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OPEN CHANNEL
HYDRAULICS

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 COURSE OUT LINE
CHAPTER-ONE
INTRODUCTION OF OPEN CHANNEL CLASIFICATION AND TYPE
1. Classification and types
2. Velocity and Pressure Distributions

CHAPTER TWO
Basic hydraulics principles:
2.1 Geometry of Open Channels
2.2 Energy and Momentum Principle in open channel.
CHAPTER THREE
Flow computation formulas:
3.1 Flow measurement
3.2 Control section (flow control)
3.3 Specific Energy; Critical Depth
3.4 Uniform and critical flow and its computation
3.5 Discharge computation in compound section.
 CHAPTER FOUR
Gradually varied flow:
4.1 Differential equation of GVF
4.2 Classification of flow profiles
4.3 GVF Computations
4.4 Control sections and GVF in changing grads
CHAPTER FIVE
Rapidly varied flow:
5.1 Characteristics of rapid varied flow
5.2 Flow over spillways
5.3 Hydraulic jump analysis and Flow under Gates.
CHAPTER SIX
6.1 Waves
6.2 Development of St.Venant Equations
6.3 The Methods of Characteristics and Dynamic Equation.
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06/30/24 SOLOMON
CHAPTER ONE

INTRODUCTION

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What Is Channel?
-waterway used to convey flow
-conveyance structure release the flow from environment
- transmitting water from source to a place of need
- conduit, canal used to drain flow to water bodies
-used to dispose
Classification of channel
Two types of channel
-Closed /Pipe line/ channel and
-Open channel
The two kinds of flow are similar in many ways but differ in
one important aspect.

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 INTRODUCTION
 An open channel is a conduit in which a
liquid flows with a free surface.
 The free surface is actually an interface
between the moving liquid and an
overlying fluid medium and will have
constant pressure.
 The prime motivating force for open
channel flow is that due to gravity.
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 Classification of channels
 Depending on the channel is manmade:
1) Natural channel
2) Artificial channel

Natural channel Artificial channel

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Based on boundary characteristics
1) Rigid boundary:- lined channel no problem of
sediment
2) Mobile boundary:-unlined channels where sediment
problem exists

Rigid boundary Mobile boundary

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Based on cross section and slope
1)Prismatic: - Cross section and slope remain constant in the reach.
2)Non-Prismatic: - cross section and slope vary with space and time

Prismatic Non-Prismatic

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 Kind of open channel
CANAL is usually a long and mild- sloped channel
built in the ground

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Cont.
FLUME is a channel usually supported on or above
the surface of the ground to carry water across a
depression.

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Cont.
CHUTE is a channel having steep slopes

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Cont.
DROP is similar to a chute, but the change in
elevation is affected in a short distance.

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Cont.
CULVERT is a covered channel flowing partly full,
which is installed to drain water through highway
and railroad embankments.

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Cont.
OPEN–FLOW TUNNEL is a comparatively long
covered channel used to carry water through a hill
or any obstruction on the ground.

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 CLASSIFICATION OF FLOWS
Steady and Unsteady Flows
 steady flows occurs when the flow properties, such
as the depth or discharge at a section do not change
with time.
As a corollary, if the depth or discharge changes with
time the flow is termed unsteady.
Flood flows in rivers and rapidly-varying surges in
canals are some example of unsteady flows.
Unsteady flows are considerably more difficult to
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analysis than steady flows.
 Cont.
Uniform and non-uniform Flows
 If the flow properties, say the depth of flow, in an open channel
remain constant along the length of channel, the flow is said to be
uniform.
 As a corollary of this, a flow in which the flow properties vary
along the channel is termed as non-uniform flow or varied flow.
 A prismatic channel carrying a certain discharge with a constant
velocity is an example of uniform flow (Fig. 1.1(a)).

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 Flow in a non-prismatic channel and flow with varying
velocities in a prismatic channel are examples of varied flow.
 Varied flow can be either steady or unsteady.

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 Gradually-varied and Rapidly –varied Flows
If the change of depth in a varied flow is gradual so that the
curvature of streamlines is not excessive, such a flow is said to be a
gradually –varied flow (GVF).
The passage of a flood wave in a flood wave in a river is a case
of unsteady GVF (Fig. 1.1(b)).

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 A hydraulic jump occurring below a spillway or a
sluice gate is an example of steady RVF.
 A surge , moving up a canal (Fig. 1.1(c)) and a bore
traveling up a river are examples of unsteady RVF.

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 Cont.
Spatially-varied flow
 Varied flow classified as GVF and RVF assumes that no flow is
externally added to or taken out of the canal system.
 The volume of water in a known time interval is conserved in the
channel system.
 In steady-varied flow the discharge is constant at all sections.

 However, if some flow is added to or abstracted from the system

the resulting varied flow is known as a spatially varied flow
(SVF).
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 SVF can be steady or unsteady.

 In the steady SVF the discharge while being steady-varies along

the channel length.
 rack is an example of steady SVF (Fig 1.1(d)).

 The production of surface runoff due to rainfall, known as

overland flows, is a typical example unsteady SVF.

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 VELOCITY DISTRIBUTION
 The distribution of V in a channel is
dependent on the geometry of channel.
 Figure 1.2(a) and (b) show isohels (contours
of equal velocity) of for a natural and
rectangular channel respectively.
 It might be expected to find the maximum
velocity at the free surface where the shear
force is zero but this is not the case.
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Fig. 1.2

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Cont.
 A typical velocity profile at a section in a
plan normal to the direction of flow is
presented in Fig. 1.2(c).

