by g. parodi wrs – itc – the netherlands g. parodi wrs-itc- niderlandebi
DESCRIPTION
HECRAS Basic Principles of Water Surface Profile Computations HECRAS wylis zedapiris profilis agebis ZiriTadi principebi. by G. Parodi WRS – ITC – The Netherlands g. parodi WRS-ITC- niderlandebi. Incompressible fluid ukumSvadi siTxe - PowerPoint PPT PresentationTRANSCRIPT
HECRAS Basic Principles of Water
Surface Profile ComputationsHECRAS
wylis zedapiris profilis agebis ZiriTadi
principebi
by G. ParodiWRS – ITC – The Netherlands
g. parodiWRS-ITC- niderlandebi
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.
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
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
VA = constant A = mudmivaDischarge is expressed as Q = VAxarji gamoixateba rogorc Q = VA
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.
(conservation of mass) (მასის შენახვის principi)
Continuity Equationuwyvetobis gantoleba
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 / SpillwayswyalgadasaSvebi
Abrupt changes in slope or widthuecari cvlileba dinebis daxris kuTxeSi an siganeSi.
Friction - over a distancexaxuni – garkveul distanciaze
Open Channel Flow – ControlsRia kalapotis dineba - kontroli
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.
Uniform or Normal FlowerTgvari da normuli dineba
Gravity Friction
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
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)
W
F
Y
So
WS
V
Hydrostatic pressure distributionhidravlikuri wnevis gadanawileba
V2/2g
EGL
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.
Assume a Hypothetical ChannelwarmovidginoT hipoTeturi kalapotiLong prismatic (same section over a long distance) channelgrZeli prizmuli (erTi da igive seqcia did manZilze) kalapotiNo change in slope, section, discharge ar gvaqvs cvlileba dinebis daqanebSi, seqciebSi, xarjSi
What does that mean?ras niSnavs es?
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
Uniform flow occurs when:erTgvari dineba warmoSveba roca:
Therefore: It can only occur in very long, straight, prismatic channels where the terminal velocity of the flow is achievedSesabamisad: es SeiZleba moxdes mxolod Zalian grZel, swor, prizmul kalapotSi, sadac dineba aRwevs zRvrul siCqares
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.
Yn
Yc
Yc
Yn
Normal Depth Applies to Different Types of SlopessaSualo siRrme ukavSirdeba ferdobis sxvadasxva tipis
daqanebas.
‘n’ stands for normal“n” igulisxmeba saSualo‘s’ stands for critical“s” igulisxmeba kritikuli
Steep Slopecicabo ferdobi
Mild Slopesustad daxrili ferdobi
Critical Slopekritikuli ferdobi
Cvalebadi nakadi
cvalebadi nakadi
Cvalebadi nakadi
erTgvari nakadi
erTgvari nakadi
erTgvari nakadi
cvalebadi nakadi
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?
maFIf 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
0
0
2
20
0
sin
sin
0sin
RSK
V
S
small
ALPLKV
equationrearrange
KV
where
WPL
Newton's second lawniutonis meore kanoni
Antoine Chezy (18th century)antoni Cezi (18 saukune)
oRSCV
Gravity Friction
0
wheresadac
rearrange equationgadavaTamaSoT gantoleba
smallmcire
Gravitygravitacia
Frictionxaxuni
PAR
perimeterwettedP
slopeS
areaA
coeffn
cfsflowQ
RASn
Q
)(
49.1 32
21
One of the most widely used to account for friction losseserT erTi yvelaze farTod gavrcelebuli meTodi xaxunis danakargis dasaTvlelad
Manning’s equationmaningis gantoleba
dineba
koeficienti
farTobi
ferdobis daxra
dasvelebis perimetri
PAR
RASn
Q
32
2149.1
nLLTL ))((/
322
3
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.)
