is
neat. Sloppy work will be returned ungraded. Forward-thinking students
realize that these course notes and homework should be organized and
retained for future use.
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Course Policies
e. Study Groups: I encourage the use of study groups for homework and exams. I do
not mind if you do homework assignments together as long as each person turns in
their own work and understands what s/he has done regarding the homework
solutions.
f. Interruptions: It is common courtesy to put devices such as cell phones and laptops
away during presentations and discussions as alerts and notifications from devices
can distract you and others.
You need to turn off your cell phones while in the class. Also, use of laptops during
lectures is prohibited (if you write it down, it stays with you longer). Time spent in the
classroom is designed to promote your learning; make the most of that time to grow
and be the professional you aspire to become.
Disruptive students including those texting or browsing on their phones will be asked
to leave class.
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Disability Support Services (DSS) Statement
If you have a physical, psychological, medical or learning disability that may impact
your course work, please contact Disability Support Services, ECC (Educational
Communications Center) Building, room128, (631) 632-6748. They will determine
with you what accommodations, if any, are necessary and appropriate. All
information and documentation are confidential.
Students who require assistance during emergency evacuation are encouraged to
discuss their needs with their professors and Disability Support Services. For
procedures and information go to the following website:
http://www.stonybrook.edu/ehs/fire/disabilities ]
Students with disability will be provided accommodations for their exams as
instructed by DDS.
Academic Integrity Statement
Each student must pursue his or her academic goals honestly and be personally accountable
for all submitted work. Representing another person's work as your own is always wrong.
Faculty are required to report any suspected instances of academic dishonesty to the
Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology &
Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are
required to follow their school-specific procedures. For more comprehensive information on
academic integrity, including categories of academic dishonesty, please refer to the
academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/
Critical Incident Management
Stony Brook University expects students to respect the rights, privileges, and property of
other people. Faculty are required to report to the Office of Judicial Affairs any disruptive
behavior that interrupts their ability to teach, compromises the safety of the learning
environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School
of Medicine are required to follow their school-specific procedures.
Course Outline
The instructor reserves the right to modify this syllabus as circumstances warrant.
SESSION
1–2
3–4
5–8
9 – 11
12
13
14 – 17
18 – 20
21 – 22
23
24 – 26
According to University Calendar
TOPIC
Course introduction. Basic concepts
Course introduction. Basic concepts
Conservation laws, specific energy
Critical flow
Critical flow
Mid-term
Uniform flow
Gradually varied flow
Computation of Gradually varied flow
Channel Design
Pipe Flow
Final
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Chapter 2: BASIC CONCEPTS
Introduction
Liquids are transported from one location to another using natural or constructed
conveyance structures.
Cross-section of these structures may be open or closed at the top.
Structures with closed tops are referred to as closed conduits.
Those with the top open are called open channels.
Example: Tunnels and pipes are closed conduits
Rivers, streams, estuaries are open channels.
Flow in open channel or in a closed conduit having a free surface is referred to as freesurface flow or open-channel flow (Discussed in this course).
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Definitions
The terms open-channel flow or free-surface flow are the same.
The free surface is usually subjected to atmospheric pressure.
If there is no free surface and the conduit is flowing full, then the flow is called pipe flow, or
pressurized flow.
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• In a closed conduit, it is possible to have both free-surface flow and pressurized flow at
different times.
• It is also possible to have these flows at a given time in different reaches of a conduit.
• For example, the flow in a storm sewer may be free-surface flow at a certain time. Then, due
to large inflows produced by a sudden storm, the sewer may flow full and pressurize it.
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Classification of Flows
Free-surface flows may be classified into various types.
Flow
Unsteady
Uniform
Steady
Varied
Gradually
Uniform
Rapidly
Varied
Gradually
Rapidly
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Steady and Unsteady Flows
If the flow velocity at a given point does not change with respect to time, then the flow is
called steady flow.
