hydraulic chapter1

7/23/2019 hydraulic Chapter1

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BFC21103Hydraulics

Chapter1.FlowinOpenChannel

TanLaiWai,WanAfnizan &Zarina Md Ali

[email protected]

Updated:September2014


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LearningOutcomes

Attheendofthischapter,studentsshouldbeableto:

i.

Defineand

explain

on

types

and

states

of

flow

ii. Identifytypesofopenchannels

iii. Defineopen

channel

geometries

BFC21103Hydraulics

Tanetal.([email protected])


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Openchannel

flow

is

flow

of

aliquid

in

aconduit

with

afree

surface

subjectedtoatmosphericpressure.

Examples:flowofwaterinrivers,canals,partiallyfullsewers and

drainsandflowofwateroverland.

Freesurface

Flow

Datum

x

y

u

yA

B

T

Figure.Sketchofopenchannelgeometry

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Stormwater Managementand

Road

Tunnel

(SMART),KualaLumpur,Malaysia

Tahan river

rapids

Siberianmeandering

river


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Practicalapplications:

a. flowdepthinrivers,canalsandotherconveyanceconduits,

b. changesin

flow

depth

due

to

channel

controls

e.g.

weirs,

spillways,andgates,

c. changesinriverstageduringfloods,

d. surfacerunofffromrainfalloverland,

e. optimalchanneldesign,andothers

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1.1FlowParametersandGeometricElements

a.Depthofflowyistheverticalmeasureofwaterdepth.

Normaldepthdismeasurednormaltothechannelbottom.

d=ycos

Formostapplications,dywhen10%,e.g.cos 1 =0.9998.

Freesurface

FlowQ

Datum

x

y d

So=bottomslope

Sw=watersurfaceslope

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b.FlowordischargeQisthevolumeoffluidpassingacrosssection

perpendiculartothedirectionofflowperunittime.

Meanvelocity

Vis

the

discharge

divided

by

the

cross

sectional

area

A

QV=

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c.WettedperimeterPisthelengthofchannelperimeterthatis

wettedorcoveredbyflowingwater.

A=crosssectionalarea

coveredby

flowing

water

B

=bottom

width

T

=top

width

A

P

y

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d.HydraulicradiusRistheratiooftheflowareaAtowetted

perimeterP.

B

T

A

P

y

P

AR =

e.HydraulicdepthDistheaveragedepthofirregularcrosssection.

T

AD ==

widthtop

areaflow


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Channelsection Area

A

Topwidth

T

Wettedperimeter

P

By B B+2y

Table.Openchannelgeometries

y

B

T

Rectangular

yz

T

Triangular

1 zy2 2zy

212 zy +

By

+

zy2 B+2zy 2

12 zyB ++yz

T

Trapezoidal

1

B

y

T

Circle

D ( )

sin8

2

D

2

D

2

sinD


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Find:

(a) TopsurfacewidthT,flowareaA,wettedperimeterP,and

hydraulicradiusR.

(b) If

Q=

2.4

m

3

/s,

determine

the

state

of

flow.(c) IflongitudinallengthL=50m,findthecosttoconstructthe

channel.Givenexcavationcost=RM3/m3 andliningcost=

RM5/m2.

Activity1.1

3m

2m

1m

60


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BFC21103Hydraulics


5774.060tan

1==

o

z

zyBT 2+=

( )( )25774.023+=T

m309.5=T

212 zyBP ++=

( ) 25774.01223 ++=P

m619.7=P

2zyByA +=

( ) ( )225774.023 +=A

2m309.8=A

P

AR =

619.7

309.8=R

m091.1=R

(a) TopsurfacewidthT,wettedareaA,wettedperimeterPand

hydraulic

radius

R.


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(b) IfQ=2.4m3/s,determinethestateofflow.

m/s2888.0309.8

4.2===

A

Qv

gDV=Fr

VR=Re


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(c) If thelengthofthechannelisL=50m,findthecosttoconstructthe

channel.

Given

excavation

cost

=

RM

3/m3

and

lining

cost

=

RM

5/m2

.

Volumeofexcavation LA = channel

5035774.033 2 +=

3m81.709=

Costofexcavation = costUnit 81.709m/3RM 3 =

42.2129RM=

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Areaoflining LPA = channellining

505774.01323 2

lining ++=A

3

lining m41.496=

A

Costoflining liningcostUnit A= 41.496m/5RM 2 =

05.2482RM=

Totalcost 05.2482RM42.2129RM += 611.474RM=

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Find:

(a) Flowarea

A

(b) WettedperimeterP

(c) HydraulicradiusR

Activity1.2

3m4m2m1m

2m

2m

1m A1

A2A

3

A4


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1.2TypesofOpenChannel

Prismaticandnonprismaticchannels

Prismaticchannelisthechannelwhichcrosssectionalshape,

sizeand

bottom

slope

are

constant.

