slides 1 flow in open channel_2

7/29/2019 Slides 1 Flow in Open Channel_2

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1.1 Types of Flow

1.2 Geometric Characteristics of Channels/Types of

Channel

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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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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Types of Flow

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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Geometric Characteristics of Channels


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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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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 materials orartificial 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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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 withtime (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 arelatively short distance such as is the case with hydraulic jump

Gradually varied (GVF)the depth of flow changes rather slowwith distance such as is the case of a reservoir behind the dam


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Steady and Non-Steady Flow

Unsteady

Steady

Depth, y

Time, t


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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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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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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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Types of flow

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 f 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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slides 1 flow in open channel_2

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