If the velocity at a given location changes with respect to time, then the flow is called
unsteady flow.
This classification is based on the time variation of velocity v at a specified location. Thus,
the local acceleration: ∂v/∂t= 0.
In two- or three-dimensional steady flows, the time variation of all components of
velocity is zero.
It is possible in some situations to transform unsteady flow into steady flow by having
coordinates with respect to a moving reference.
This simplification is helpful in the visualization of flow and in the derivation of governing
equations.
Such a transformation is possible only if the wave shape does not change as the wave
propagates.
If the wave shape changes as it propagates, then it is not possible to transform such a
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wave motion into steady flow.
Uniform and Non-uniform flows
If flow velocity at a given instant of time does not vary within a given length of channel, then
the flow is called uniform flow.
If flow velocity at a time varies with respect to distance, then the flow is called non-uniform
flow, or varied flow.
This classification is based on the variation of flow velocity with respect to space at a specified
instant of time. Thus, the convective acceleration in uniform flow is zero.
In mathematical terms, the partial derivatives of the velocity components with respect to x, y,
and z direction are all zero.
A flow is considered uniform as long as the velocity in the direction of flow remains the same
spatially.
Depending upon the rate of variation with respect to distance, flows may be classified as
gradually varied flow or rapidly varied flow.
Flow is called gradually varied if the flow depth varies at a slow rate with respect to distance.
Flow is called rapidly varied flow if the flow depth varies significantly in a short distance.
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Note: the steady and unsteady flows are characterized by the variation with respect to time
at a given location, whereas uniform or varied flows are characterized by the variation at a
given instant of time with respect to distance.
Thus, in a steady, uniform flow, the total derivative dv/dt = 0.
In one-dimensional flow, this means that ∂v/∂t = 0, and ∂v/∂x = 0.
In two- and three-dimensional flow, the partial derivatives of the velocity components in the
other two coordinate directions with respect to time and space are also zero.
Total derivative
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Laminar and Turbulent Flows
Flow is called laminar flow if the liquid particles appear to move in definite smooth paths and
the flow appears to be as a movement of thin layers on top of each other.
In turbulent flow, the liquid particles move in irregular paths which are not fixed with respect
to either time or space.
The relative magnitude of viscous and inertial forces determines whether the flow is laminar
or turbulent:
The flow is laminar if the viscous forces dominate, and the flow is turbulent if the inertial
forces dominate.
The ratio of inertial force to viscous force is defined as the Reynolds number,
Re = Reynolds number; V = mean flow velocity; L = a
characteristic
length; and ν = kinematic viscosity of the liquid.
The transition from laminar to turbulent flow in free surface flows occurs for Re of about 600,
in which Re is based on the hydraulic radius as the characteristic length.
In real-life applications, laminar free-surface flows are extremely rare.
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Pipe flow: Pipe diameter is used for the characteristic length.
Free surface flows: Either hydraulic depth or hydraulic radius used as the characteristic length.
Hydraulic depth: Flow area divided by the top water-surface width.
Hydraulic radius: Flow area divided by the wetted perimeter.
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Subcritical, Supercritical, and Critical Flows
A flow is called 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.
The flow is called subcritical flow, if the flow velocity is less than the critical velocity, and the
flow is called supercritical flow if the flow velocity is greater than the critical velocity.
The Froude number, Fr, is equal to the ratio of inertial and gravitational forces and, for a
rectangular channel, it is defined as
in which y = flow depth. Depending upon the value of Fr, flow is classified as subcritical if Fr < 1;
critical if Fr = 1; and supercritical if Fr > 1.
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http://www.globalspec.com/reference/24097/203279/4-3-significance-of-froude-number-in-gradually-varied-flow-calculations
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Terminology
Channels may be natural or artificial.
Various names have been used for the artificial channels:
A long channel having mild slope usually excavated in the ground is called a canal.
A channel supported above ground and built of wood, metal, or concrete is called a flume.
