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ADDIS COLLEGE
CIVIL ENGINEERING DEPARTMENT
Lecture Notes
Open Channel Hydraulics
Instructor: Behailu N.
Contents
Open Channel Flow and Its
Classifications
Basic Principles Of Hydraulics
Flow Computation Formula
Gradually Varied Flow (GVF)
Rapidly Varied Flow(RVF)
Unsteady Flow In Open Channels
Sediment Transport in an Open
Channel
Course Objectives
The aim of the course is to present a review of the main principles of
hydraulics and to apply them to Civil, Hydraulic, and Irrigation
Engineering problems.
After the completion of the course, the student should understand
and should
be able to apply the principles of hydraulics in
engineering problems,
be capable to make uniform and non-uniform flow and
steady and unsteady flow computations.
Lecture 1
Types of Flow in Open Channel
Uniform Flow in Open Channel
Channel of Efficient Cross-section
CHAPTER 1
1.1. INTRODUCTION TO OPEN CHANNEL FLOW
Open channel open-channel flow is the flow of a liquid in a conduit
with a free surface. There are many practical examples, both artificial
(flumes, pipe lines (not completely full), spillways, sewers, canals,
weirs, drainage ditches, and culverts) and natural (streams, rivers,
estuaries, floodplains).
Structures like, culverts, and spillways are designed as an open
channel
It is a flow in a channel in which the stream is not completely
enclosed by solid boundaries
It has a free surface subjected to atmospheric pressure ( the
pressure distribution is equal to the Patm)..
5
Free Surface: which is essentially at atmospheric pressure, both helps
and hurts the analysis.
It helps because the pressure can be taken constantly along the
free surface, which therefore is equivalent to the hydraulic grade
line (HGL) of the flow.
Unlike flow in closed ducts, the pressure gradient is not a direct
factor in open channel flow, where the balance of forces is
confined to gravity and friction.
 But the free surface complicates the analysis because its shape is a
priori unknown. The depth profile changes with conditions and must
be computed as part of the problem, especially in unsteady problems
involving wave motion.
Due to the fact that the flow condition in open channel flow varies as per
time and place.
oThis makes the flow condition in an open channel is more difficult and
complex to solve the problems
Flow condition it includes depth of flow, cross-sectional area and slope of
the channel.
®of interest to hydraulic engineers
• location of free surface
• velocity distribution
• discharge - stage (depth) relationships
• optimal channel design
Practical
example
Site plan
Profile Analysis
Energy and Head
• A liquid in motion may possess three forms of energy
1. Potential energy /Potential head /
Potential energy =mgh= Wh
Potential energy per unit weight = Potential head(h)
2. Pressure energy /pressure head/piezometric head
Pressure energy per unit weight = = pressure head
3. Kinetic energy
• If a mass of fluid (m) moves at some velocity (v),
• Kinetic energy = ½ mv2 = ½ W/g v2
• Kinetic energy per unit weight = = kinetic head
10
1.1. Types of channels
Natural channels: These channels naturally exist without the
influence of human beings. E.g. Rivers, streams, tidal estuaries,
aqueducts.
As surface roughness will often change with time, distance, and even
elevation, it becomes more difficult to accurately analyses and obtain
satisfactory results for natural channels than is does for manmade
ones.
Artificial channels: Such channels are formed by man’s activity for
various purposes. E.g. irrigation channel, navigation channel,
sewerage channel, culverts, power canal
13
Based on shape
Rectangular
Trapezoidal
Triangular
Circular
Based on the change
in cross section &
slope
Prismatic--
channels with
constant shape and
slope.
Non Prismatic---
channels with
varying shape and
slopes.
1.2. Types of open Channel flow
Steady Flow
Unsteady Flow
Uniform flow
Varied Flow
Unsteady uniform flow
(Quasi uniform flow)
Unsteady Flow (i.e.
unsteady varied flow)
Gradually Varied (non-
uniform) Flow
Rapidely Varied (non-
uniform) Flow
Gradually varied
unsteady Flow
Rapidly varied unsteady
flow
15
Changes in slope, thumbs, turning, and varying input from source /RF are
some causes for flow to vary in time and space.
