bfc21103 chapter1

BFC21103Hydraulics

Chapter1.FlowinOpenChannel

TanLaiWai,WanAfnizan&[email protected]

Updated:February2015

LearningOutcomes

Attheendofthischapter,studentsshouldbeableto:

i. Defineandexplainontypesandstatesofflowinopenchannels

ii. Identifytypesofopenchannels

iii. Defineopenchannelgeometries

BFC21103HydraulicsTanetal.([email protected])

Openchannelflowisflowofaliquidinaconduitwithafreesurfacesubjectedtoatmosphericpressure.

Examples:flowofwaterinrivers,canals,partiallyfullsewers anddrainsandflowofwateroverland.

Freesurface

Flow

Datum x

y

uyA

B

T

Figure.Sketchofopenchannelgeometry


StormwaterManagementandRoadTunnel(SMART),KualaLumpur,Malaysia

Tahanriverrapids

Siberianmeanderingriver

Comparisonbetweenpipeflowandopenchannelflow

Channelbottom

Watersurface

Datumline

1 2

V1

V2

Energyline

y1

y2

z2

hf

gV2

22

z1

gV2

21

Centerlineofpipe

Hydraulicgradeline

Datumline

1 2

V1

V2

Energyline

y1

y2

z2

hf

gV2

22

z1

gV2

21

Practicalapplicationsofopenchannelflowstudies:

a. flowdepthinrivers,canalsandotherconveyanceconduits,

b. changesinflowdepthduetochannelcontrolse.g.weirs,spillways,andgates,

c. changesinriverstageduringfloods,

d. surfacerunofffromrainfalloverland,

e. optimalchanneldesign,andothers


1.1FlowParametersandGeometricElementsa. Depthofflowy istheverticalmeasureofwaterdepth.

Normaldepthd ismeasurednormaltothechannelbottom.

d =y cosFormostapplications,d y when 10%,e.g.cos1 =0.9998.

Freesurface

FlowQ

Datum x

y d

So =bottomslope

Sw =watersurfaceslope


b. Flow ordischargeQ isthevolumeoffluidpassingacrosssectionperpendiculartothedirectionofflowperunittime.

MeanvelocityV isthedischargedividedbythecrosssectionalarea

AQ

V =


c.WettedperimeterP isthelengthofchannelperimeterthatiswettedorcoveredbyflowingwater.

A=crosssectionalareacoveredbyflowingwater

B=bottomwidth

T=topwidth

AP

y



d. HydraulicradiusR istheratiooftheflowareaA towettedperimeterP.

B

T

AP

y

PA

R =

e. HydraulicdepthD istheaveragedepthofirregularcrosssection.

TA

D ==widthtopareaflow

ChannelsectionAreaA

TopwidthT

WettedperimeterP

By B B +2y

Table.Openchannelgeometries

y

B

T

Rectangular

yz

T

Triangular

1 zy2 2zy212 zy +

By+zy2 B +2zy 212 zyB ++yz

T

Trapezoidal

1

B

y

T

Circle

2D( ) sin22

8

2

D DsinD


Find:

(a) TopsurfacewidthT,flowareaA,wettedperimeterP,andhydraulicradiusR.

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

(c) IflongitudinallengthL =50m,findthecosttoconstructthechannel.Givenexcavationcost=RM3/m3 andliningcost=RM5/m2.

Activity1.1

3m

2m

1m

60


5774.060tan1 == oz

zyBT 2+=( )( )25774.023+=Tm309.5=T

212 zyBP ++=( ) 25774.01223 ++=Pm619.7=P

2zyByA +=( ) ( )225774.023 +=A

2m309.8=A

PA

R =

619.7309.8=R

m091.1=R

(a) TopsurfacewidthT,wettedareaA,wettedperimeterP andhydraulicradiusR.