A chute is a channel having very steep bottom slope and almost vertical sides.
A tunnel is a channel excavated through a hill or a mountain.
A short channel flowing partly full is referred to as a culvert.
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Panama Canal
https://priceonomics.com/how-the-panama-canal-got-itsgroove-back/
Alqueva dam chute spillway, in Portugal
https://www.123rf.com/photo_7497699
_one-of-alqueva-dam-chute-spillway-inportugal-it-is-designed-to-create-anhydraulic-jump-protecting-.html
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Wood box flume, after nearly 100 years of service, passing over
the emptied Little Sandy riverbed. Rail tracks are mounted on the
top of the flume for a maintenance trolley (note the dog at the
footings for scale).
Bull Run Hydroelectric Project
https://en.wikipedia.org/wiki/Bull_Run_Hydroelectric_Project
Flume in Sweden
https://en.wikipedia.org/wiki/Flume#/media/File:H%C3%A4vla_bruk_s%C3%A5gverket.jpg
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Hoover Dam Tunnel
http://digital.library.unlv.edu/objects/lv_water/220
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Culvert
http://www.ecy.wa.gov/programs/wr/dams/pp_BoxCulvertOutlet.html
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Panama Canal
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• A channel having the same cross section and bottom slope throughout is referred to as a prismatic
channel, whereas a channel with varying cross section and/or bottom slope is called a non-prismatic
channel.
• A cross section taken normal to the direction of flow is called a channel section.
• The depth of flow, y, at a section is the vertical distance of the lowest point of the channel section from
the free surface.
• The depth of flow section, d, is the depth of flow normal to the direction of flow.
• The stage, Z, is the elevation or vertical distance of free surface above a specified datum .
• The top width, B, is the width of channel section at the free surface. The flow area, A, is the crosssectional area of flow normal to the direction of flow.
• The wetted perimeter, P is defined as the length of line of intersection of channel wetted surface with a
cross-sectional plane normal to the flow direction.
The hydraulic radius, R, and hydraulic depth, D, are defined as
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Velocity Distribution
The flow velocity in a channel section varies from one point to another.
Why? because of shear stress at the bottom and at the sides of the channel and due to the
presence of free surface.
Only the flow velocity in the direction of flow needs to be considered because the other velocity
components are small.
The main velocity component varies with depth from the free surface.
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Energy Coefficient
Flow velocity in a channel section usually varies from one point to another.
Mean velocity head in a channel section, (V 2/2g)m is not the same as the velocity head, V 2m/(2g),
computed by using the mean flow velocity, Vm
This difference can be reflected in energy coefficient, α, which is also referred to as the velocity
head, or Coriolis coefficient.
The mass of liquid flowing through area ΔA per unit time (mass flux) = ρV ΔA
ρ = mass density of the liquid.
The kinetic energy of mass m traveling at velocity V is (1/2)mV 2,
Kinetic energy transfer through area ΔA per unit time
Kinetic energy transfer through area A per unit time
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Kinetic energy transfer through area ΔA per unit time
= (γV ΔA)V2/(2g)
= Weight of liquid passing through area ΔA per unit time × velocity head,
γ = specific weight of the liquid.
∫
Weight of liquid passing through total area per unit time =γVm dA
Vm : mean flow velocity for the channel section
The velocity head for the channel section =αVm2 /(2g)
α = velocity head coefficient.
Kinetic energy transfer through area per unit time
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Figure above shows a typical cross section of a natural river comprising of the main river channel and the
flood plain on each side of the main channel.
Flow velocity in the floodplain is usually very low as compared to that in the main section.
Variation of flow velocity in each subsection is small. Therefore, each subsection may be assumed to have the
same flow velocity throughout.
In such a case, the integration of various terms of
may be replaced by summation:
where:
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For a general case in which total area A may be subdivided into N such subareas each having uniform
velocity
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Momentum Coefficient
Similar to the energy coefficient, a coefficient for the momentum transfer through a channel section
may account for nonuniform velocity distribution.
