HECRAS Basic Principles of Water Surface Profile Computations HECRAS wylis zedapiris profilis agebis ZiriTadi principebi

1
HECRAS Basic Principles of Water Surface Profile
ComputationsHECRAS wylis zedapiris profilis
agebis ZiriTadi principebi

• by G. Parodi
• WRS ITC The Netherlands
• g. parodi
• WRS-ITC- niderlandebi

2
What about water...wylis Sesaxeb . . .

• Incompressible fluid
• ukumSvadi siTxe
• must increase or decrease its velocity and depth
  to adjust to the channel shape
• siCqare da siRrme icvleba, matulobs an klebulobs
  raTa moergos kalapotis formas.
• High tensile strength
• maRali gaWimulobis Zala
• allows it to be drawn smoothly along while
  accelerating
• SesaZleblobas aZlevs gluvad gaiWimos aCqarebisas
• No shear strength
• ar xasiaTdeba gamWoli simtkiciT
• does not decelerate smoothly, results in standing
  waves, good canoeing, air entrainment, etc
• ar neldeba Seuferxebliv, Sedegad warmoiSveba
  mdgari (stacionaruli) talRebi, kargia kanoeTi
  curvisas, haeris CaTreva, a.S.

3
What about open channel flow...Ria kalapotis
dineba . . .

• A free surface
• Tavisufali zedapiri
• Liquid surface is open to the atmosphere
• siTxis zedapiri urTierTqmedebs atmosferosTan
• Boundary is not fixed by the physical boundaries
  of a closed conduit
• sazRvrebi araa dadgenili fizikuri sazRvriT,
  daxuruli wyalsadenis saxiT

4
Since the flow is incompressible, the product of
the velocity and cross sectional area is a
constant. Therefore, the flow must increase or
decrease its velocity and depth to adjust to the
shape of a channel. vinaidan dineba ukumSvadia,
aCqarebis da ganivi kveTis farTobis warmoebuli
aris mudmivi. Sesabamisad dinebis siCqare da
siRrme cvalebadia, matulobs an klebulobs raTa
moergos kalapotis formas.
VA constant A mudmiva Discharge is expressed
as Q VA xarji gamoixateba rogorc Q VA

• Q is flow Q - Q aris dineba Q
• V is velocity V - V aris siCqare V
• A is cross section area A
• A aris ganivi kveTis farTobi A

5
Open Channel Flow ControlsRia kalapotis dineba
- kontroli
Definition A control is any feature of a channel
for which a unique depth - discharge relationship
occurs. gansazRvreba kontroli aris dinebis
nebismieri maxasiaTebeli, romlisTvisac yalibdeba
erTaderTi (unikaluri) siRrme-xarjis
damokidebuleba. Weirs / Spillways wyalgadasaSvebi
Abrupt changes in slope or width uecari
cvlileba dinebis daxris kuTxeSi an siganeSi.
Friction - over a distance xaxuni garkveul
distanciaze
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Water goes downhill. What does that mean to
us?wyali miedineba damrecad. ras niSnavs es
CvenTvis?

• Water flowing in an open channel typically gains
  energy (kinetic) as it flows from a higher
  elevation to a lower elevation
• wylis dineba Ria kalapotSi rogorc wesi matebs
  energias (kinetikur energias) vinaidan is
  miedineba maRali wertilidan dabali wertilisken.
• It loses energy with friction and obstructions.
• xaxunTan da obstruqciasTan (dabrkoleba) erTad
  xdeba energiis dakargva.

7
Uniform or Normal FlowerTgvari da normuli dineba
The gravitational forces that are pushing the
flow along are in balance with the frictional
forces exerted by the wetted perimeter that are
retarding the flow. gravitaciuli Zalebi,
romlebic aCqareben dinebas imyofebian
wonasworobaSi xaxunis ZalebTan, daZabulobis
mateba xdeba sveli perimetris zegavleniT, rac
anelebs dinebas
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Over a long stretch of a river...mdinaris mTel
sigrZeze...
Average velocity is a function (slope and the
resistance to drag along the boundaries) saSualo
siCqare aris funqcia (ferdobis daxra da
winaRoba, romelic amuxruWebs dinebas zRurblis
gaswvriv)
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What does that mean?ras niSnavs es?
Assume a Hypothetical Channel warmovidginoT
hipoTeturi kalapoti Long prismatic (same section
over a long distance) channel grZeli prizmuli
(erTi da igive seqcia did manZilze) kalapoti No
change in slope, section, discharge ar gvaqvs
cvlileba dinebis daqanebSi, seqciebSi, xarjSi
Channel bottom is parallel to water surface is
parallel to energy grade line. The streamlines
are parallel. kalapotis fskeri wylis zedapiris
paraleluria da energiis xarisxis wrfis
paraleluria. veqtoruli wrfeebi paraleluria.
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Uniform flow occurs when the gravitational forces
are exactly offset by the resistance
forces ucvleli dineba warmoSveba maSin, rodesac
xdeba winaRobis Zalebis mier gravitaciuli Zalebis
kompensireba.
Uniform flow occurs when erTgvari dineba
warmoSveba roca