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Cont.

 Field observations in rivers and canals have

show that the average velocity at any vertical
Vav, occurs at a level of 0.6yo from the free
surface,

 where Yo =depth of flow. Further, it is found that

v0.2  v0.8
vav 
2
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 Cont.

 Where: V0.2 = velocity at a depth of 0.2 Y0 from the

free surface, and V0.8 = velocity at a depth of 0.8 Y0

from the free surface.
 This property of the velocity distribution is
commonly used in stream-gauging practice to
determine the discharge using the area-velocity
method.
 The surface velocity vs is related to the average
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velocity vav as
 Cont.

vav  kvs (1.2)

 where, K = a coefficient with a value between

0.8 and 0.95.
 The proper value of K depends on the channel
section and has to be determined by field
calibrations.
 Knowing K, one can estimate the average
velocity in an open channel by using floats and
other surface velocity measuring devices. 34
 PRESSURE DISTRIBUTION

 The intensity of pressure for a liquid at its

free surface is equal to that of the
surrounding atmosphere.
 Since the atmospheric pressure is commonly
taken as a reference and of value equal to
zero, the free surface of the liquid is thus a
surface of zero.
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 Cont.
The distribution of pressure in an open channel flow is
governed by the acceleration due to gravity g and other
accelerations and is given by the Euler’s equation as
below:
In any arbitrary direction s, and in the
direction normal to s direction, i.e., in the n
direction,
  p  Z 
  a s
s 36
 2
v
an 
r
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 Hydrostatic Pressure Distribution
The normal acceleration an will be zero
(i)if v = 0, i.e., when there is no motion, or
(ii)if r → ∞, i.e., when the streamlines are straight lines.
Consider the case of no motion, i.e. the still water case
(Fig. 1.4(a)).
From Eq. 1.13, since an = 0, taking n in the Z direction
and integrating

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From Eq. (1.13), since an= 0, taking n in the Z direction and
integrating

At the free surface [point 1 in Fig. 1.4(a)] P1/γ =0 and Z =

Z1 , giving C = Z1. At any point A at a depth y below the free
surface, 39
 This linear variation of pressure with depth having
the constant of proportionality equal to the unit
weight of the liquid is known as hydrostatic-pressure
distribution.

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 Channels with Small Slope
 Let us consider a channel with a very small value of the
longitudinal slope θ. Let θ ~ sin θ ~ 1/1000.
 For such channels the vertical section is practically the same as
the normal section.
 If a flow takes place in this channel with the water surface parallel
to the bed, i.e. uniform flow, the streamlines will be straight lines
and as such in a vertical direction [Section 0–1 in Fig. 1.4(b)] the
normal acceleration an = 0.

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 Following the argument of the previous paragraph, the
pressure distribution at the Section 0 – 1 will be hydrostatic.
At any point A at a depth y below the water surface,

=Elevation of water surface

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 Thus the piezometric head at any point in the channel will be
equal to the water-surface elevation.
 The hydraulic grade line will therefore lie essentially on the
water surface.
Channels with Large Slope
Figure 1.5 shows a uniform free-surface flow in a channel with
a large value of inclination θ. The flow is uniform, i.e. the water
surface is parallel to the bed.
An element of length ΔL and unit width is considered at the
Section 0 –1.
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 At any point A at a depth y measured normal to the water
surface, the weight of column A1 1′A′ = γΔLy and acts
vertically downwards.
 The pressure at AA′ supports the normal component of the
column A1 1′A′. Thus

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 The pressure pA varies linearly with the depth y but the
constant of proportionality is γcosθ. If h = normal depth of
flow, the pressure on the bed at point 0, p0 = γhcosθ.
 If d = vertical depth to water surface measured at the point
O, then h = dcosθ and the pressure head at point O, on the
bed is given by

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 The piezometric height at any point
A = Z + ycosθ = Z0 + hcosθ.
 Thus for channels with large values of the slope, the
conventionally defined hydraulic gradient line does not lie on the
water surface.
 Channels of large slopes are encountered rarely in practice
except, typically in spillways and chutes.
 On the other hand, most of the canals, streams and rivers with
which a hydraulic engineer is commonly associated will have
slopes (sin θ) smaller than 1/100.
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 PRESSURE DISTRIBUTION IN
CURVILINEAR FLOWS
 Figure 1.6(a) shows a curvilinear flow in a vertical plane
on an upward convex surface.
 For simplicity consider a Section 01A2 in which the r
direction and Z direction coincide.
 Replacing the n direction in Eq. 1.13 by (−r) direction,

p  an
  Z   (1.20)
r    g
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 Let us assume a simple case in which an = constant.
 Then, the integration of Eq. 1.20 yields

 In which C = constant.
 With the boundary condition that at point 2 which lies on the
free surface, r = r2 and p/γ = 0 and Z = Z2 ,

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 Let Z2 − Z = depth below the free surface of any point A in
the Section 01A2 = y. Then for point A,

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 Normal Acceleration
In the previous discussion on curvilinear flows, the
normal acceleration an was assumed to be constant.
However, it is known that at any point in a
curvilinear flow an an  v r
2

 where v = velocity and r = radius of curvature of the

streamline at that point.

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 In general, one can write v = f (r) and the pressure distribution can
then be expressed by

 This expression can be evaluated if v = f (r) is

known.
 For simple analysis, the follow
(i) v = constant = V = mean velocity of flow
(ii) v  c r (free-vortex model)
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(iii) v  cr, (forced-vortex model)
(iv) an = constant = V 2/R, where R = radius of
curvature at mid-depth.

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