# University of Palestine Engineering Hydraulics 2nd semester - PowerPoint PPT Presentation

PPT – University of Palestine Engineering Hydraulics 2nd semester PowerPoint presentation | free to download - id: 3cd11f-M2VlZ The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## University of Palestine Engineering Hydraulics 2nd semester

Description:

### University of Palestine Engineering Hydraulics 2nd semester 2010-2011 CHAPTER 6: Water Flow in Open Channels * ... – PowerPoint PPT presentation

Number of Views:152
Avg rating:3.0/5.0
Slides: 84
Provided by: moodleUp
Category:
Tags:
Transcript and Presenter's Notes

Title: University of Palestine Engineering Hydraulics 2nd semester

1
CHAPTER 6 Water Flow in Open Channels
University of Palestine Engineering
Hydraulics 2nd semester 2010-2011
2
Content
• Introduction.
• Type of Open Channels.
• Types of Flow in Open Channels.
• Flow Formulas in Open Channels.
• Most Economical Section of Channels.
• Energy Principles in Open Channel Flow.
• Non-uniform Flow in Open Channels.
• Hydraulic Jump.

3
Introduction
• Open channel hydraulics, a subject of great
importance to civil engineers, deals with flows
having a free surface in channels constructed for
water supply, irrigation, drainage, and
hydroelectric power generation in sewers,
culverts, and tunnels flowing partially full and
in natural streams and rivers.
• An open channel is a duct in which the liquid
flows with a free surface.
• This is in contrast with pipe flow in which the
liquid completely fills the pipe and flow under
pressure.
• The flow in a pipe takes place due to difference
of pressure (pressure gradient), whereas in open
channel it is due to the slope of the channel bed
(i.e. due to gravity).

4
Introduction
• It may be noted that the flow in a closed conduit
is not necessarily a pipe flow. It must be
classified as open channel flow if the liquid has
a free surface.
• for a pipe flow
• The hydraulic gradient line (HGL) is the sum of
the elevation and the pressure head (connecting
the water surfaces in piezometers).
• The energy gradient line (EGL) is the sum of the
• The amount of energy loss when the liquid flows
from section 1 to section 2 is indicated by hL.

5
Introduction
Pipe system
6
Introduction
• For open channel flow
• The hydraulic gradient line (HGL) corresponds to
the water surface line (WSL) the free water
surface is subjected to only atmospheric pressure
which is commonly referred to as the zero
pressure reference in hydraulic engineering
practice.
• The energy gradient line (EGL) is the sum of the
• The amount of energy loss when the liquid flows
from section 1 to section 2 is indicated by hL.
For uniform flow in an open channel, this drop in
the EGL is equal to the drop in the channel bed.

7
Introduction
Open Channel
8
Type of Open Channels
• Based on their existence, an open channel can be
natural or artificial
• Natural channels such as streams, rivers, valleys
, etc. These are generally irregular in shape,
alignment and roughness of the surface.
• Artificial channels are built for some specific
purpose, such as irrigation, water supply,
wastewater, water power development, and rain
collection channels. These are regular in shape
and alignment with uniform roughness of the
boundary surface.

9
Type of Open Channels
10
Type of Open Channels
11
Type of Open Channels
• Based on their shape, an open channel can be
prismatic or non-prismatic
• Prismatic channels a channel is said to be
prismatic when the cross section is uniform and
the bed slop is constant.
• )Non-prismatic channels when either the cross
section or the slope (or both) change, the
channel is referred to as non-prismatic. It is
obvious that only artificial channel can be
prismatic.
• The most common shapes of prismatic channels are
rectangular, parabolic, triangular, trapezoidal
and circular.

12
Type of Open Channels
• The most common shapes of prismatic channels are
rectangular, parabolic, triangular, trapezoidal
and circular.

13
Types of Flow in Open Channels
• The flow in an open channel can be classified
into the following types
• A).Uniform and non-uniform flow
• If for a given length of the channel, the
velocity of flow, depth of flow, slope of the
channel and cross-section remain constant, the
flow is said to be uniform.
• Otherwise it is said to be non-uniform.
• Non-uniform flow is also called varied flow which
can be further classified as
• Gradually varied flow (GVF) where the depth of
the flow changes gradually along the length of
the channel.
• Rapidly varied flow (RVF) where the depth of flow
changes suddenly over a small length of the
channel. For example, when water flows over an
overflow dam, there is a sudden rise (depth) of
water at the toe of the dam, and a hydraulic jump
forms.