• Mean velocity is constant from section to section
• saSualo siCqare aris ucvleli seqciidan seqciamde
• Depth of flow is constant from section to section
• dinebis siRrme aris ucvleli seqciidan seqciamde
• Area of flow is constant from section to section
• dinebis farTobi aris ucvleli seqciidan seqciamde

Therefore It can only occur in very long,
straight, prismatic channels where the terminal
velocity of the flow is achieved Sesabamisad es
SeiZleba moxdes mxolod Zalian grZel, swor,
prizmul kalapotSi, sadac dineba aRwevs zRvrul
siCqares
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Normal Depth Applies to Different Types of
SlopessaSualo siRrme ukavSirdeba ferdobis
sxvadasxva tipis daqanebas.
cvalebadi nakadi
cvalebadi nakadi
n stands for normal n igulisxmeba saSualo s
stands for critical s igulisxmeba kritikuli
erTgvari nakadi
Yn
Yc
Cvalebadi nakadi
erTgvari nakadi
Mild Slope sustad daxrili ferdobi
Cvalebadi nakadi
erTgvari nakadi
Critical Slope kritikuli ferdobi
Yc
Yn
Steep Slope cicabo ferdobi
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If the flow is a function of the slope and
boundary friction, how can we account for it?Tu
dineba aris funqcia ferdobis daxrisa da xaxunis
Zalis, rogor SegviZlia gamoviangariSoT is?
13
0
Newton's second law niutonis meore kanoni
If velocity is constant, then acceleration is
zero. So use a simple force balance. Tu siCqare
aris mudmivi, maSin aCqareba nulis tolia.
Sesabamisad SegviZlia gamoviyenoT martivi Zalebis
balansi
where sadac
rearrange equation gadavaTamaSoT gantoleba
Gravity gravitacia
Friction xaxuni
small mcire
Antoine Chezy (18th century) antoni Cezi (18
saukune)
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Mannings equationmaningis gantoleba
dineba
koeficienti
farTobi
ferdobis daxra
dasvelebis perimetri
One of the most widely used to account for
friction losses erT erTi yvelaze farTod
gavrcelebuli meTodi xaxunis danakargis dasaTvlelad
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Mannings Equation - n unitsmaningis gantoleba
- n erTeuli
L length (feet, meters, inches, etc) L sigrZe
(futi, metri, inCi d.a.S. T time (seconds,
minutes, hours, etc) T dro (wami, wuTi, saaTi,
a.S.)
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Mannings nmaningis n
A bulk term, a function of grain size, roughness,
irregularities, etc Values been suggested since
turn of century (King 1918) niadagis zRvari aris
funqcia marcvlis zomis, xorklianobis (simqisis),
araerTgvarovnebis, a.S. sidide SemoRebuli iyo
gasuli saukunis dasawyisSi (kingi 1918)
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Mannings nmaningis n
A bulk term, a function of grain size, roughness,
irregularities, etc Values been suggested since
turn of century (King 1918) niadagis zRvari aris
funqcia marcvlis zomis, xorklianobis (simqisis),
araerTgvarovnebis, a.S. sidide SemoRebuli iyo
gasuli saukunis dasawyisSi (kingi 1918)
18
Guidance Available seek bibliography and the
WEBsaxelmZRvaneloebi moZebneT bibliografia da
internet saitebi
n0.018
NRCS - Fasken, 1963
n0.018
n0.014
n0.016
n0.020
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Mannings n in Steep Channelmaningis n cicabod
daxril kalapotSi

• Streams may appear to be super critical but are
  just fast subcritical
• nakadi SeiZleba Candes super kritikuli, magram
  iyos mxolod swrafi subkritikuli
• Jarrets Eqn (ASCE J. of Hyd Eng, Vol. 110(11)) (
  R hydraulic radius in feet)
• jaretis gantoleba (ASCE J. of Hyd Eng, Vol.
  110(11)) ( R hidravlikuri radiusi futebSi)

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What can we do with Mannings Equation?ra
SesaZlebloba aqvs maningis gantolebas praqtikaSi?

