slides 1 flow in open channel
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1.1 Types of channel
1.2 Types of Flow
1.3 Geometric Characteristics of Channels
CHAPTER 1 : FLOW IN OPEN CHANNEL
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Introduction
Open Channel
A conduit in which a liquid flows with a free surface
any flow path with a free surface, which means that the flow path is
open to the atmosphere
Open channel hydraulics
The study of the physics of fluids flow in conveyances in which the
following fluids forms a free surface and is driven by gravity
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Free Surface
Essentially an interface between two fluids of different density
An interface between the moving liquid and overlying fluid medium and will
have constant pressure
In the case of atmosphere, the density of air is much lower than the density
for liquid such as water. In addition the pressure is constant. In the case of flowing liquid, the motion is usually caused by gravitational
effects and the pressure distribution within the fluid is generally hydrostatic
(flows are almost turbulent and unaffected by surface tension).
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1.1 : Types of Channel
There are 2 types of open channel; natural and artificial
Natural open channel are rivers, creeks and .... (have
irregular cross section)
All channels which have been developed by natural
processes and have not been significant improved by
humans Artificial open channel (human construction) are flumes
and canals.
All channels which have been developed by human
efforts
Within the broad category of artificial, open channel are
following subdivisions
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Open channel
Open channel flow can be classified into many types and described in
various way.
The types of flow encountered in open channel are classified with respect
to time, space, viscosity, density and gravity.
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Category of artificial open channel
Prismatic: A prismatic channel has both a constant cross-sectional shape
and bottom slope. Channels which do not meet this criteria are termed
non prismatic.
Canal: the term canal refer to a rather long channels may be either
unlined or lined with concrete, cement, grass, wood, bituminous materialsor artificial membrane.
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Category of artificial open channel
Flume: In practice, the term refers to a channels built above the ground
surface to convey a flow across a depression. Flumes are usually
constructed of wood, metal, masonry or concrete. The term flumes is also
applied to laboratory channels constructed for basic and applied research.
Chute & Drop: A chute is a channel having a steep slope. A drop channelalso has a steep slope but is much shorter than a chute.
Culvert: A culvert flowing only partially full is an open channel primarily
used to convey a flow under highways, railroad embankments or runways.
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Category of artificial open channel
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Natural Open Channel
All natural channels generally have varying cross-sections and
consequently are non prismatic.
A nonprismatic channel varies in both the cross-sectional shape
and bed slope between any two selected points along the
channel length
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1.2 : Types of flow
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Primary criteria of classification
Variation of the depth of flow y in time, t and space, x.
Time
a flow can be classified as being:
Steady - which implies that the depth and velocity do not change with time( y/ t = 0)
Unsteady - which implies that the depth and velocity vary with time ( y/ t 0) Space
a flow can be classified as being:
Uniformif the depth and velocity of flow do not vary with distance( y/ x = 0)
Non uniform (varied flow) - if the depth and velocity vary with distance( y/ x 0)
Rapidly variedthe depth of flow changes rapidly over a relativelyshort distance such as is the case with hydraulic jumpGradually varied (GVF)the depth of flow changes rather slow withdistance such as is the case of a reservoir behind the dam
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Steady and Unsteady Flow
Unsteady
Steady
Depth, y
Time, t
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Cont : Steady-unsteady flows
The manner in which water moves through a open
channel or stream can vary from simple to complex.
Certain sections of the river often transition from one
type of flow condition to another and back again.
The changes of flow pattern with respect to timeand distance along the flow direction, it thus
classified into few types.
To classify types of flow, two condition were
examined: the uniformity of the flow within the
stream and the steadiness of the flow over time.
A steady flow is one in which the conditions ofvelocity, pressure, and cross-section may differ
from point to point but do not change with time.
If at any point in the fluid, the conditions
change with time, the flow is described as
unsteady. [v constant with time at any point]
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Uniform and Non-uniform flows
If the flow velocity is assumed to have the
same speed and direction at every point
within the fluid, it is said to be uniform
[uniform flowv remain at the samespeed and direction].
If at a given instant, the velocity is not thesame at every point, the flow is non-
uniform
[two types of non-uniform flow :
Gradually Varied Flow (GVF) and
Rapidly Varied Flow (RVF)].
