hydraulics topic 1 flow in open channel.pdf

8/18/2019 hydraulics Topic 1 Flow in Open Channel.pdf

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Hydraulics

Topic 1. Flow in Open Channel

Assoc. Prof. Dr. Tan Lai [email protected]

Dr. Mohd Ariff bin Ahmad [email protected]


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Open channel flow is flow of a liquid in a conduit with a free surface

subjected to atmospheric pressure.

Examples: flow of water in rivers, canals, partially full sewers and

drains and flow of water over land.

Free surface

Datum

y A

B

T

Figure. Sketch of open channel geometry

BFC21103 HydraulicsTan et al. ([email protected])


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Stormwater Management and Road Tunnel

(SMART), Kuala Lumpur, Malaysia

Tahan river

rapids

Siberian meandering

river


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Practical applications:

a. flow depth in rivers, canals and other conveyance conduits,

b. changes in flow depth due to channel controls e.g. weirs,

spillways, and gates,

c. changes in river stage during floods,

d. surface runoff from rainfall over land,

e. optimal channel design, and others



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1.1 Flow Parameters and Geometric Elements

a. Depth of flow y is the vertical measure of water depth.

Normal depth d is measured normal to the channel bottom.

d = y cos

For most applications, d y when 10%, e.g. cos 1° = 0.9998.

Free surface

Datum

So = bottom slope

Sw = water surface slope



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b. Flow or discharge Q is the volume of fluid passing a cross-sectionperpendicular to the direction of flow per unit time.

Mean velocity V is the discharge divided by the cross-sectional area

A

QV



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c. Wetted perimeter P is the length of channel perimeter that is

wetted or covered by flowing water.

A = cross sectional area

covered by flowing water

B = bottom

width

T = top width

A

P

y



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d. Hydraulic radius R is the ratio of the flow area A to wetted

perimeter P.

B

T

A

P

y

P

AR

e. Hydraulic depth D is the average depth of irregular cross section.

T

AD

widthtop

areaflow


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Channel sectionArea

A

Top width

T

Wetted perimeter

P

By B B + 2y

Table. Open channel geometries

y

B

T

Rectangular

yz

T

Triangular

1 zy 2

2zy2

12 zy

By + zy 2 B + 2zy2

12 zy B y

z

T

Trapezoidal

1

B

y

T

Circle

2 D

sin228

2

D

D sinD


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5774.060tan1

z

zy BT 2

25774.023T

m309.5T

212 zy BP

25774.01223 P

m619.7P

2zy By A

225774.023 A

2m309.8 A

P

AR

619.7

309.8R

m091.1R

(a) Top surface width T , wetted area A, wetted perimeter P and

hydraulic radius R.


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(b) If Q = 2.4 m3/s, determine the state of flow.

m/s2888.0309.8

4.2

A

Qv

gD

V Fr

VRRe


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(c) If the length of the channel is L = 50 m, find the cost to construct the

channel. Given excavation cost = RM 3/m3 and lining cost = RM 5/m2.

Volume of excavation L A channel

5035774.0332

3m81.709

Cost of excavation costUnit 81.709m/3RM3

42.2129RM



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Area of lining LP A channellining

505774.01323 2lining A

3

lining m41.496 A

Cost of lining l inincost Unit A 41.496m/5RM2

05.2482RM

Total cost 05.2482RM42.2129RM 611.474RM



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Find T , A, P, R, and D

Additional Question for Assignment #1

1.2 m

1.5 m

3

2 1.2 m

1.5 m

0.3 m


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Find:

(a) Flow area A

(b) Wetted perimeter P

(c) Hydraulic radius R

Activity 1.2

3 m4 m2 m1 m

2 m

2 m

1 m A1

A2 A3

A4


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1.2 Types of Open Channel

Prismatic and non-prismatic channels

Prismatic channel is the channel which cross-sectional shape,

size and bottom slope are constant. Most of the man-made

(artificial) channels are prismatic channels over long stretches.

Examples of man-made channels are irrigation canal, flume,drainage ditches, roadside gutters, drop, chute, culvert and

tunnel.

All natural channels generally have varying cross-sections and

therefore are non-prismatic. Examples of natural channels aretiny hillside rivulets, through brooks, streams, rivers and tidal

estuaries.


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Rigid and mobile boundary channels

Rigid channels are channels with boundaries that is not

deformable. Channel geometry and roughness are constant

over time. Typical examples are lined canals, sewers and non-

erodible unlined canals.

Mobile boundary channels are channels with boundaries that

undergo deformation due to the continuous process of

erosion and deposition due to the flow. Examples are unlined

man-made channels and natural rivers.


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Canals

is usually a long and mild-sloped

channel built in the ground, whichmay be unlined or lined with stoned

masonry, concrete, cement, wood

or bituminous material.

Griboyedov Canal, St. Petersburg, Russia

Terusan Wan Muhammad Saman, Kedah


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This flume diverts water from White River,

Washington to generate electricity Bull Run Hydroelectric Project diversion flume

Flumes

is a channel of wood, metal, concrete, or masonry, usuallysupported on or above the surface of the ground to carry water

across a depression.


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Open-channel flume in laboratory


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Chute

is a channel having steep slopes.