• Can compute many of the parameters that we are
  interested in
• SegviZlia gamoviTvaloT CvenTvis saWiro sxvadasxva
  parametri
• Velocity
• siCqare
• Trial and error for depth, width, area, etc
• siRrmis, siganis, farTobis da sxva parametrebis
  gadamowmeba da cdomilebis dadgena

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Sowhy make things any more complicated?Sesabamis
ad... ratom gavarTuloT saqme?
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How sensitive is the equation? ramdenad
mgrZnobiarea gantoleba?
W100 d5 S0.004 n0.035
Q3700 cfs
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How often do we see normal depth in real
channels? ramdenad xSirad vxvdebiT saSualo
siRrmes bunebriv nakadebSi?
Steep slope normal depth below critical cicabo
ferdobi saSualo siRrme kritikulze naklebia
Streams go towards normal depth but seldom get
there nakadebi miiswrafian saSualo siRrmisken
magram iSviaTad aRweven mas
Mild slope normal depth above critical sustad
daxrili ferdobi saSualo siRrme kritikulze metia.
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Limitations of a Normal Depth ComputationSezRudv
ebi saSualo siRrmis gaTvlebSi

• Constant Section - natural channel?
• mudmivi seqcia bunebrivi arxi?
• Constant Roughness - overbank flow?
• ucvleli xorklianoba (simqise) wylis napirebze
  gadasvla?
• Constant Slope
• ferdobis ucvleli daqaneba
• No Obstructions - bridges, weirs, etc
• wylis gamavlobis SenarCuneba xidebi, jebirebi,
  a.S.

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Open Channel Flow is typically variedRia arxis
dineba xasiaTdeba cvalebadobiT
B. Uniform vs. Varied b. ucvleli cvalebadis
winaaRmdeg
Uniform Flow ucvleli dineba Depth and velocity
are constant with distance along the
channel. siRrme da siCqare aris mudmivi arxis
gaswvriv mTel sigrZeze
Varied Flow cvalebadi dineba Depth and velocity
vary with distance along the channel. siRrme da
siCqare cvalebadia arxis gaswvriv mTel sigrZeze
B. Uniform versus Varied Flow b. ucvleli dineba
cvalebadis winaaRmdeg
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Subcritical subkritikuli
Critical kritikuli
Both man made and natural channels orive,
xelovnuri da bunebrivi nakadebi
Supercritical superkritikuli
Hydraulic Jump hidravlikuri naxtomi
Subcritical subkritikuli
Subcritical subkritikuli
Lynn Betts , IA NRCS
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In natural gradually varied flow
channelsbunebriv, TandaTanobiT cvalebad
dinebebSi

• Velocity and depth changes from section to
  section. However, the energy and mass is
  conserved. siCqare da siRrme icvleba seqciidan
  seqciamde. Tumca, energia da masa SenarCunebulia.

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Can use the energy and continuity equations to
step from the water surface elevation at one
section to the water surface at another section
that is a given distance upstream (subcritical)
or downstream (supercritical)SegiZliaT
gamoiyenoT energiis da uwyvetobis gantolebebi
 wylis zedapiris simaRlis erTi monakveTidan wylis
zedapiris simaRlis meore monakveTze
gadasasvlelad, romelic TavisTavad aris
zedadinebisTvis (subkritikuli) an
qvedadinebisTvis (superkritikuli)  mocemuli
manZili.
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• HEC-RAS uses the one dimensional energy equation
  with energy losses due to friction evaluated with
  Mannings equation to compute water surface
  profiles. This is accomplished with an iterative
  computational procedure called the Standard Step
  Method.
• HEC-RAS - i iyenebs erTganzomilebian energiis
  gantolebas, maningis gantolebis gamoyenebiT
  miRebuli, energiis danakargis gaTvaliswinebiT,
  raTa gamoiangariSos wylis zedapiris profili. amas
  Tan mohyveba ganeorebiTi gaTvlebis procedura,
  romelsac vuwodebT standartuli bijis meTods.