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Flow categories
For steady uniform flow, the depth is constant with both time and distance. This constitutes the
fundamental type of flow in an open channel in which the gravity forces and the
resistance forces are balanced.
Steady non-uniform also called as steady varied flow. Depth varies with distance, but
not with time. This type of flow may either be gradually varied or rapidly varied.
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Cont : flow categories
Depth varies with both time and distance (very rare situation)
Every condition of the flow may change from point to point and with time at
every point.
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Flow classification
Laminar flow
one in which the viscous forces are so large relative to the inertial forces
that the flow is dominated by the viscous forces
In such a flow, the fluid particles move along definite, smooth paths in a
coherent fashion Transitional flow
One which can be classified as neither laminar nor turbulent.
In open channel flow, the characteristic length commonly
Turbulent flow The inertial forces are large relative to the viscous forces; hence, the
inertial forces dominate the situation
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Flow classification
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Viscosity
Depending on the ratio of the inertial forces to the viscous forces, a flow maybe classified as laminar, transitional or turbulent
The basis for this classification is a dimensionless parameter known as theReynolds number
Re= vL/
v = characteristic velocity of flow, often taken as the average velocity offlow
L = characteristic length
= kinematics viscosity = /
= dynamic viscosity
= density
In open channel flow, the characteristic length commonly used is the hydraulicradius, R which is the ratio of the flow area, A to the wetted perimeter, P.
Re < 2000 Laminar flow2000 < Re
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Density
Flow are classified as homogeneous or stratified on the basis of the
variation of density within the flow.
HomogeneousAll spatial dimensions the density of flow is constant
StratifiedThe density of the flow varies in any direction
The absence of a density gradient in most natural open-channel flowsdemonstrates that either the velocity of flow is sufficient to completely mix
the flow with respect to density or that the phenomena which tend to induce
density gradients are unimportant.
The importance of density stratification is that when stable density
stratification exists, i.e., density increase with depth or lighter fluid overliesheavier fluid, the effectiveness of turbulence as mixing mechanism is
reduced.
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Gravity
Depending on the magnitude of the ratio of inertial forces to gravity forces,
a flow is classified as subcritical, critical or supercritical.
The parameter on which this classification is based is known as the Froude
Number:
Where;
v = a characteristic velocity of flow
L = a characteristic of lengthA = flow area
T = width of free surface
gL
vFr
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Flow states
If Fr = 1, the flow is in a critical state with the inertial and the gravitationalforces in equilibrium.
If Fr < 1, the flow is in a subcritical state and the gravitational forces aredominant.
If Fr > 1, the flow is in supercritical state and the inertial forces are dominant.
The denominator of the Froude number is the celerity of an elementary gravitywave in shallow water.
Through theory of Mechanics of Wave;
c = gy
Where;
c = celerity
g = gravity
y d = the depth of flow which is a value assumption if the
channel is wide
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With this observation, the following interpretation can be applied to the
subcritical and supercritical of flow:
When the flow is subcritical, F1, the velocity of flow is greater than
the celerity of an elementary gravity wave. Therefore, such a wave can
propagate upstream against the flow and the upstream areas of the
channel are not in hydraulic communication with the downstream areas.
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1.3 : Geometric characteristic/Channel properties
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Velocity distribution
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The measured velocity in open channels are always vary across a
channel section because of friction along the boundary
The velocity distribution is not symmetric (as in pipe)
Flow may be either laminar or turbulent and determined by Reynolds
Number
Re4000 = Turbulent flow
2 0 U if fl i
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2.0 Uniform flow in open
channel
Energy grade line for open channel
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Fundamental equations
Equations describing fluid flows can be derived from 3 fundamental laws of physics
Conservation of mass
Conservation of energy
Conservation of momentum
Conservation of mass (continuity equation) : in incompressible flow system, mass must
be constant, i.e : mass in = mass out, thus
Consevation of energy (Bernuolli equation)
Conservation of momentum (newton 2nd Law)
2211 vAvAQ
lossheadenergy22
2
222
2
111
gv
gpz
gv
gpz
12 vvQF
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General Flow Equation
AVQWhere;
Q = discharge
A = cross section areaV = velocity
2 0 U if fl i
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InflowOutflow = Change in Storage
Inflow
1 2
A
A
3
Section AA
Change in Storage
Outflow
3a
3b
2.0 Uniform flow in open
channel
Continuity equations
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