16
humbs
 Obstructions cause the flow depth to vary.
 Rapidly varied flow (RVF) occurs over a short distance near the obstacle.
 Gradually varied flow (GVF) occurs over larger distances and usually connects UF and RVF
Classification of OCF based on the characteristics of the flow with respect to time
and place
A. variation of flow depth with time as a criterion
Steady flow:- A flow can be said steady, if the fluid characteristics like velocity, pressure
density, and depth of flow don’t change between the time of consideration.
and
17
Unsteady flow: - Here the fluid characteristics vary with time such
that
In most open channel problems it is necessary to study flow behavior only under steady conditions.
If, however, the change in flow condition with respect to time is of major concern, the flow should be
treated as unsteady.
Typical examples of unsteady flow
Passage of a Flood Wave. Flood-wave movement is unsteady, but in flood-insurance studies, an
approximate maximum-elevation envelope resulting from a flood wave is computed under the assumption
of steady flow.
Operation of Irrigation and Power Canals.
Tidal Effects. Analysis of the effects of tides on streams requires consideration of unsteady flow.
Junctions. The complex interactions at stream junctions often require unsteady-flow analysis.
Measures to Control Flood
B. Based on Space as the criterion
Uniform flow: - A space as a criterion is used. Open channel flow is said to be uniform if
the depth of flow, and velocity remain constant or the same at every section of the channel.
Nonuniform flow: - In case when the velocity and, depth of flow in a channel change with
space]
A uniform flow may be steady or unsteady, depending on whether or not the depth
changes with time.
Steady uniform flow is the fundamental type of flow treated in open-channel hydraulics.
The depth of flow does not change during the time interval under consideration and along
the length of the channel
19
Classification of OCF based on governing forces (the effects of viscosity and
gravity relative to the inertia forces of the flow:
Effect of viscosity: Depending on the effect of viscosity relative to inertia,
the flow is classified as:
laminar,
turbulent, or
transitional.
20
Flow R taken as characteristic length
Laminar
Transitional
Turbulent
Re  500
500  Re  2000
2000  Re
Effect of gravity: the effect of gravity upon the state of flow is
represented by a ratio of inertial forces to gravity forces.
 This ratio is given by the Froude Number, defined as:
21
gL
V
Gravity
Inertia
Fr
2
2

 gL
V
Fr 
Based on the Froude Number Flow Classified as:
Critical When Fr
2 is equal to unity
Sub critical When Fr
2 is less than unity
Supercritical When Fr
2 is greater than unity
1.3.1. Geometric elements & Channel efficient Section
Geometric elements of open channel section: Geometric elements are properties of a channel
section that can be defined entirely by the geometry of the section and the depth of flow. The
most used geometric properties include:
 Depth of flow(y): it is the vertical distance from the lowest point of the channel to the free
surface.
Top width (T): it is the width of the channel section at the free surface.
Stage (h): the elevation or vertical distance of the free surface above a datum.
Wetted perimeter (p): it is the length of the channel boundary which is in contact with water.
Wetted area (A): is the cross-sectional area of the flow normal to the direction of flow.
Hydraulic radius (R) : it is the ratio of the wetted area to its wetted perimeter
22
R=
P
A
Hydraulic depth(D): the ratio of wetted area to the top width
Section factor (Z): is the product of the wetted area and the
two third power of the hydraulic radius
Conveyance (K)– indicate the carrying capacity of channel

T
b
Y
Optimal (efficient) channel cross section
A section of a channel is said to be most economical when the cost of construction of the
channel is minimum. But the cost of construction of a channel depends on excavation and
the lining.
A channel section is said to be efficient if it gives the maximum discharge for the given
shape, area and roughness.