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How about that energy equation?energiis
gantolebis Sesaxeb

• First law of thermodynamics
• Termodinamikis pirveli kanoni

• Kinetic energy pressure energy potential
  energy is conserved
• kinetikuri energia wnevis energia potenciuri
  energia aris SenarCunebuli

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Remember - its an open channel and a hydrostatic
pressure distributiondaimaxsovreT es aris Ria
nakadi da hidrostatikuli wnevis ganawileba
Y2
Y1
Pressure head can be represented by water depth,
measured vertically (can be a problem if very
steep - streamlines converge or diverge
rapidly) mCqarebluri wneva SeiZleba warmodgenili
iyos vertikalurad gazomili wylis doniT
(SesaZlebelia problemuri iyos, cicabo daqanebis
SemTxvevaSi nakadis xazi Tavsdeba an gadaixreba
uecrad)
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Energy Equationenergiis gantoleba
33
Standard Step Methodstandartuli nabijis meTodi
Energy Grade Line energiis xarisxis grafiki
Water Surface wylis zedapiri
Channel Bottom kalapotis fskeri
Datum datumi

• Start at a known point.
• daiwyeT nacnobi wertilidan
• How many unknowns?
• ramdeni ramea ucnobi?
• Trial and error
• Semowmeba da cdomileba

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HEC-RAS - Computation ProcedureHEC-RAS -
gamoTvlebis procedurebi

1. Assume water surface elevation at upstream/
   downstream cross-section.
2. savaraudo wylis zedapiris simaRle zeda/qveda
   dinebis gaswvriv.
3. Based on the assumed water surface elevation,
   determine the corresponding total conveyance and
   velocity head.
4. savaraudo wylis zedapiris simaRleze dayrdnobiT,
   gansazRvreT Sesabamisi xarji da zewolis siCqare.
5. With values from step 2, compute and solve
   equation for he.
6. meore safexuris Sedegad miRebuli sididis
   gamoyenebiT iTvlis da xsnis gantolebas misTvis
7. With values from steps 2 and 3, solve energy
   equation for WS2.
8. meore da mesame bijis Sedegad miRebuli sididiT
   ixsneba energiis gantoleba WS2-sTvis.
9. Compare the computed value of WS2 with value
   assumed in step 1 repeat steps 1 through 5 until
   the values agree to within 0.01 feet, or the
   user-defined tolerance.
10. SevadaroT WS2 gamoangariSebuli sidide pirvel
    bijSi miRebul sididesTan gavimeoroT nabiji 1-5
    manam sanam sidide ar iqneba 0.01 futi an
    momxmareblis mier gansazRvruli sizustis.

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Energy Loss - important stuffenergiis danakargi
mniSvnelovani faqtori

• Loss coefficients Used
• gamoyenebuli danakargis koeficienti
• Mannings n values for friction loss
• maningis sidide xaxunis danakargi
• very significant to accuracy of computed profile
• Zalian mniSvnelovania gaangariSebuli profilis
  sizustisTvis
• calibrate whenever data is available
• daakalibreT (SeamowmeT) rogorc ki monacemebi
  xelmisawvdomia
• Contraction and expansion coefficients for
  X-Sections
• kumSvis da gafarTovebis koeficienti X seqciisTvis
• due to losses associated with changes in
  X-Section areas and velocities
• danakargis gamo, romelic dakavSirebulia X
  seqciaSi farTobis da siCqaris cvlilebasTan.
• contraction when velocity increases downstream
• SekumSva, roodesac siCqare matulobs qveda
  dinebaSi
• expansion when velocity decreases downstream
• gafarToveba, rodesac siCqare klebulobs qveda
  dinebaSi
• Bridge and culvert contraction expansion loss
  coefficients
• xidi da wyalsadenis SekumSvis da gafarTovebis
  danakargis koeficientebi
• same as for X-Sections but usually larger values

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• Friction loss is evaluated as the product of the
  friction slope and the discharge weighted reach
  length
• xaxunis danakargi fasdeba, rogorc xaxunis kuTxis
  da gawvdomis xarjis wonis mTeli sigrZis
  warmoebuli