14
Types of Flow in Open Channels
15
Uniform Flow
Types of Flow in Open Channels
16
Types of Flow in Open Channels
• The flow is steady when, at a particular section,
the depth of the liquid and other parameters
(such as velocity, area of cross section,
discharge) do not change with time. In an
unsteady flow, the depth of flow and other
parameters change with time.
• C). Laminar and turbulent flow
• The flow in open channel can be either laminar or
turbulent. In practice, however, the laminar flow
occurs very rarely. The engineer is concerned
mainly with turbulent flow. In the case of open
channel Reynolds number is defined as

17
Types of Flow in Open Channels
Recall that Reynolds number is the measure of
relative effects of the inertia forces to viscous
forces.
18
Types of Flow in Open Channels
19
Types of Flow in Open Channels
• D). Sub-critical, critical, and supercritical
flow
• The criterion used in this classification is what
is known by Froude number, Fr, which is the
measure of the relative effects of inertia forces
to gravity force

20
Types of Flow in Open Channels
• D). Sub-critical, critical, and supercritical
flow
• The criterion used in this classification is what
is known by Froude number, Fr, which is the
measure of the relative effects of inertia forces
to gravity force

21
Flow Formulas in Open Channels
• In the case of steady-uniform flow in an open
channel, the following main features must be
satisfied
• The water depth, water area, discharge, and the
velocity distribution at all sections throughout
the entire channel length must remain constant,
i.e. Q , A , y , V remain constant through the
channel length.
• The slope of the energy gradient line (S), the
water surface slope (Sws), and the channel bed
slope (S0) are equal.
• S Sws S0

22
Flow Formulas in Open Channels
• The depth of flow, y , is defined as the vertical
distance between the lowest point of the channel
bed and the free surface.
• The depth of flow section, D , is defined as the
depth of liquid at the section, measured normal
to the direction of flow.

Unless mentioned otherwise, the depth of flow and
the depth of flow section will be assumed equal.
For uniform flow the depth attains a constant
value known as the normal depth, yn
23
Flow Formulas in Open Channels
Many empirical formulas are used to describe the
flow in open channels The Chezy formula is
probably the first formula derived for uniform
flow. It may be expressed in the following form
1.The Chezy Formula(1769)
C is the Chezy coefficient (Chezys resistance
factor), m1/2/s, a dimensional factor which
characterizes the resistance to flow .
24
Flow Formulas in Open Channels
2. The Manning Formula (1895)
where n Mannings coefficient for the channel
roughness, m-1/3/s.
Substituting manning Eq. into Chezy Eq, we
obtain the Mannings formula for uniform flow
25
Flow Formulas in Open Channels
26
Flow Formulas in Open Channels
3. The Strickler Formula
where kstr Strickler coefficient, m1/3/s
Comparing Manning formula and Strickler formulas,
we can see that
27
Example 1
Flow Formulas in Open Channels
open channel of width 3m as shown, bed slope
15000, d1.5m find the flow rate using Manning
equation, n0.025.
28
Example 2
Flow Formulas in Open Channels
open channel as shown, bed slope 691584, find
the flow rate using Chezy equation, C35.
29
Flow Formulas in Open Channels
Example 2 cont.
30
Flow Formulas in Open Channels
Example 3 Group work
The cross section of an open channel is a
trapezoid with a ottom width of 4 m and side
slopes 12, calculate the discharge if the depth
of water is 1.5 m and bed slope 1/1600. Take
Chezy constant C 50.
31
Most Economical Section of Channels
During the design stages of an open channel, the
channel cross-section, roughness and bottom slope
are given. The objective is to determine the
flow velocity, depth and flow rate, given any one
of them. The design of channels involves
selecting the channel shape and bed slope to
convey a given flow rate with a given flow depth.
For a given discharge, slope and roughness, the
designer aims to minimize the cross-sectional
area A in order to reduce construction costs
32
Most Economical Section of Channels
• 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. To keep the cost
down or minimum, the wetted perimeter, for a
given discharge, should be minimum.
• This condition is utilized for determining the
dimensions of economical sections of different
forms of channels.

33
Most Economical Section of Channels
• Most economical section is also called the best
section or most efficient section as the
discharge, passing through a most economical
section of channel for a given cross sectional
area A, slope of the bed S0 and a resistance
coefficient, is maximum.

