Flow types

CONTENT

Introduction

Types of Open Channel

Classification based on channel flow

Geometric properties of open channels

Experiment

2

INTRODUCTION

An open channel is a waterway, canal or conduit in which a liquid

flows with a free surface.

A channel is open or closed as long as its surface is exposed to

constant pressure.

In the absence of any other channel control, the flow is controlled

only by friction with the bed and the sides of the channel.

3

TYPES OF OPEN CHANNEL

Natural flows: rivers,

creeks, floods, etc.

Human-made systems:

fresh-water aqueducts,

irrigation, sewers,

drainage ditches, etc.

4

CLASSIFICATION BASED ON CHANNEL FLOW

Steady flow & Unsteady flow

Uniform flow& Non-Uniform flow

Laminar flow & turbulent flow

Subcritical flow, critical flow, Supercritical flow

5

Steady flow

Following remain

constant w.r.t time:

Depth of flow

velocity of flow

Flow rate

Unsteady flow

Following changes w.r.t

time:

Depth of flow

velocity of flow

Flow rate

Open

Channel

Steady Flow

= 0

Open Channel

Unsteady Flow

≠ 0

6

Uniform flow

Following remain

constant w.r.t Length of

channel:

Depth of flow

Velocity of flow

Slope of channel

Cross section

Non-Uniform flow

Following changes w.r.t

Length of channel:

Depth of flow

Velocity of flow

Slope of channel

Cross section

Rapidly

Varied Flow

i.e : hydraulic

jump

Non-Uniform Flow

≠ 0

Uniform Flow

= 0

Gradually

Varied flow

i.e : upstream

of obstruction7

Flow Classifications

Depending on the Reynolds number, Re

Laminar Flow (if Re < 500): very slow and shallow flowing

water in very smooth open channels.

Turbulent Flow (if Re > 1000): ordinary flow in ordinary

open channels.

Transition Flow (if 500 < Re < 1000)

V = average channel velocity

L = length of channel

v = kinematic viscosity of fluid

8

Depending on Froude number, Fr

Fr = 1 : Critical Flow

Fr < 1 : Subcritical Flow – slow flowing water

Fr > 1 : Supercritical Flow – fast flowing water

V = average channel velocity

g = gravity acceralation

D = hydraulics water depth

9

Prismatic Channel

It has constant shape & shize & is laid to a constant slope

Ex.

Some artificial channel

Laboratory flumes

Non- Prismatic channel

If its size, shape or slope changes along he length

Ex.

All natural nallas, stream, rivers, etc.,

10

GEOMETRIC PROPERTIES OF OPEN CHANNELS

Open Channel

11

GEOMETRIC PROPERTIES OF OPEN CHANNELS

The terminology of geometric elements

12

Type of channel

TOP WIDTH, T

AREA, A WETTED PERIMETER, P

RECTANGULAR B By B + 2y

TRAPEZOIDAL B+2my By + my2 B+2y √ 1+m2

Where,

GEOMETRIC PROPERTIES OF OPEN CHANNELS

13

Hydraulic Jump

The hydraulic jump is defined as the rise of water

level, which takes place due to transformation of the

unstable shooting flow (super-critical) to the stable

streaming flow (sub-critical).

When hydraulic jump occurs, a loss of energy due to

eddy formation and turbulence flow occurs.

Hydraulic Jump

Applications of Hydraulic Jump

Usually hydraulic jump reverses the flow of water. This

phenomenon can be used to mix chemicals for water

purification.

Hydraulic jump usually maintains the high water level on the

down stream side. This high water level can be used for

irrigation purposes.

Hydraulic jump can be used to remove the air from water

supply and sewage lines to prevent the air locking.

It prevents the scouring action on the down stream side of the

dam structure

Location of Hydraulic Jump

The most typical cases for the location of hydraulic

jump are:

1. Below control structures like weir, sluice are used in

the channel

2. when any obstruction is found in the channel,

3. when a sharp change in the channel slope takes

place.

4. At the toe of a spillway dam

Effect of Hydraulic Jump

Actually the hydraulic jump usually acts as the energy

dissipator. It clears the surplus energy of water.

Due to the hydraulic jump, many noticeable able disturbances

are created in the flowing water like eddies, reverse flow.

Usually when the hydraulic jump takes place, the considerable

amount of air is trapped in the water. That air can be helpful in

removing the wastes in the streams that are causing pollution.

Hydraulic jump also make the work of different hydraulic

structures, effective like weirs, notches and flumes etc.

Where,

Geometric Properties of channels

UNIFORM FLOW IN OPEN CHANNELS

Definitions

a) Open Channel: Duct through whichLiquid Flows with a Free Surface - River,Canal

b) Steady and Non- Steady Flow: InSteady Flows, all the characteristics of floware constant with time. In unsteady flows,there are variations with time.