The most hydraulically-efficient shape of, the channel is the one that can pass the
greatest quantity of flow for any given area or, equivalently, the smallest area for a
given quantity of flow.
 most economical section
As the cost of construction(excavation, channel lining is directly related to the area
of the channel & perimeter.
However, hydraulic efficiency is not the only consideration and
one must also consider, for example, fabrication costs,
excavation and, for loose granular linings, the maximum slope of
the sides.
The best hydraulic (the most efficient) cross-section for a given
Q, n, and So is the one with a minimum excavation and minimum
lining cross-section. A = Amin and P = Pmin. The minimum
cross-sectional area and the minimum lining area will reduce
construction expenses and therefore that cross-section is
economically the most efficient one.
Exercise
Q#1: A concrete-lined trapezoidal channel with a uniform flow has a normal depth of
2m. The base width of the channel is 5m and the side slopes are at 1:2. Take
manning‘s “n” =0.015 and bed slope = 0.001. Compute A. Discharge (Q), Mean
Velocity, and Reynolds number
Solution:
Step 1: Calculate the section properties ( A, P)
Step 2: compute Q by manning and Then find V.
Step 3: Compute Reynolds number ( Re channel=(density * Velocity* Area) / (dynamic viscosity* Perimeter)
Dynamic viscosity= 1.08*10^-5
Q#2 Calculate the uniform water depth of an open channel flow to convey Q=10 m3/sec discharge with manning
coefficient n=0.014, channel slope S0=0.0004, and channel width B=4 m. (consider the channel to be rectangular &
trapezoidal).
Q#3. Derive the most efficient channel section for rectangular, trapezoidal and triangular channel
Home Assignment
Design the trapezoidal channel as best hydraulic cross-section with Q= 10 m3/sec,
n= 0.014, S0= 0.0004, and m= 3/2.

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Lecture 1.pptx

  • 1. 1 ADDIS COLLEGE CIVIL ENGINEERING DEPARTMENT Lecture Notes Open Channel Hydraulics Instructor: Behailu N.
  • 2. Contents Open Channel Flow and Its Classifications Basic Principles Of Hydraulics Flow Computation Formula Gradually Varied Flow (GVF) Rapidly Varied Flow(RVF) Unsteady Flow In Open Channels Sediment Transport in an Open Channel
  • 3. Course Objectives The aim of the course is to present a review of the main principles of hydraulics and to apply them to Civil, Hydraulic, and Irrigation Engineering problems. After the completion of the course, the student should understand and should be able to apply the principles of hydraulics in engineering problems, be capable to make uniform and non-uniform flow and steady and unsteady flow computations.
  • 4. Lecture 1 Types of Flow in Open Channel Uniform Flow in Open Channel Channel of Efficient Cross-section
  • 5. CHAPTER 1 1.1. INTRODUCTION TO OPEN CHANNEL FLOW Open channel open-channel flow is the flow of a liquid in a conduit with a free surface. There are many practical examples, both artificial (flumes, pipe lines (not completely full), spillways, sewers, canals, weirs, drainage ditches, and culverts) and natural (streams, rivers, estuaries, floodplains). Structures like, culverts, and spillways are designed as an open channel It is a flow in a channel in which the stream is not completely enclosed by solid boundaries It has a free surface subjected to atmospheric pressure ( the pressure distribution is equal to the Patm).. 5
  • 6. Free Surface: which is essentially at atmospheric pressure, both helps and hurts the analysis. It helps because the pressure can be taken constantly along the free surface, which therefore is equivalent to the hydraulic grade line (HGL) of the flow. Unlike flow in closed ducts, the pressure gradient is not a direct factor in open channel flow, where the balance of forces is confined to gravity and friction.  But the free surface complicates the analysis because its shape is a priori unknown. The depth profile changes with conditions and must be computed as part of the problem, especially in unsteady problems involving wave motion.
  • 7. Due to the fact that the flow condition in open channel flow varies as per time and place. oThis makes the flow condition in an open channel is more difficult and complex to solve the problems Flow condition it includes depth of flow, cross-sectional area and slope of the channel. ®of interest to hydraulic engineers • location of free surface • velocity distribution • discharge - stage (depth) relationships • optimal channel design
  • 9.