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Friction loss is evaluated as the product of the
friction slope and the discharge weighted reach
lengthxaxunis danakargi fasdeba, rogorc xaxunis
kuTxis da gawvdomis xarjis wonis mTeli sigrZis
warmoebuli.
Channel Conveyance Senakadis gadazidva
38
Friction Slopes in HEC-RASxaxunis kuTxe
HEC-RAS-Si
Average Conveyance (HEC-RAS default) - best
results for all profile types (M1, M2,
etc.) saSualo gadazidva (HEC-RAS-is winapiroba)
saukeTeso Sedegi yvela tipis profilisTvis (M1,
M2, ?? sxva.)
Average Friction Slope - best results for M1
profiles saSualo xaxunis kuTxe - saukeTeso Sedegi
M1 tipis profilebisTvis.
Geometric Mean Friction Slope - used in USGS/FHWA
WSPRO model geometriuli saSualo xaxunis kuTxe
gamoiyeneba USGS/FHWA WSPRO modelisTvis
Harmonic Mean Friction Slope - best results for
M2 profiles harmoniuli saSualo xaxunis kuTxe
saukeTeso Sedegi M2 tipis profilebisTvis
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FlowClassificationdinebis klasifikacia
Steep slope normal depth below critical cicabo
ferdobi saSualo siRrme kritikul siRrmeze naklebia
Mild slope normal depth above critical susti
daxra saSualo siRrme kritikulze metia
40
Friction Slopes in HEC-RASxaxunis kuTxe
HEC-RAS-Si
HEC-RAS has option to allow the program to select
best friction slope equation to use based on
profile type. HEC-RAS s aqvs ?????????, romelic
saSualebas aZlevs programas SearCiios da
gamoiyenos saukeTeso xaxunis kuTxis funqcia
profilebis tipebis mixedviT.
gamoyenebuli gantoleba
aris Tu ara xaxunis kuTxe mocemuli ganivi
kveTisTvis meti vidre xaxunis kuTxe Semdeg ganiv
kveTSi?
profilis tipi
ki ara ki ara
saSualo xaxunis kuTxe harmoniuli saSualo saSualo
xaxunis kuTxe geometriuli saSualo
?ubkritikuli ?ubkritikuli ?uperkritikuli superkrit
ikuli
41
Friction Slopes in HEC-RASxaxunis kuTxe
HEC-RAS-Si
HEC-RAS has option to allow the program to select
best friction slope equation to use based on
profile type. HEC-RAS s aqvs ?????????, romelic
saSualebas aZlevs programas SearCiios da
gamoiyenos saukeTeso xaxunis kuTxis funqcia
profilebis tipebis mixedviT.
42
HEC-RASHEC-RAS
????? 2.2 HEC-RAS ???????????? ????????????
???????????
The default method of conveyance subdivision is
by breaks in Mannings n values. gadazidvebis
(gadatanis) qvedanayofis, winapirobiT miRebuli
meTodi warmoadgens maningis N sidides
43
HEC-2 style
????? 2.3 ???????????? ???????????? ????????????
?????? (HEC-RAS2 ?????)
An optional method is as HEC-2 does it -
subdivides the overbank areas at each individual
ground point. SemoTavazebuli meTodi rom?????
iyenebs HEC-2 hyofs datborvis zonas yovel
individualur zedapiris wertilSi. Note can get
biggest differences when have big changes in
overbanks SniSnva SesaZlebelia mogvces
mniSvnelovani gansxvaveba, rodesac gvaqvs didi
cvlileba datborvaSi
44
Other losses includesxva danakargebi

• Contraction losses
• SekumSvis danakargi
• Expansion losses
• gafarToebis danakargi

C contraction or expansion coefficient C
SekumSvis an gafarToebis koeficienti
45
Contraction and Expansion Energy Loss
CoefficientsSekumSvis da gafarToebis energiis
danakargis koeficientebi

• Note 1 WSP2 uses the upstream section for the
  whole reach below it while HEC-RAS averages
  between the two X-sections.
• SeniSnva 1 WSP2 iyenebs zeda dinebis seqcias,
  mis qveviT arsebuli mTeli gawvdomisTvis, maSin
  roca HEC-RAS-i asaSualoebs or X seqcias Soris
  arsebul koeficientebs.
• Note 2 WSP2 only uses LSf in older versions and
  has added C to its latest version using the
  LOSS card.
• SeniSnva 2 WSP2 iyenebs mxolod LSf-s Zvel
  versiebSi da damatebuli aqvs C uaxles versiebSi,
  iyenebs ra danakargis baraTs.

