chapter 1open channel hydraulics
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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
8/3/2019 Chapter 1Open Channel Hydraulics
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8/3/2019 Chapter 1Open Channel Hydraulics
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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
8/3/2019 Chapter 1Open Channel Hydraulics
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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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