Hence the discharge Q will be maximum when the
wetted perimeter P is minimum.
34
Most Economical Section of Channels
• The most efficient cross-sectional shape is
determined for uniform flow conditions.
Considering a given discharge Q, the velocity V
is maximum for the minimum cross-section A.
According to the Manning equation the hydraulic
diameter is then maximum.
• It can be shown that
• the wetted perimeter is also minimum,
• the semi-circle section (semi-circle having its
centre in the surface) is the best hydraulic
section

35
Most Economical Rectangular Channel
Most Economical Section of Channels
Because the hydraulic radius is equal to the
water cross section area divided by the wetted
parameter, Channel section with the least wetted
parameter is the best hydraulic section
Rectangular section
36
Most Economical Section of Channels
Most Economical Rectangular Channel
37
Most Economical Section of Channels
Most Economical Trapezoidal Channel
or
38
Most Economical Section of Channels
Other criteria for economic Trapezoidal section
k
The best side slope for Trapezoidal section
39
Most Economical Section of Channels
Most Economical Circular Channel
Circular section
Maximum Flow using Manning
Maximum Velocity using Manning or Chezy
Maximum Flow using Chezy
40
Most Economical Section of Channels
41
Example 4
Most Economical Section of Channels
Circular open channel as shown d1.68m, bed slope
15000, find the Max. flow rate the Max.
velocity using Chezy equation, C70.
Max. flow rate
42
Most Economical Section of Channels
Example 4 cont.
Max. Velocity
43
Most Economical Section of Channels
Example 5
Trapezoidal open channel as shown Q10m3/s,
velocity 1.5m/s, for most economic section. find
wetted parameter, and the bed slope n0.014.
44
Most Economical Section of Channels
Example 5 cont.
To calculate bed Slope
45
Most Economical Section of Channels
Example 6
Use the proper numerical method to calculate
uniform water depth flowing in a Trapezoidal open
channel with B 10 m, as shown Q10m3/s if the
bed slope 0.0016, n0.014. k 3/2. to a
precision 0.01 m, and with iterations not more
than 15. Note you may find out two roots to the
equation.
46
Most Economical Section of Channels
Example 6 cont.
47
Variation of flow and velocity with depth in
circular pipes
48
Energy Principles in Open Channel Flow
Referring to the figure shown, the total energy
of a flowing liquid per unit weight is given by
Where Z height of the bottom of channel above
datum, y depth of liquid, V mean velocity of
flow.
If the channel bed is taken as the datum (as
shown), then the total energy per unit weight
will be. This energy is known as specific energy,
Es. Specific energy of a flowing liquid in a
channel is defined as energy per unit weight of
the liquid measured from the channel bed as datum
49
Energy Principles in Open Channel Flow
The specific energy of a flowing liquid can be
re-written in the form
50
Energy Principles in Open Channel Flow
Specific Energy Curve (rectangular channel)
It is defined as the curve which shows the
variation of specific energy (Es ) with depth of
flow y. It can be obtained as follows Let us
consider a rectangular channel in which a
constant discharge is taking place.
But
Or
51
Energy Principles in Open Channel Flow
Specific Energy Curve (rectangular channel)
The graph between specific energy (x-axis) and
depth (yaxis) may plotted.
52
Energy Principles in Open Channel Flow
Specific Energy Curve (rectangular channel)
• Referring to the diagram above, the following
features can be observed
• The depth of flow at point C is referred to as
critical depth, yc. It is defined as that depth
of flow of liquid at which the specific energy is
minimum, Emin, i.e. Emin _at_ yc . The flow that
corresponds to this point is called critical flow
(Fr 1.0).
• For values of Es greater than Emin , there are
two corresponding depths. One depth is greater
than the critical depth and the other is smaller
then the critical depth, for example Es1 _at_
y1 and y2 These two depths for a given specific
energy are called the alternate depths.
• If the flow depth y gt yc , the flow is said to be
sub-critical (Fr lt 1.0). In this case Es
increases as y increases.
• If the flow depth y lt yc , the flow is said to be
super-critical (Fr gt 1.0). In this case Es
increases as y increases.