This coefficient, is also called Boussinesq coefficient.
The mass of liquid passing through area ΔA per unit time = ρV ΔA.
Thus, the momentum passing through area ΔA per unit time = (ρV ΔA)V = ρV2ΔA.
By integrating this expression over the total area, we get:
Momentum transfer through area A per unit time
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By introducing the momentum coefficient, β, we may write the momentum transfer through area A in
terms of the mean flow velocity, Vm, for the channel section:
Momentum transfer through area A per unit time
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Theoretical values for α and β can be derived from the power law and the logarithmic law for
velocity distribution in wide channels.
Theoretical values of α and β using the power law distribution for typical channel sections
For turbulent flow in a straight channel having a rectangular, trapezoidal, or circular cross section, α is
usually less than 1.15. Hence, it may not be included in the computations since its value is not precisely known
and it is nearly equal to unity.
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Example
The velocity distribution in a channel section may be approximated by the equation, V = Vo(y/yo)n,
in which V is the flow velocity at depth y; Vo is the flow velocity at depth yo, and n = a constant.
Derive expressions for the energy and momentum coefficients.
Consider a unit width of the channel. Then, we can replace area A in the equations for the energy
and momentum coefficients by the flow depth y.
By substituting the expression for V into this equation
v0
y0
y
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Energy Coefficient
By substituting V = Vo(y/yo)n , Vm = Vo/(n+1), and dA = dy into 
we obtain:
Momentum Coefficient
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Pressure Distribution
The pressure distribution in a channel section depends upon the flow conditions.
1. Static Conditions
The pressure is directly proportional to the depth below the free surface.
Since ρ is constant for typical engineering applications, the relationship between the pressure
intensity and depth plots as a straight line, and the liquid rises to the level of the free surface
in a piezometer.
The linear relationship, based on the assumption that ρ is constant, is usually valid except at
very large depths, where large pressures result in increased density.
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2. Horizontal, Parallel Flow
Liquid flowing in a horizontal, frictionless channel.
Assumptions: no acceleration in the direction of flow, flow velocity is parallel to the channel bottom, flow is
uniform.
Since there is no acceleration in the direction of flow, the component of the resultant force in this direction is
zero.
Which is the same as if the liquid were stationary; it is, therefore, referred to as the hydrostatic pressure distribution.
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3. Parallel Flow in Sloping Channels
Assumptions: no acceleration in the flow direction, the flow velocity is uniform at a channel cross section and is
parallel to the channel bottom.
ΔA = cross-sectional area of the column
θ = slope of the channel bottom
W= weight of column acting along the column = ρgdΔAcosθ
the force acting at the bottom of the column = pΔA
pΔA = ρgdΔAcos θ, or
p = ρgd cos θ = γd cos θ
with d = y cos θ, we get:
where:
y = flow depth measured vertically
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Note:
If the slope of the channel bottom is small, then cos θ ≈ 1 and d ≈ y.
Hence:
Hydrostatic pressure
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4. Curvilinear Flow
Streamlines have pronounced curvature.
Forces acting in the vertical direction on a column of liquid with cross-sectional
area ΔA is:
r = radius of curvature of the streamline
V = Flow velocity at the point under consideration
Divide centrifugal force by the area of the column ΔA.
Converting the pressure to pressure head (divide pressure by ρg).
Then, pressure head, ya acting due to centrifugal acceleration:
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Concave curvature: pressure due to centrifugal force is in the same direction as the weight of column
Convex curvature: pressure due to centrifugal force is in a direction opposite to the weight of column
Total pressure head acting at the bottom of the column is:
Pressure due to centrifugal action + Weight of the liquid column
or
Positive sign is for concave, and a negative sign is for convex stream flows.
Pressure increases due to centrifugal action in concave flows and decreases in convex flows.
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