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

m/s2888.0309.84.2 ===

AQ

V

gDV=Fr

VR=Re

(c) IfthelengthofthechannelisL =50m,findthecosttoconstructthechannel.Givenexcavationcost=RM3/m3 andliningcost=RM5/m2.

Volumeofexcavation LA = channel( ) 5035774.033 2 +=

3m81.709=

Costofexcavation = costUnit 81.709m/3RM 3 =42.2129RM=


Areaoflining LPA = channellining ( ) 505774.01323 2lining ++=A3

lining m41.496=A

Costoflining liningcostUnit A= 41.496m/5RM 2 =05.2482RM=

Totalcost 05.2482RM42.2129RM += 611.474RM=



Find:

(a) FlowareaA

(b) WettedperimeterP

(c) HydraulicradiusR

Activity1.2

3m4m2m1m

2m

2m

1m A1

A2 A3A4


1.2TypesofOpenChannel

Prismatic andnonprismatic channelsPrismaticchannel isthechannelwhichcrosssectionalshape,sizeandbottomslopeareconstant.Mostofthemanmade(artificial)channelsareprismaticchannelsoverlongstretches.Examplesofmanmadechannelsareirrigationcanal,flume,drainageditches,roadsidegutters,drop,chute,culvertandtunnel.

Allnaturalchannels generallyhavevaryingcrosssectionsandthereforearenonprismatic.Examplesofnaturalchannelsaretinyhillsiderivulets,throughbrooks,streams,riversandtidalestuaries.


Rigid andmobileboundary channelsRigidchannels arechannelswithboundariesthatisnotdeformable.Channelgeometryandroughnessareconstantovertime.Typicalexamplesarelinedcanals,sewersandnonerodibleunlinedcanals.

Mobileboundarychannels arechannelswithboundariesthatundergodeformationduetothecontinuousprocessoferosionanddepositionduetotheflow.Examplesareunlinedmanmadechannelsandnaturalrivers.


Canalsisusuallyalongandmildslopedchannelbuiltintheground,whichmaybeunlinedorlinedwithstonedmasonry,concrete,cement,woodorbituminousmaterial.

GriboyedovCanal,St.Petersburg,Russia

TerusanWanMuhammadSaman,Kedah


ThisflumedivertswaterfromWhiteRiver,Washingtontogenerateelectricity BullRunHydroelectricProjectdiversionflume

Flumesisachannelofwood,metal,concrete,ormasonry,usuallysupportedonorabovethesurfaceofthegroundtocarrywateracrossadepression.


Openchannelflumeinlaboratory


Chuteisachannelhavingsteepslopes.

Naturalchute(falls)ontheleftandmanmadeloggingchuteontherightontheCoulongeRiver,Quebec,Canada


Dropissimilartoachute,butthechangeinelevationiswithinashortdistance.

ThespillwayofLeasburgDiversionDamisaverticalhardbasindropstructuredesignedtodissipateenergy


Stormwatersewerisadrainordrainsystemdesignedtodrainexcessrainfrompavedstreets,parkinglots,sidewalksandroofs.

Stormdrainreceivingurbanrunoff

Stormsewer


1.3TypesandClassificationofOpenChannelFlows

Openchannelflow

Steadyflow Unsteadyflow

Uniformflow Nonuniformflow

GraduallyvariedflowRapidlyvariedflow

Varioustypesofopenchannelflow


Openchannelflowconditionscanbecharacterisedwithrespecttospace (uniformornonuniformflows)andtime (steadyorunsteadyflows).