Natural chute (falls) on the left and man-made logging chute on the right

on the Coulonge River, Quebec, Canada


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Drop

is similar to a chute, but the change in elevation is within ashort distance.

The spillway of Leasburg Diversion Dam is a vertical hard

basin drop structure designed to dissipate energy


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Stormwater sewer

is a drain or drain system

designed to drain excess rainfrom paved streets, parkinglots,

sidewalks and roofs.

Storm drain receiving urban runoff

Storm sewer


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Open channel flow conditions can be characterised with respect to

space (uniform or non-uniform flows) and time (steady or unsteadyflows).

Space - how do the flow conditions change along the reach of an

open channel system.

a. Uniform flow - depth of flow is the same at every

section of the flow dy /d x = 0

b. Non-uniform flow - depth of flow varies along the flow

dy /d x 0


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a. Uniform flow

b. Non-uniform flow y 1

y 2

y

y

x

Depth of flow is the same at every section along the channel, 0d

d

x

y

Depth of flow varies at different sections along the channel, 0d

d

x

y


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Time - how do the flow conditions change over time at a specific

section in an open channel system.

c. Steady flow - depth of flow does not change/ constant

during the time interval under

consideration dy /dt = 0

d. Unsteady flow - depth of flow changes with time

dy /dt 0


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c. Steady flow

d. Unsteady flow

y 1

Time = t 1

y 2

Time = t 2

y 1

t 3

t 2

t 1

Depth of flow is the same at every time interval, 0

d

d

t

y

Depth of flow changes from time to time, 0d

d

t

y

y 1 = y 2

y 1 y 2 y 3


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The flow is rapidly varied if the depth changes abruptly over a

comparatively short distance. Examples of rapidly varied flow (RVF) are hydraulic jump, hydraulic drop, flow over weir and flow

under a sluice gate.

The flow is gradually varied if the depth changes slowly over acomparatively long distance. Examples of gradually varied flow

(GVF) are flow over a mild slope and the backing up of flow

(backwater).


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RVF RVFGVF RVFGVF RVFGVF

Sluice

Hydraulic

jump Flow overweir

Hydraulic

dropContraction

below the sluice


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1.4 State of Flow

The state or behaviour of open-channel flow is governed basically

by the viscosity and gravity effects relative to the inertial forces ofthe flow.

Effect of visco sity - depending on the effect of viscosity relative to

inertial forces, the flow may be in laminar,

turbulent, or transitional state.

- Reynolds number represents the effect of

viscosity relative to inertia,

VR

Rewhere V is the velocity, R is the hydraulic radius of a

conduit and is the kinematic viscosity (for water at

20C, = 1.004 106 m2/s, dynamic viscosity =

1.002 103 Ns/m2 and density = 998.2 kg/m3).


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Re < 500 the flow is laminar

500 < Re < 12500 the flow is transitional

Re > 12500 the flow is turbulent

The flow is laminar if the viscous forces are dominant relative

to inertia. Viscosity will determine the flow behaviour. In

laminar flow, water particles move in definite smooth paths.

The flow is turbulent if the inertial forces are dominant than

the viscous force. In turbulent flow, water particles move in

irregular paths which are not smooth.

VRRe


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Effect of gravity - depending on the effect of gravity forces relative

to inertial forces, the flow may be subcritical,critical and supercritical.

- Froude number represents the ratio of inertial

forces to gravity forces,

gDV Fr

where V is the velocity, D is the hydraulic depth

of a conduit and g is the gravity acceleration (g =

9.81 m/s

2

).


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Fr < 1 , the flow is in subcritical state

Fr = 1 , the flow is in critical state

Fr > 1 , the flow is in supercritical state

gDV

gDV

gDV


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1.5 Regimes of Flow

A combined effect of viscosity and gravity may produce any one ofthe following four regimes of flow in an open channel:

a. subcritical - laminar , when Fr < 1 and Re < 500

b. supercritical - laminar , when Fr > 1 and Re < 500

c. supercritical - turbulent , when Fr > 1 and Re > 12500

d. subcritical - turbulent , when Fr < 1 and Re > 12500


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Assignment #1

Q1. [Final Exam Sem I, Session 2010/2011]

Justify the difference between:(a) uniform flow and non-uniform flow

(b) state of flow using Reynolds number Re and Froude number Fr.

Q2. [Final Exam Sem I, Session 2008/2009](a) Define

(i) Wetted perimeter

(ii) Gradually-varied flow

(iii) Non-uniform flow

(iv) Froude number

(b) Explain the differences between canal and sewer.


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Q3. [Final Exam Sem I, Session 2006/2007]

Define(a) Reynolds number

(b) Froude number

(c) Hydraulic radius

(d) Prismatic channel

(e) Uniform flow

Q4. A discharge of 16.0 m3/s flows with a depth of 2.0 m in a rectangular

channel of 4.0 m wide. Determine the state of flow based on

(a) Froude number, and

(b) Reynolds number.


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Q5. A triangular channel of apex angle 120° carries a discharge of 1573 L/s.

Calculate the critical depth.

- End of Question -


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THANK YOU

d l

hydraulics topic 1 flow in open channel.pdf

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