LLL
2
Manning’s Equation - ‘n’ unitsmaningis gantoleba - ‘n’ erTeuli
Manning’s nmaningis n
Manning's n values for small, natural streams (top width <30m)Lowland Streams Minimum Normal Maximum(a) Clean, straight, no deep pools 0.025 0.030 0.033(b) Same as (a), but more stones and weeds 0.030 0.035 0.040( c) Clean, winding, some pools and shoals 0.033 0.040 0.045(d) Same as (c ), but some weeds and stones 0.035 0.045 0.050(e) Same as (c ), at lower stages, with less effective 0.040 0.048 0.055
and sections(f) Same as (d) but more stones 0.045 0.050 0.060(g) Sluggish reaches, weedy, deep pools 0.050 0.070 0.080(h) Very weedy reaches, deep pools and 0.075 0.100 0.150
floodways with heavy stand of timber and brushMountain streams (no vegetation in channel, banks steep, trees and brush submerged at high stages(a) Streambed consists of gravel, cobbles and
few boulders 0.030 0.040 0.050(b) Bed is cobbles with large boulders 0.040 0.050 0.070(Chow, 1959)
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)
Manning’s nmaningis nA 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)
n=0.014
n=0.016
n=0.018
n=0.018
n=0.020
n=0.060
n=0.080
n=0.110
n=0.125
n=0.150
n=0.050
NRCS - Fasken, 1963
Guidance Available: seek bibliography and the WEBsaxelmZRvaneloebi: moZebneT bibliografia da internet saitebi
Streams may appear to be super critical but are just fast subcritical nakadi SeiZleba Candes super kritikuli, magram iyos mxolod
swrafi subkritikuli Jarret’s 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)
16.038.039.0 RSn
Manning’s n in Steep Channelmaningis n cicabod daxril kalapotSi
32
21
32
21
49.1
49.1
RASn
Q
RSn
V
What can we do with Manning’s 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
W=100’d=5’S=0.004n=0.035
Q=3700 cfs
n=0.03 to 0.04 13% to 17%
d=4.5 to 5.5 ft 16% to 17%
w =90 to 110 ft 11%
S=0.003 to 0.005 12% to 13%
All 40% to 70%
How sensitive is the equation?ramdenad mgrZnobiarea gantoleba?
Mild slope: normal depth above criticalsustad daxrili ferdobi: saSualo siRrme kritikulze metia.
Steep slope: normal depth below criticalcicabo ferdobi: saSualo siRrme kritikulze naklebia
How often do we see normal depth in real channels?ramdenad xSirad vxvdebiT saSualo siRrmes bunebriv nakadebSi?
Streams go towards normal depth but seldom get therenakadebi miiswrafian saSualo siRrmisken magram iSviaTad aRweven mas
Limitations of a Normal Depth Computation:SezRudvebi 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.
Open Channel Flow is typically variedRia arxis dineba xasiaTdeba cvalebadobiT
B. Uniform vs. Variedb. ucvleli cvalebadis winaaRmdeg
Uniform Flowucvleli dinebaDepth and velocity are constantwith distance along the channel.siRrme da siCqare aris mudmiviarxis gaswvriv mTel sigrZeze
Varied Flowcvalebadi dinebaDepth and velocity vary withdistance along the channel.siRrme da siCqare cvalebadia arxis gaswvriv mTel sigrZeze
B. Uniform versus Varied Flowb. ucvleli dineba cvalebadis winaaRmdeg
Hydraulic Jumphidravlikuri naxtomi
Criticalkritikuli
Subcriticalsubkritikuli
Supercriticalsuperkritikuli
Lynn Betts , IA NRCS
Tim McCabe, IA NRCS
Both man made and natural channelsorive, xelovnuri da bunebrivi nakadebi
Subcriticalsubkritikuli
Hydraulic Jumphidravlikuri naxtomi
Subcriticalsubkritikuli
Supercriticalsuperkritikuli
Subcriticalsubkritikuli
Criticalkritikuli
In natural gradually varied flow channels:bunebriv, 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.
