chapter 1open channel hydraulics

8/3/2019 Chapter 1Open Channel Hydraulics

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OpenChannelFlowBudiS.Wignyosukarto

September12,2011

GrandCouleeDam

hAp://users.owt.com/chubbard/gcdam/html/gallery.html



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ProperesofOpenChannels

• Freewatersurface

– Posionofwatersurfacecanchangeinspaceand

me

• Manydifferenttypes

– River,streamorcreek;canal,flume,orditch;

culverts

• Manydifferentcross-seconalshapes

FundamentalofOpenChannel

• GeometricelementsofOpenChannel

• VelocityandDischarge

• HydrostacPressure

• Mass,MomentumandEnergytransferin

OpenChannel.

• OpenChannelFlowClassificaon• Conservaonlaws



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Hydrostac

Pressure

GeometricElement

• Kedalamanaliranh

• LebarMukairT

• KelilingBasahP

• Luastampangbasah

• RadiushidraulikR

• KemiringandasarSo



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Definition of Geometric Elements

R = hydraulic radius = A/PD = hydraulic depth = A/T

y = depth of flowd = depth of flow sectionT = top widthP = wetted perimeter

A = flow areaGupta, Fig. 10.1



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FlowClassificaon

• Uniform(normal)flow:Depthisconstantat

everyseconalonglengthofchannel

• Nonuniform(varied)flow:Depthchanges

alongchannel

– Rapidly-variedflow:Depthchangessuddenly

– Gradually-variedflow:Depthchangesgradually



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Kedalamanairnormal,pembendungan,loncat

airdanpengaruhmukaairhilir



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StateofFlow

• Flowinopenchannelsisaffectedbyviscous

andgravitaonaleffects

• ViscouseffectsdescribedbyReynolds

number,Re=VR/ν

• GravitaonaleffectsdescribedbyFroude

number,F=V/(gD)1/2

ViscousEffectsinopenchannels

• ForRe<500,viscousforcesdominateand

flowislaminar

• ForRe>2000,viscousforcesareweakand

flowisturbulent

• ForRebetween500and2000,thereisa

transionbetweenlaminarandturbulentflow



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GravitaonalEffects

• Cricalflowisthepointwherevelocityis

equaltothespeedofawaveinthewater,

FroudeNumber(Fr)

• ForFr=1,flowiscrical

• ForFr<1,flowissubcrical

– Wavecanmoveupstream

•

ForFr>1,flowissupercrical – Wavecannotmoveupstream

VelocityDistribuonInChannel

Depth-averagedvelocityisabove

thebedatabout0.48mesthedepth



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EquaonsofMoon

• Therearethreegeneralprinciplesusedin

solvingproblemsofflowinopenchannels:

– Connuity(conservaonofmass)

– Energy

– Momentum

• Forproblemsinvolvingsteadyuniformflow,

connuityandenergyprinciplesaresufficient

ConservaonofMass

• Sincewaterisessenallyincompressible,

conservaonofmass(connuity)reducesto

thefollowing:dischargein=dischargeout

• Statedintermsofvelocityandarea:

Q = V1A1 = V2A2



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Control Volume for Open Channels

Gupta, Fig. 10.4

ConservaonofEnergy

• Conservaonofenergyappliedtocontrol

volumeresultsinthefollowing:

f h g

V y Z

g

V y Z +++=++

22

2

2

222

2

1

111α α (10.6)

where Z1,Z2areelevaonsofthebed,

y1,y2aredepthsofflow,

V1,V2arevelocies,

α1,α2arekinecenergycorrecons,and

hf isthefriconalloss.



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Momentum

( )ss

mvF Δ=∑

Basicrelaonshipinmechanics:

Sumofforcesinthes

direcon

Changeinmomentuminthes

direcon

mass

Velocityinthes

direcon

Momentumcont.

• Foraconstantmassandaperunitwidth

consideraon:(rectangularchannel)

( ) ( )12 vvqmv s−=Δ

ρ



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Momentumforces–OpenChannelpplicaon

v2

v1

P1

P2

W

Θ

WsinΘ

Rf

L

f 21sR PsinWPF −−θ+=∑

MomentumForcescont.

• Rf isthefriconalresistance.

• P1andP2arepressureforcesperunitwidthgiven

by:

2yP

2

γ=



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Momentumcontd.• Combiningtermsweget:

)vv(qR sinW2

y

2

y12f

2

2

2

1 −ρ=−θ+

γ−

γ

Exercises

chapter 1open channel hydraulics

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