Loading...

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

CHAPTER 6 Water Flow in Open Channels

University of Palestine Engineering

Hydraulics 2nd semester 2010-2011

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.

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).

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

HGL and velocity head. - The amount of energy loss when the liquid flows

from section 1 to section 2 is indicated by hL.

Introduction

Pipe system

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

HGL and velocity head. - 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.

Introduction

Open Channel

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.

Type of Open Channels

Type of Open Channels

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.

Type of Open Channels

- The most common shapes of prismatic channels are

rectangular, parabolic, triangular, trapezoidal

and circular.

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.

Types of Flow in Open Channels

Uniform Flow

Types of Flow in Open Channels

Types of Flow in Open Channels

- B). Steady and unsteady flow
- 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

Types of Flow in Open Channels

Recall that Reynolds number is the measure of

relative effects of the inertia forces to viscous

forces.

Types of Flow in Open Channels

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

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

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

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

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 .

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

Flow Formulas in Open Channels

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

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.

Example 2

Flow Formulas in Open Channels

open channel as shown, bed slope 691584, find

the flow rate using Chezy equation, C35.

Flow Formulas in Open Channels

Example 2 cont.

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.

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

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.

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.

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

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

Most Economical Section of Channels

Most Economical Rectangular Channel

Most Economical Section of Channels

Most Economical Trapezoidal Channel

or

Most Economical Section of Channels

Other criteria for economic Trapezoidal section

k

The best side slope for Trapezoidal section

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

Most Economical Section of Channels

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

Most Economical Section of Channels

Example 4 cont.

Max. Velocity

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.

Most Economical Section of Channels

Example 5 cont.

To calculate bed Slope

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.

Most Economical Section of Channels

Example 6 cont.

Variation of flow and velocity with depth in

circular pipes

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

Energy Principles in Open Channel Flow

The specific energy of a flowing liquid can be

re-written in the form

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

Energy Principles in Open Channel Flow

Specific Energy Curve (rectangular channel)

The graph between specific energy (x-axis) and

depth (yaxis) may plotted.

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.

Froude Number (Fr)

Energy Principles in Open Channel Flow

Critical Flow

Energy Principles in Open Channel Flow

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.

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 .

Energy Principles in Open Channel Flow

Rectangular Channel

d) Minimum Specific Energy in terms of critical

depth At (Emin , yc ) ,

Other Sections

Energy Principles in Open Channel Flow

at critical flow Fr 1 where

Rectangular section

Trapezoidal section

Circular section

Triangle section

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

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

Energy Principles in Open Channel Flow

Example 2 cont.

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.

Non-uniform Flow in Open Channels

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.

Non-uniform Flow in Open Channels

Classification of Channel-Bed Slopes

Non-uniform Flow in Open Channels

Classification of Flow Profiles (water surface

profiles)

Non-uniform Flow in Open Channels

Classification of Flow Profiles (water surface

profiles)

Non-uniform Flow in Open Channels

Classification of Flow Profiles (water surface

profiles)

Non-uniform Flow in Open Channels

Classification of Flow Profiles (water surface

profiles)

Non-uniform Flow in Open Channels

Classification of Flow Profiles (water surface

profiles)

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.

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.

Hydraulic Jump

Hydraulic Jump in Rectangular Channels

But for Rectangular section

Hydraulic Jump

Hydraulic Jump in Rectangular Channels

Hydraulic Jump

Hydraulic Jump in Rectangular Channels

Hydraulic Jump

Hydraulic Jump in Rectangular Channels

Hydraulic Jump

Hydraulic Jump

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

Example 2

Hydraulic Jump

dn Depth can calculated from manning equation

Hydraulic Jump

a)

b)

Hydraulic Jump

c)

http//www.haestad.com/library/books/awdm/online/w

whelp/wwhimpl/java/html/wwhelp.htm