Can use the energy and continuity equations to stepstep 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.
HEC-RAS uses the one dimensional energy equation with energy losses due
to friction evaluated with Manning’s 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.
How about that energy equation?energiis gantolebis Sesaxeb:
First law of thermodynamics Termodinamikis pirveli kanoni
(V2/2g)2+ P2/w + Z2 = (V2/2g)1
+ +P1/w + Z1 he
Bernoulli ‘s Equationbernulis gantoleba:
• Kinetic energy + pressure energy + potential energy is conserved• kinetikuri energia + wnevis energia + potenciuri energia aris SenarCunebuli
Remember - it’s an open channel and a hydrostatic pressure distribution
daimaxsovreT – es aris Ria nakadi da hidrostatikuli wnevis ganawileba
(V2/2g)2+ P2/w +Z2 = (V2/2g)1
+ +P1/w + Z1 he
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)
(V2/2g)2+ Y2 Z2+ = (V2/2g)1 + + +Y1 Z1 he
Water Surfacewylis zedapiri
Energy Grade Lineenergiis xarisxis grafiki
Y2
Y1
he
(V2/2g)1
(V2/2g)2
Z2
Z1Datumdatumi
Channel Bottomkalapotis fskeri
g
V
g
VCSLh fe 22
21
22
Energy Lossesenergiis danakargi
Energy Equationenergiis gantoleba
Y2
Y1
he
(V2/2g)1
(V2/2g)2
Z2
Z1
ehVVg
WSWS )(2
1 222
21112
Standard Step Methodstandartuli nabijis meTodi
Start at a known point. daiwyeT nacnobi wertilidan How many unknowns? ramdeni ramea ucnobi? Trial and error Semowmeba da cdomileba
Water Surfacewylis zedapiri
Energy Grade Lineenergiis xarisxis grafiki
Datumdatumi
Channel Bottomkalapotis fskeri
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.
HEC-RAS - Computation ProcedureHEC-RAS - gamoTvlebis procedurebi
Loss coefficients Used:
gamoyenebuli danakargis koeficienti
Manning’s 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
igivea, rac X seqciisTvis, magram rogorc wesi sidide ufro didia.
Energy Loss - important stuffenergiis danakargi – mniSvnelovani faqtori
robchlob
robrobchchloblob
fe
QQQ
QLQLQLL
g
V
g
VCSLh
22
21
22
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
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.
221
21
21
32
21
22
)(,
49.1
22
KQSK
QS
KSSARn
Q
g
V
g
VCSLh
ff
ff
fe
Channel ConveyanceSenakadis gadazidva
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, და sxva.)
2
21
21f
KK
QQS
Average Friction Slope - best results for M1 profiles
saSualo xaxunis kuTxe - saukeTeso Sedegi M1 tipis profilebisTvis.
2
SSS 21 ff
f
21 fff SSS
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
21
21
ff
fff
SS
S2SS
Friction Slopes in HEC-RASxaxunis kuTxe HEC-RAS-Si
Mild slope: normal depth above criticalsusti daxra: saSualo siRrme kritikulze metia
Steep slope: normal depth below criticalcicabo ferdobi: saSualo siRrme kritikul siRrmeze naklebia
FlowClassification
dinebis klasifikacia
HEC-RAS has option to allow the program to select best friction slope equation to use based on profile type.
HEC-RAS –s aqvs პარამეტრი, romelic saSualebas aZlevs programas SearCiios da gamoiyenos saukeTeso xaxunis kuTxis funqcia profilebis tipebis mixedviT.
Friction Slopes in HEC-RASxaxunis kuTxe HEC-RAS-Si
profilis tipiaris Tu ara xaxunis kuTxemocemuli ganivi kveTisTvis meti vidre xaxunis kuTxe Semdeg ganiv kveTSi?
gamoyenebuli gantoleba
სubkritikuliსubkritikuliსuperkritikulisuperkritikuli
kiarakiara
saSualo xaxunis kuTxeharmoniuli saSualosaSualo xaxunis kuTxegeometriuli saSualo
HEC-RAS has option to allow the program to select best friction slope equation to use based on profile type.