  • 10. Energy and Head • A liquid in motion may possess three forms of energy 1. Potential energy /Potential head / Potential energy =mgh= Wh Potential energy per unit weight = Potential head(h) 2. Pressure energy /pressure head/piezometric head Pressure energy per unit weight = = pressure head 3. Kinetic energy • If a mass of fluid (m) moves at some velocity (v), • Kinetic energy = ½ mv2 = ½ W/g v2 • Kinetic energy per unit weight = = kinetic head 10
  • 11.
  • 12.
  • 13. 1.1. Types of channels Natural channels: These channels naturally exist without the influence of human beings. E.g. Rivers, streams, tidal estuaries, aqueducts. As surface roughness will often change with time, distance, and even elevation, it becomes more difficult to accurately analyses and obtain satisfactory results for natural channels than is does for manmade ones. Artificial channels: Such channels are formed by man’s activity for various purposes. E.g. irrigation channel, navigation channel, sewerage channel, culverts, power canal 13
  • 14. Based on shape Rectangular Trapezoidal Triangular Circular Based on the change in cross section & slope Prismatic-- channels with constant shape and slope. Non Prismatic--- channels with varying shape and slopes.
  • 15. 1.2. Types of open Channel flow Steady Flow Unsteady Flow Uniform flow Varied Flow Unsteady uniform flow (Quasi uniform flow) Unsteady Flow (i.e. unsteady varied flow) Gradually Varied (non- uniform) Flow Rapidely Varied (non- uniform) Flow Gradually varied unsteady Flow Rapidly varied unsteady flow 15 Changes in slope, thumbs, turning, and varying input from source /RF are some causes for flow to vary in time and space.
  • 16. 16 humbs  Obstructions cause the flow depth to vary.  Rapidly varied flow (RVF) occurs over a short distance near the obstacle.  Gradually varied flow (GVF) occurs over larger distances and usually connects UF and RVF
  • 17. Classification of OCF based on the characteristics of the flow with respect to time and place A. variation of flow depth with time as a criterion Steady flow:- A flow can be said steady, if the fluid characteristics like velocity, pressure density, and depth of flow don’t change between the time of consideration. and 17 Unsteady flow: - Here the fluid characteristics vary with time such that
  • 18. In most open channel problems it is necessary to study flow behavior only under steady conditions. If, however, the change in flow condition with respect to time is of major concern, the flow should be treated as unsteady. Typical examples of unsteady flow Passage of a Flood Wave. Flood-wave movement is unsteady, but in flood-insurance studies, an approximate maximum-elevation envelope resulting from a flood wave is computed under the assumption of steady flow. Operation of Irrigation and Power Canals. Tidal Effects. Analysis of the effects of tides on streams requires consideration of unsteady flow. Junctions. The complex interactions at stream junctions often require unsteady-flow analysis. Measures to Control Flood
  • 19. B. Based on Space as the criterion Uniform flow: - A space as a criterion is used. Open channel flow is said to be uniform if the depth of flow, and velocity remain constant or the same at every section of the channel. Nonuniform flow: - In case when the velocity and, depth of flow in a channel change with space] A uniform flow may be steady or unsteady, depending on whether or not the depth changes with time. Steady uniform flow is the fundamental type of flow treated in open-channel hydraulics. The depth of flow does not change during the time interval under consideration and along the length of the channel 19
  • 20. Classification of OCF based on governing forces (the effects of viscosity and gravity relative to the inertia forces of the flow: Effect of viscosity: Depending on the effect of viscosity relative to inertia, the flow is classified as: laminar, turbulent, or transitional. 20 Flow R taken as characteristic length Laminar Transitional Turbulent Re  500 500  Re  2000 2000  Re
  • 21. Effect of gravity: the effect of gravity upon the state of flow is represented by a ratio of inertial forces to gravity forces.  This ratio is given by the Froude Number, defined as: 21 gL V Gravity Inertia Fr 2 2   gL V Fr  Based on the Froude Number Flow Classified as: Critical When Fr 2 is equal to unity Sub critical When Fr 2 is less than unity Supercritical When Fr 2 is greater than unity
  • 22. 1.3.1. Geometric elements & Channel efficient Section Geometric elements of open channel section: Geometric elements are properties of a channel section that can be defined entirely by the geometry of the section and the depth of flow. The most used geometric properties include:  Depth of flow(y): it is the vertical distance from the lowest point of the channel to the free surface. Top width (T): it is the width of the channel section at the free surface. Stage (h): the elevation or vertical distance of the free surface above a datum. Wetted perimeter (p): it is the length of the channel boundary which is in contact with water. Wetted area (A): is the cross-sectional area of the flow normal to the direction of flow. Hydraulic radius (R) : it is the ratio of the wetted area to its wetted perimeter 22 R= P A
  • 23. Hydraulic depth(D): the ratio of wetted area to the top width Section factor (Z): is the product of the wetted area and the two third power of the hydraulic radius Conveyance (K)– indicate the carrying capacity of channel 
  • 24. T b Y
  • 25.