46
Expansion and Contraction CoefficientsSekumSvis
da gafarToebis koeficientebi
Expansion gafarToveba Contraction SekumSva
No transition loss ar aris gadasvlis danakargi 0 0
Gradual transitions TandaTanobiTi gadasva 0.3 0.1
Typical bridge sections ??????? xidis seqcia 0.5 0.3
Abrupt transitions wyvetili gadasvla 0.8 0.6
Notes maximum values are 1. Losses due to
expansion are usually much greater than
contraction. Losses from short abrupt transitions
are larger than those from gradual
changes. SeniSvna maqsimaluri sidide aris 1.
gafarToebiT gamowveuli danakargi aris rogorc wesi
bevrad didi sidide, vidre SekumSviT gamowveuli
danakargi. mokle, wyvetili gadasvlis Sedegad
miRebuli danakargi aris ufro didi vidre
TandaTanobiTi gadasvlis Sedegad miRebuli
danakargi.
47
Specific Energyspecifikuri energia
Definition available energy of the flow with
respect to the bottom of the channel rather than
in respect to a datum. gansazRvreba dinebis
xelmisawvdomi energia nakadis fskerTan
mimarTebaSi ufro prioritetulia vidre datumTan
mimarTebaSi
Assumption that total energy is the same across
the section. Therefore we are assuming
1-D. vuSvebT, rom totaluri energia aris ucvleli,
mTel seqciaSi, Sesabamisad Cven vRebulobT 1-D
Note Hydraulic depth (y) is cross section area
divided by top width SeniSnva hidravlikuri
siRrme (y) aris ganivi kveTis farTobi gayofili
udides siganeze
48
Specific Energyspecifikuri energia
The Specific Energy equation can be used to
produce a curve. Q What use is it? A It is
useful when interpreting certain aspect of open
channel flow specifikuri energiis gantoleba
SeiZleba gamoviyenoT mrudis asagebad. kiTxva ra
gamoyeneba aqvs mruds? pasuxi is gamoiyeneba
maSin, rodesac saWiroa interpretacia gavukeToT
Ria dinebis konkretul aspeqts.
Y1
Note Angle is 45 degrees for small
slopes SeniSnva mcire ferdobisTvis kuTxe aris 45.
or y
Y2
or E
49
Specific Energyspecifikuri energia
For any pair of E and q, we have two possible
depths that have the same specific energy. One is
supercritical, one is subcritical. The curve has
a single depth at a minimum specific
energy. nebismieri E da q wyvilisTvis, Cven
gvaqvs ori SesaZlo siRrme, romelTac aqvT erTnairi
specifikuri energia. erTi aris superkritikuli,
meore subkritikuli. mruds axasiaTebs erTi siRrme
minimaluri specifikuri energiisTvis.
Minimum specific energy minimaluri specifikuri
energia
Y1
Y2
50
Specific Energyspecifikuri energia

Q What is that minimum? A Critical
flow!! kiTxva ra aris minimumi? pasuxi
kritikuli dineba
Minimum specific energy minimaluri specifikuri
energia
51
Froude Numberfrudes ricxvi

• Ratio of stream velocity (inertia force) to wave
  velocity (gravity force)
• Tanafardoba nakadis siCqaresa (inerciis Zala) da
  talRis siCqares Soris (gravitaciuli Zala)

52
Froude Numberfrudes ricxvi

• Ratio of stream velocity (inertia force) to wave
  velocity (gravity force)
• Tanafardoba nakadis siCqaresa (inerciis Zala) da
  talRis siCqares Soris (gravitaciuli Zala)

Fr gt 1, supercritical flow Fr gt 1, superkritikuli
dineba Fr lt 1, subcritical flow Fr lt 1,
subkritikuli dineba
wylis zedapiris simaRle
1 subcritical, deep, slow flow, disturbances
only propagate upstream 1 subkritikuli, Rrma,
neli dineba, arRvevs, Slis mxolod zeda dinebas 3
supercritical, fast, shallow flow, disturbance
can not propagate upstream superkritikuli, Cqari,
zedapiruli dineba, aRreva, aSliloba SeiZleba ar
vrceldebodes zeda dinebaSi.
Subcritical subkritikuli
Supercritical superkritikuli
53
Critical Flowkritikuli dineba