HEC-RAS –s aqvs პარამეტრი, romelic saSualebas aZlevs programas SearCiios da gamoiyenos saukeTeso xaxunis kuTxis funqcia profilebis tipebis mixedviT.
Friction Slopes in HEC-RASxaxunis kuTxe HEC-RAS-Si
The default method of conveyance subdivision is by breaks in Manning’s ‘n’ values.
gadazidvebis (gadatanis) qvedanayofis, winapirobiT miRebuli meTodi warmoadgens maningis N sidides
HEC-RASHEC-RAS
გრაფა 2.2 HEC-RAS წინაპირობითი გადაზიდვების ქვედანაყოფი
An optional method is as HEC-2 does it - subdivides the overbank areas at each individual ground point.
SemoTavazebuli meTodi romელსაც 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
HEC-2 style
გრაფა 2.3 ალტერნატიული გადაზიდვების ქვედანაყოფის მეთოდი (HEC-RAS–2 სტილი)
Other losses include:sxva danakargebi:
Contraction losses SekumSvis danakargi Expansion losses gafarToebis danakargi
g
V
g
VCSLh fe 22
21
22
C = contraction or expansion coefficient
C = SekumSvis an gafarToebis koeficienti
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.
g
V
g
VCSLh fe 22
21
22
Expansion and Contraction CoefficientsSekumSvis da gafarToebis koeficientebi
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.
ExpansiongafarToveba
ContractionSekumSva
No transition lossar aris gadasvlis danakargi
0 0
Gradual transitionsTandaTanobiTi gadasva
0.3 0.1
Typical bridge sectionsტიპიური xidis seqcia
0.5 0.3
Abrupt transitionswyvetili gadasvla
0.8 0.6
2
2
2
2
2
gy
qyE
yqV
byQV
bQq
g
VyE
b
y
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 widthSeniSnva: hidravlikuri siRrme (y) aris ganivi kveTis farTobi gayofili udides siganeze
Specific Energyspecifikuri energia
yE
consty
constg
qyyE
.
.2
)(
2
22 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.
Note: Angle is 45 degrees for small slopesSeniSnva: mcire ferdobisTvis kuTxe aris 45.
Y1
Y2
or E
ory
Specific Energyspecifikuri energia
yE
consty
constg
qyyE
.
.2
)(
2
22
Minimum specific energyminimaluri specifikuri 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.
Y1
Y2
Specific Energyspecifikuri energia
Minimum specific energyminimaluri specifikuri energia
1
01
2
3
2
3
2
2
2
gy
q
gy
q
dy
dE
gy
qyE Q: What is that minimum?
A: Critical flow!!kiTxva: ra aris minimumi?pasuxi: kritikuli dineba
Specific Energyspecifikuri energia
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)
gy
V
gy
qFroude
Froudegy
q
dy
dE
gy
qyE
3
23
2
2
2
11
2
Ratio of stream velocity (inertia force) to wave velocity (gravity force)
Tanafardoba nakadis siCqaresa (inerciis Zala) da talRis siCqares Soris (gravitaciuli Zala)
gravity
inertiaFr
Fr > 1, supercritical flowFr > 1, superkritikuli dinebaFr < 1, subcritical flowFr < 1, subkritikuli dineba
1: subcritical, deep, slow flow, disturbances only propagate upstream1: subkritikuli, Rrma, neli dineba, arRvevs, Slis mxolod zeda dinebas3: supercritical, fast, shallow flow, disturbance can not propagate upstreamsuperkritikuli, Cqari, zedapiruli dineba, aRreva, aSliloba SeiZleba ar vrceldebodes zeda dinebaSi.