Parameters of Open Channels

a) Wetted Perimeter, P : The Length of contactbetween Liquid and sides and base of Channel

P = B + 2 D ; D = normal depth

Hydraulic Mean Depth or Hydraulic Radius (R): Ifcross sectional area is A, then R = A/P, e.g. forrectangular channel, A = B D, P = B +2D

Area, A

Wetted Perimeter

D

B

Empirical Flow Equations for Estimating Normal Flow Velocities

a) Chezy Formula (1775):

Can be derived from basic principles. It states that: ;

Where: V is velocity; R is hydraulic radius and S isslope of the channel. C is Chezy coefficient and is afunction of hydraulic radius and channel roughness.

SRCV

Definitions

a) Freeboard: Vertical distance between

the highest water level anticipated in the

design and the top of the retaining banks. It

is a safety factor to prevent the overtopping of

structures.

b) Side Slope (Z): The ratio of the

horizontal to vertical distance of the sides of

the channel. Z = e/d = e’/D

DESIGN OF CHANNELS FOR STEADY UNIFORM FLOW

Channels are very important in Engineering projects

especially in Irrigation and, Drainage.

Channels used for irrigation are normally called canals

Channels used for drainage are normally called drains.

MOST EFFICIENT SECTION

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 reduceconstruction costs

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:

1.the wetted perimeter is also minimum,

2.the semi-circle section (semi-circle having its centre in the surface)

is the best hydraulic section

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 SECTIONFor a rectangular section

Q=AV, where Q=discharge through the

channel,

A=area of flow.

V=velocity with which

water is flowing in the

channel.

For Q to be maximum ,V needs to be

maximum, Since A = constant.

But V=Cmi

Where m= hydraulic mean depth.

i= bed slope.

m=A/P where P=wetted perimeter.

For m to be maximum ,P minimum

A=BDB=A/D;P=B+2D ,thenP=A/D+2D

𝑑𝑃

𝑑𝐷=

−𝐴

𝐷2+ 2

𝑑𝑃

𝑑𝐷= 0

−𝐴

𝐵2+ 2 = 0

𝐷2 =𝐴

2=

𝐵𝐷

2

D =𝐵

2

𝑚 =𝐵𝐷

𝐵 + 2𝐷=

2𝐷2

2𝐷 + 2𝐷=

𝐷

2

𝑚 =𝐷

2

TRAPEZOIDAL SECTION

For a rectangular section

Q=AV, where Q=discharge through the

channel,

A=area of flow.

V=velocity with which

water is flowing in the

channel.

For Q to be maximum ,V needs to be

maximum, Since A = constant.

But V=Cmi

Where m= hydraulic mean depth.

i= bed slope.

m=A/P where P=wetted perimeter.

For m to be maximum ,P minimum

𝐴 = 𝐵𝐷 + 𝑛𝐷2

𝑃 = 𝐵 + 2𝐷 1 + 𝑛2

𝐵 =𝐴

𝐷−𝑛𝐷2

𝐷=

𝐴

𝐷− 𝑛𝐷

𝑃 =𝐴

𝐷− 𝑛𝐷 + 2𝐷 1 + 𝑛2

𝑑𝑃

𝑑𝐷=

−𝐴

𝐷2− 𝑛 + 2 1 + 𝑛2

𝑑𝑃

𝑑𝐷= 0,⇒

−𝐴

𝐷2− 𝑛 + 2 1 + 𝑛2 = 0

2 1 + 𝑛2 = 𝑛 +𝐴

𝐷2

2 1 + 𝑛2 = 𝑛 +𝐵𝐷

𝐷2+ 𝑛

𝐵

𝐷= 2( 1 + 𝑛2 − 𝑛

𝐵 + 2𝑛𝐷

2= 𝐷 1 + 𝑛2

CONCLUSION:HALF OF THE TOP WIDTH = SIDE WALL LENGTH

m = D/2

The best side slope for

Trapezoidal section

𝑃 =𝐴

𝐷− 𝑛𝐷 + 2𝐷 1 + 𝑛2

𝑑𝑃

𝑑𝑛= 0 − 𝐷 +

2𝐷

2 1 + 𝑛2∗ 2𝑛

𝑑 𝑃 𝑑 𝑛 = 0

𝑛 = 1 √3

𝜃 = 600

open channel as shown Q=10m3/s, velocity =1.5m/s, for most

economic section. find wetted parameter, and the bed slope n=0.014.

Trapezoidal

Example 4

mD

DDDA

DkDBA

mV

QA

BD

DBD

kDBkD

78.1

667.6)2

36055.0(

667.65.1

10

6055.0

2

232

231

2

21

2

2

2

mP

kDDP

kDBP

49.72

3178.12)78.1(6055.0

126055.0

12

2

2

2

To calculate bed Slope

6.1941:1

5.189.0014.0

1

89.049.7

667.6

m 49.7

m 667.6

1

3

2

2

3

2

S

SV

P

AR

P

A

SRn

V

h

h