• Froude 1
• frude 1
• Minimum specific energy
• minimaluri specifikuri energia
• Transition
• ????????
• Small changes in energy (roughness, shape, etc)
  cause big changes in depth
• mcire cvalebadoba energiaSi (xorklianoba, forma,
  da sxva) warmoqmnis did cvlilebebs siRrmeSi
• Occurs at overfall/spillway
• xdeba wyalgadasaSvebSi

wylis zedapiris simaRle
Subcritical subkritikuli
Supercritical superkritikuli
Note Critical depth is independent of roughness
and slope SeniSvna kritikuli siRrme araa
damokidebuli daxraze da xorklianobaze
54
Critical Depth Determinationkritikuli dinebis
gansazRvra
HEC-RAS computes critical depth at a x-section
under 5 different situations HEC-RAS iTvlis
kritikul dinebas X seqciaSi 5 gansxvavebul
situaciisTvis

• Supercritical flow regime has been specified.
• superkritikuli dinebis reJimi iyo gansazRvruli
• Calculation of critical depth requested by user.
• kritikuli siRrmis gaangariSeba momxmareblis
  moTxovniT
• Critical depth is determined at all boundary
  x-sections.
• kritikuli siRrme ganisazRvreba yvela X seqciis
  sazRvarze
• Froude number check indicates critical depth
  needs to be determined to verify flow regime
  associated with balanced elevation.
• fraudis ricxvis dadgeniT ganisazRvreba sabalanso
  simaRlesTan dakavSirebuli dinebis reJimis
  gansazRvrisaTvis saWiro kritikuli siRrme.
• Program could not balance the energy equation
  within the specified tolerance before reaching
  the maximum number of iterations.
• programul uzrunvelyofas ar SeuZlia gaawonasworos
  energiis gantoleba mocemuli daSvebis farglebSi
  manam ar miaRwevs ??????????????? maqsimalur
  zRvars.

55
In HEC-RAS, we have a choice for the
calculationsHEC-RAS-Si Cven gvaqvs arCevani
gaTvlebisTvis
Still need to examine transitions closely jer
kidevs saWiroa zedmiwevniT Semowmdes gadaadgileba
56
How about hydraulic jumps?hidravlikuri naxtomi?

• Water surface jumps up
• wylis zedapiri daxtis
• Typical below dams or obstructions
• rogorc wesi ????????? ?? ??????????? SemTxvevaSi
• Very high-energy loss/dissipation in the
  turbulence of the jump
• Zalian maRali energiis danakargi/gaflangva
  naxtomis turbulentur zonaSi

57
General Shape Of Profileprofilis zogadi forma
dc
dn
Sluice gate ????? ??????????
dn
M
S
M
58
A rapidly varying flow situationuecrad cvalebadi
dinebis SemTxveva

• Going from subcritical to supercritical flow, or
  vice-versa is considered a rapidly varying flow
  situation.
• gadis subkritikulidan superkritikulisken an
  piriqiT miiReba uecarad cvalebadi dinebis
  SemTxvevaSi.
• Energy equation is for gradually varied flow
  (would need to quantify internal energy losses)
• energiis gantoleba gamoiyeneba TandaTanobiT
  cvalebadi dinebisTvis (saWiroebs Sida energiis
  danakargis gadaTvlas)
• Can use empirical equations
• SesaZlebelia empiriuli gantolebis gamoyeneba
• Can use momentum equation
• SesaZlebelia momentis gantolebis gamoyeneba

59
Momentum Equationmomentis gantoleba

• Derived from Newtons second law, Fma
• miRebulia niutonis meore kanonidan, Fma
• Apply F ma to the body of water enclosed by the
  upstream and downstream x-sections.
• miusadageT F ma wylis tans yvelaze axlosmdebare
  zeda dinebasTan da qvedadinebis X seqcias

Difference in pressure weight of water -
external friction mass x acceleration gansxvaveb
a wnevaSi wylis wona gare xaxuni masis X
aCqarebas
60
Momentum Equationmomentis gantoleba
2
2 ( V / 2g ) Y Z ( V / 2g)
Y Z hm 2 2
2 1 1 1 The
momentum and energy equations may be written
similarly. Note that the loss term in the energy
equation represents internal energy losses while
the loss in the momentum equation (hm) represents
losses due to external forces. momentis da
energiis gantolebebi SesaZlebelia erTnairad
gamoixatos. aRsaniSnavia, rom danakargi energiis
gantolebaSi gamoxatavs Sinagani energiis
danakargs maSin, rodesac danakargi momentis
gantolebaSi (hm) gamoxatavs gare xaxunis ZalebiT
ganpirobebul danakargs. In uniform flow, the
internal and external losses are identical. In
gradually varied flow, they are close. ucvlel
dinebaSi, Sinagani da garegani danakargi
identuria. TandaTanobiT cvalebad dinebaSi, isini
erTmaneTTan miaxloebuli sidideebia.
61
HECRAS can use the momentum equation forHECRAS
SeuZlia gamoiyenos momentis gantoleba

