slides 1 flow in open channel

7/29/2019 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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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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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

24


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Velocity distribution

26

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

slides 1 flow in open channel

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