53
Froude Number (Fr)
Energy Principles in Open Channel Flow
54
Critical Flow
Energy Principles in Open Channel Flow
55
Rectangular Channel
Energy Principles in Open Channel Flow
For rectangular section
At critical Flow
a) Critical depth, yc , is defined as that depth
of flow of liquid at which the specific energy is
minimum, Emin,
qQ/B
b) Critical velocity, Vc , is the velocity of
flow at critical depth.
56
Energy Principles in Open Channel Flow
Rectangular Channel
c) Critical, Sub-critical, and Super-critical
Flows Critical flow is defined as the flow at
which the specific energy is minimum or the flow
that corresponds to critical depth. Refer to
point C in above figure, Emin _at_ yc .
and
therefore for critical flow Fr 1.0
If the depth flow y gt yc , the flow is said to be
sub-critical. In this case Es increases as y
increases. For this type of flow, Fr lt 1.0 . If
the depth flow y lt yc , the flow is said to be
super-critical. In this case Es increases as y
decreases. For this type of flow, Fr gt 1.0 .
57
Energy Principles in Open Channel Flow
Rectangular Channel
d) Minimum Specific Energy in terms of critical
depth At (Emin , yc ) ,
58
Other Sections
Energy Principles in Open Channel Flow
at critical flow Fr 1 where
Rectangular section
Trapezoidal section
Circular section
Triangle section
59
Example 1
Energy Principles in Open Channel Flow
Determine the critical depth if the flow is
1.33m3/s. the channel width is 2.4m
60
Example 2
Energy Principles in Open Channel Flow
Rectangular channel , Q25m3/s, bed slope 0.006,
determine the channel width with critical flow
using manning n0.016
61
Energy Principles in Open Channel Flow
Example 2 cont.
62
Non-uniform Flow in Open Channels
• Non-uniform flow is a flow for which the depth
of flow is aried. This varied flow can be either
Gradually varied flow (GVF) or Rapidly varied
flow (RVF).
• Such situations occur when control structures are
used in the channel or when any obstruction is
found in the channel
• Such situations may also occur at the free
discharges and when a sharp change in the channel
slope takes place.
• The most important elements, in non-uniform flow,
that will be studied in this sectionare
• Classification of channel-bed slopes.
• Classification of water surface profiles.
• The dynamic equation of gradually varied flow.
• Hydraulic jumps as examples of rapidly varied
flow.

63
Non-uniform Flow in Open Channels
64
Non-uniform Flow in Open Channels
Classification of Channel-Bed Slopes
• The slope of the channel bed can be classified
as
• 1) Critical Slope the bottom slope of the
channel is equal to the critical slope. In this
case S0 Sc or yn yc .
• 2) Mild Slope the bottom slope of the channel is
less than the critical slope. In this case S0 lt
Sc or yn gt yc .
• 3) Steep Slope the bottom slope of the channel
is greater than the critical slope. In this case
S0 gt Sc or yn lt yc .
• 4) Horizontal Slope the bottom slope of the
channel is equal to zero (horizontal bed). In
this case S0 0.0 .
• 5) Adverse Slope the bottom slope of the channel
rises in the direction of the flow (slope is
opposite to direction of flow). In this case S0
negative .
• The first letter of each slope type sometimes is
used to indicate the slope of the bed. So the
above slopes are abbreviated as C, M, S, H, and
A, respectively.

65
Non-uniform Flow in Open Channels
Classification of Channel-Bed Slopes
66
Non-uniform Flow in Open Channels
Classification of Flow Profiles (water surface
profiles)
67
Non-uniform Flow in Open Channels
Classification of Flow Profiles (water surface
profiles)
68
Non-uniform Flow in Open Channels
Classification of Flow Profiles (water surface
profiles)
69
Non-uniform Flow in Open Channels
Classification of Flow Profiles (water surface
profiles)
70
Non-uniform Flow in Open Channels
Classification of Flow Profiles (water surface
profiles)
71
Hydraulic Jump
A hydraulic jump occurs when flow changes from a
supercritical flow (unstable) to a sub-critical
flow (stable). There is a sudden rise in water
level at the point where the hydraulic jump
occurs. Rollers (eddies) of turbulent water form
at this point. These rollers cause dissipation of
energy.
72
Hydraulic Jump
General Expression for Hydraulic Jump In the
analysis of hydraulic jumps, the following
assumptions are made (1) The length of hydraulic
jump is small. Consequently, the loss of head due
to friction is negligible. (2) The flow is
uniform and pressure distribution is due to
hydrostatic before and after the jump. (3) The
slope of the bed of the channel is very small, so
that the component of the weight of the fluid in
the direction of the flow is neglected.
73
Hydraulic Jump
Hydraulic Jump in Rectangular Channels
But for Rectangular section
74
Hydraulic Jump
Hydraulic Jump in Rectangular Channels
75
Hydraulic Jump
Hydraulic Jump in Rectangular Channels
76
Hydraulic Jump
Hydraulic Jump in Rectangular Channels
77
Hydraulic Jump
78
Hydraulic Jump
79
Example 1
Hydraulic Jump
A 3-m wide rectangular channel carries 15 m3/s of
water at a 0.7 m depth before entering a jump.
Compute the downstrem water depth and the
critical depth
80
Example 2
Hydraulic Jump
dn Depth can calculated from manning equation
81
Hydraulic Jump
a)
b)
82
Hydraulic Jump
c)
83