• Hydraulic jumps
• hidravlikuri naxtomi
• Hydraulic drops
• hidravlikuri wveTi
• Low flow hydraulics at bridges
• dabali dinebis hidravlika xidTan
• Stream junctions.
• nakadebis SekavSireba

Since the transition is short, the external
energy losses (due to friction) are assumed to be
zero vinaidan gadaadgileba moklea, gare energiis
danakargi (xaxunis gamo) miCneulia nulad
62
Classifications of Open Steady versus
UnsteadyRia ??????? dinebis klasifikacia
????????? dinebis sapirispirod
a. ??????? ?????????? ??????????????
?????? (???????) dineba siRrme da siCqare mocemul
wertilSi ar icvleba drois mixedviT
??????? (?????????) dineba siRrme da siCqare
mocemul wertilSi icvleba drois mixedviT
63
Unsteady Examples????????? dinebis magaliTebi
Natural streams are always unsteady - when can
the unsteady component not be ignored? bunebrivi
dineba yovelTvis arastabiluria rodisaa saWiro
arastabilurobis komponentebis gaTvaliswineba?

• Dam breach
• kaSxlis garRveva
• Estuaries
• mdinaris SesarTavebi
• Bays
• yureebi, ubeebi
• Flood wave
• wyaldidobis talRebi
• others...
• sxva

64
HEC-RAS is a 1-Dimensional ModelHEC-RAS-i aris
1D ganzomilebiani modeli

• Flow in one direction
• miedineba erTi mimarTulebiT
• It is a simplification of a chaotic system
• es aris ??????? sistemis gamartiveba
• Can not reflect a super elevation in a bend
• ar SeuZlia asaxos aratipiuri simaRleebi moxvevis
  adgilebSi
• Can not reflect secondary currents
• ar SeuZlia asaxos meoradi dinebebi

65
Velocity Distribution - Its 3-DsiCqaris
gadanawileba 3D
Because of free surface and friction, velocity is
not uniformly distributed Tavisufali zedapiris da
xaxunis gamo, siCqare ar aris ucvleli sxvadsxva
doneebze
suraTi 4. magaliTi siCqaris gadanawilebis? 2-D -Si
but HEC-RAS is 1-D magram arsebobs 1-D
66
Velocity DistributionsiCqaris gadanawileba
siCqaris gadanawileba kalapotSi

• Actual Max V is at approx. 0.15D (from the top).
• realuri maqsimaluri V aris daaxloebiT 0.15D
  (zedapiridan)
• Actual Average V is at approx.. 0.6D (from the
  top).
• realuri saSualo V aris daaxloebiT 0.6D
  (zedapiridan)

Teoriuli realuri
siRrme
??????? siCqare
67
Secondary circulation pattern at a river bed
cross section meoradi cirkulaciis magaliTi
mdinaris fskeris ganiv seqciaSi
Single cell theory (Thomson, 1876 Hawthorne,
1951 Quick, 1974) erTi ujredis Teoria (tomsoni,
1876 havtorni. 1951 quiki, 1974)
Outward shoaling flow across point bar gare
napiris dineba wertilis gaswvriv
Current theory of bend flow with skew induced
outer bank cells (Hey and Thorne,
1975) cirkulaciuri dinebis dRevandeli Teoria
gaRunvis indikatoriT napiris ujredisTvis (hei da
tornei, 1975)
68
Other assumptions in HEC-RASHEC-RAS is sxva
daSvebebi

• HEC-RAS is a fixed bed model
• HEC-RAS aris fiqsirebuli kalapotis modeli
• The cross section is static
• ganivi kveTi statikuria
• HEC-6 allows for changes in the bed.
• saSualebas iZleva SevcvaloT kalapotis modeli
• HEC-RAS can not by itself reflect upstream
  watershed changes.
• HEC-RAS s ar aqvs funqcia, rom Tavad
  gaiTvaliswinos zeda dinebis wyalgasayaris
  cvlileba.

HEC-RAS is a simplification of the natural
system HEC-RAS i aris bunebrivi sistemis
gamartivebuli modeli
69
End of lecture leqciis dasasruli