Space howdotheflowconditionschangealongthereachofanopenchannelsystem.

a.Uniformflow depthofflowisthesameateverysectionoftheflowdy/dx =0

b.Nonuniformflow depthofflowvariesalongtheflowdy/dx 0


a.Uniformflow

b.Nonuniformflowy1

y2 Depthchangesalongthechannel

y y Constantwaterdepthx

Depthofflowisthesameateverysectionalongthechannel, 0dd =xy

Depthofflowvariesatdifferentsectionsalongthechannel, 0dd xy


Time howdotheflowconditionschangeovertimeataspecificsectioninanopenchannelsystem.

c.Steadyflow depthofflowdoesnotchange/constantduringthetimeintervalunderconsiderationdy/dt =0

d.Unsteadyflow depthofflowchangeswithtimedy/dt 0


c.Steadyflow

d.Unsteadyflow

y1

Time=t1

y2

Time=t2

y1

t3

t2t1

Depthofflowisthesameateverytimeinterval, 0dd =ty

Depthofflowchangesfromtimetotime, 0dd ty

y1 =y2

y1 y2 y3


Theflowisrapidlyvaried ifthedepthchangesabruptlyoveracomparativelyshortdistance.Examplesofrapidlyvariedflow(RVF)arehydraulicjump,hydraulicdrop,flowoverweirandflowunderasluicegate.

Theflowisgraduallyvaried ifthedepthchangesslowlyoveracomparativelylongdistance.Examplesofgraduallyvariedflow(GVF)areflowoveramildslopeandthebackingupofflow(backwater).


RVF RVFGVF RVFGVF RVFGVF

Sluice

Hydraulicjump

Flowoverweir

Hydraulicdrop

Contractionbelowthesluice


1.4StateofFlowThestateorbehaviourofopenchannelflowisgovernedbasicallybytheviscosity andgravityeffects relativetotheinertialforces oftheflow.

Effectofvisco sity dependingontheeffectofviscosityrelativetoinertialforces,theflowmaybeinlaminar,turbulent,ortransitional state.

Reynoldsnumber representstheeffectofviscosityrelativetoinertia,

VR=Re

whereV isthevelocity,R isthehydraulicradiusofaconduitand isthekinematicviscosity(forwaterat20C, =1.004 106 m2/s,dynamicviscosity =1.002 103 Ns/m2 anddensity =998.2kg/m3).


Re


Effectofgravity dependingontheeffectofgravityforcesrelativetoinertialforces,theflowmaybesubcritical,criticalandsupercritical.

Froudenumber representstheratioofinertialforcestogravityforces,

gDV=Fr

whereV isthevelocity,D isthehydraulicdepthofaconduitandg isthegravityacceleration(g =9.81m/s2).


Fr1 ,theflowisinsupercriticalstate

gDV


1.5RegimesofFlow

Acombinedeffectofviscosityandgravitymayproduceanyoneofthefollowingfourregimesofflowinanopenchannel:

a. subcritical laminar ,whenFr12500

d. subcritical turbulent ,whenFr12500


Assignment#1

Q1. [FinalExamSemI,Session2010/2011]Justifythedifferencebetween:(a) uniformflowandnonuniformflow(b) stateofflowusingReynoldsnumberReandFroudenumberFr.

Q2. [FinalExamSemI,Session2008/2009](a) Define

(i) Wettedperimeter(ii) Graduallyvariedflow(iii) Nonuniformflow(iv) Froudenumber

(b) Explainthedifferencesbetweencanalandsewer.


Q3. [FinalExamSemI,Session2006/2007]Define(a) Reynoldsnumber(b) Froudenumber(c) Hydraulicradius(d) Prismaticchannel(e) Uniformflow

Q4. Adischargeof16.0m3/sflowswithadepthof2.0minarectangularchannelof4.0mwide.Determinethestateofflowbasedon(a) Froudenumber,and(b) Reynoldsnumber.


Q5. Atriangularchannelofapexangle120 carriesadischargeof1573L/s.Calculatethecriticaldepth.

EndofQuestion

1.2m

1.5m

32 1.2m

1.5m

0.3m

Q6. FindT,A,P,R,andD forthefollowingcompoundsections.

THANKYOU


bfc21103 chapter1

Documents

y cosformostapplications

ra topsurfacewidtht

volumeofexcavation la

freesurfaceflowqdatum

rec ifthelengthofthechannelisl

c iflongitudinallengthl

t212 zybp