Most

of

the

man

made

(artificial)channelsareprismaticchannelsoverlong

stretches.Examplesofmanmadechannelsareirrigation

canal,

flume,

drainage

ditches,

roadside

gutters,

drop,

chute,

culvertandtunnel.

Allnaturalchannelsgenerallyhavevaryingcrosssectionsand

thereforearenonprismatic.Examplesofnaturalchannelsare

tinyhillsiderivulets,throughbrooks,streams,riversandtidalestuaries.


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Rigidandmobileboundarychannels

Rigid

channelsare

channels

with

boundaries

that

is

not

deformable.Channelgeometryandroughnessareconstant

overtime.Typicalexamplesarelinedcanals,sewersandnon

erodibleunlinedcanals.

Mobileboundarychannelsarechannelswithboundariesthatundergodeformationduetothecontinuousprocessof

erosionanddepositionduetotheflow.Examplesareunlined

manmade

channels

and

natural

rivers.


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Canalsisusuallyalongandmildsloped

channelbuiltintheground,which

maybeunlinedorlinedwith

stonedmasonry,

concrete,

cement,

woodorbituminousmaterial.

Griboyedov Canal,St.

Petersburg,

Russia

Terusan WanMuhammadSaman,Kedah


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ThisflumedivertswaterfromWhiteRiver,

Washingtontogenerateelectricity BullRunHydroelectricProjectdiversionflume

Flumesisachannelofwood,metal,concrete,ormasonry,usually

supportedonorabovethesurfaceofthegroundtocarrywater

acrossadepression.


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Openchannel

flume

in

laboratory


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Chuteisachannelhavingsteepslopes.

Naturalchute(falls)ontheleftandmanmadeloggingchuteontheright

ontheCoulonge River,Quebec,Canada


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Dropissimilartoachute,butthechangeinelevationiswithina

shortdistance.

ThespillwayofLeasburgDiversionDamisaverticalhard

basindropstructuredesignedtodissipateenergy


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Stormwater sewer

isadrainordrainsystem

designedtodrainexcessrain

frompavedstreets,parkinglots,

sidewalksand

roofs.

Stormdrain

receiving

urban

runoff

Stormsewer


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Openchannel

flow

conditions

can

be

characterised

with

respect

to

space(uniformornonuniformflows)andtime(steadyorunsteady

flows).

Space howdotheflowconditionschangealongthereachofan

openchannelsystem.

a.Uniform

flow

depth

of

flow

is

the

same

at

every

sectionoftheflowdy/dx=0

b.Nonuniformflow depthofflowvariesalongtheflow

dy/dx0


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a.Uniform

flow

b.Nonuniformflowy1

y2 Depthchanges

along

the

channel

yy Constant

waterdepth

x

Depthof

flow

is

the

same

at

every

section

along

the

channel, 0

dd =y

Depthofflowvariesatdifferentsectionsalongthechannel, 0d

d

x

y


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Time howdotheflowconditionschangeovertimeataspecific

sectioninanopenchannelsystem.

c.Steady

flow

depth

of

flow

does

not

change/

constant

duringthetimeintervalunder

considerationdy/dt=0

d.Unsteady

flow

depth

of

flow

changes

with

time

dy/dt0


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c.Steady

flow

d.Unsteadyflow

y1

Time

=

t1

y2

Time

=

t2

y1

t3

t2

t1

Depthofflowisthesameateverytimeinterval, 0d

d=

t

y

Depthofflowchangesfromtimetotime, 0d

d

t

y

y1=y2

y1y2y3


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Theflowisrapidlyvariedifthedepthchangesabruptlyovera

comparativelyshortdistance.Examplesofrapidlyvariedflow

(RVF)arehydraulicjump,hydraulicdrop,flowoverweirandflow

underasluice

gate.

Theflowisgraduallyvariedifthedepthchangesslowlyovera

comparativelylongdistance.Examplesofgraduallyvariedflow

(GVF)are

flow

over

amild

slope

and

the

backing

up

of

flow

(backwater).


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RVF RVFGVF RVFGVF RVFGVF

Sluice

Hydraulic

jumpFlowover

weir

Hydraulic

dropContraction

below

the

sluice


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1.4StateofFlow

Thestateorbehaviourofopenchannelflowisgovernedbasicallybytheviscosityandgravityeffectsrelativetotheinertialforcesof

theflow.

Effectofviscosity dependingontheeffectofviscosityrelativeto

inertialforces,theflowmaybeinlaminar,

turbulent,ortransitionalstate.

Reynoldsnumberrepresentstheeffectof

viscosityrelativetoinertia,

VR=Re

whereVisthevelocity,Risthehydraulicradiusofa

conduitandisthekinematicviscosity(forwaterat

20C,=1.004106 m2/s,dynamicviscosity=

1.00210

3 Ns/m2 anddensity

=

998.2

kg/m3).


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