  • 26. Optimal (efficient) channel cross section A section of a channel is said to be most economical when the cost of construction of the channel is minimum. But the cost of construction of a channel depends on excavation and the lining. A channel section is said to be efficient if it gives the maximum discharge for the given shape, area and roughness. The most hydraulically-efficient shape of, the channel is the one that can pass the greatest quantity of flow for any given area or, equivalently, the smallest area for a given quantity of flow.  most economical section As the cost of construction(excavation, channel lining is directly related to the area of the channel & perimeter.
  • 27. However, hydraulic efficiency is not the only consideration and one must also consider, for example, fabrication costs, excavation and, for loose granular linings, the maximum slope of the sides. The best hydraulic (the most efficient) cross-section for a given Q, n, and So is the one with a minimum excavation and minimum lining cross-section. A = Amin and P = Pmin. The minimum cross-sectional area and the minimum lining area will reduce construction expenses and therefore that cross-section is economically the most efficient one.
  • 28. Exercise Q#1: A concrete-lined trapezoidal channel with a uniform flow has a normal depth of 2m. The base width of the channel is 5m and the side slopes are at 1:2. Take manning‘s “n” =0.015 and bed slope = 0.001. Compute A. Discharge (Q), Mean Velocity, and Reynolds number Solution: Step 1: Calculate the section properties ( A, P) Step 2: compute Q by manning and Then find V. Step 3: Compute Reynolds number ( Re channel=(density * Velocity* Area) / (dynamic viscosity* Perimeter) Dynamic viscosity= 1.08*10^-5 Q#2 Calculate the uniform water depth of an open channel flow to convey Q=10 m3/sec discharge with manning coefficient n=0.014, channel slope S0=0.0004, and channel width B=4 m. (consider the channel to be rectangular & trapezoidal). Q#3. Derive the most efficient channel section for rectangular, trapezoidal and triangular channel
  • 29. Home Assignment Design the trapezoidal channel as best hydraulic cross-section with Q= 10 m3/sec, n= 0.014, S0= 0.0004, and m= 3/2.

Editor's Notes

  1. Aqueducts are under ground conduits which carry water with free surface Generally the natural channels fall into the non prismatic group. That is why intensive study of the behavior of flow in natural channels requires other fields of studies like, sediment transport, geomorphology, hydrology, river engineering.
  2. Aqueducts are under ground conduits which carry water with free surface Generally the natural channels fall into the non prismatic group. That is why intensive study of the behavior of flow in natural channels requires other fields of studies like, sediment transport, geomorphology, hydrology, river engineering.
  3. Aqueducts are under ground conduits which carry water with free surface Generally the natural channels fall into the non prismatic group. That is why intensive study of the behavior of flow in natural channels requires other fields of studies like, sediment transport, geomorphology, hydrology, river engineering.