Subcriticalsubkritikuli
Supercriticalsuperkritikuli
Froude Numberfrudes ricxvi
wylis zedapiris simaRle
Critical Flowkritikuli dineba
Froude = 1 frude = 1 Minimum specific energy minimaluri specifikuri energia Transition ცვლილება 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
Subcriticalsubkritikuli
Supercriticalsuperkritikuli
Note: Critical depth is independent of roughness and slopeSeniSvna: kritikuli siRrme araa damokidebuli daxraze da xorklianobaze
wylis zedapiris simaRle
Critical Depth Determinationkritikuli dinebis gansazRvra
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 განმეორებადობის maqsimalur zRvars.
HEC-RAS computes critical depth at a x-section under 5 different situations:
HEC-RAS iTvlis kritikul dinebas X seqciaSi 5 gansxvavebul situaciisTvis:
In HEC-RAS, we have a choice for the calculationsHEC-RAS-Si Cven gvaqvs arCevani gaTvlebisTvis
Still need to examine transitions closelyjer kidevs saWiroa zedmiwevniT Semowmdes gadaadgileba
How about hydraulic jumps?hidravlikuri naxtomi? Water surface “jumps” up wylis zedapiri “daxtis” Typical below dams or obstructions
rogorc wesi ჯებირების და დაბრკოლების SemTxvevaSi
Very high-energy loss/dissipation in the turbulence of the jump
Zalian maRali energiis danakargi/gaflangva “naxtomis” turbulentur zonaSi
Hydraulic
J ump
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
Derived from Newton’s second law, F=ma miRebulia niutonis meore kanonidan, F=ma 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
xfx12 VρQFWPP Δ
Difference in pressure + weight of water - external friction = mass x accelerationgansxvaveba wnevaSi + wylis wona – gare xaxuni = masis X aCqarebas
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.
Momentum Equationmomentis gantoleba
HECRAS can use the momentum equation for:HECRAS 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 zerovinaidan gadaadgileba moklea, gare energiis danakargi (xaxunis gamo) miCneulia nulad
Classifications of Open Steady versus UnsteadyRia უცვლელი dinebis klasifikacia ცვალებადი dinebis sapirispirod
a. უცვლელი ცვალებადის საწინააღმდეგოდ
ურყევი (უცვლელი) dinebasiRrme da siCqare mocemul wertilSi ar icvleba drois mixedviT
მერყევი (ცვალებადი) dinebasiRrme da siCqare mocemul wertilSi icvleba drois mixedviT
Unsteady Examplesცვალებადი dinebis magaliTebi
Dam breach kaSxlis garRveva Estuaries mdinaris SesarTavebi Bays yureebi, ubeebi Flood wave wyaldidobis talRebi others... sxva
Natural streams are always unsteady - when can the unsteady component not be ignored?bunebrivi dineba yovelTvis arastabiluria – rodisaa saWiro arastabilurobis komponentebis gaTvaliswineba?
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 ქაოსური 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
…but HEC-RAS is 1-Dmagram arsebobs 1-D
Because of free surface and friction, velocity is not uniformly distributedTavisufali zedapiris da xaxunis gamo, siCqare ar aris ucvleli sxvadsxva doneebze
kVjViVV zyx
Velocity Distribution - It’s 3-DsiCqaris gadanawileba – 3D
suraTi 4. magaliTi siCqaris gadanawilebisა 2-D -Si
Velocity DistributionsiCqaris gadanawileba
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)
siCqaris gadanawileba kalapotSi
Teoriulirealuris
iRrm
e
საშუალოsiCqare
Single cell theory (Thomson, 1876; Hawthorne, 1951; Quick, 1974)erTi ujredis Teoria (tomsoni, 1876; havtorni. 1951; quiki, 1974)
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)
Outward shoaling flow across point bargare napiris dineba wertilis gaswvriv
Outward shoaling flow across point bargare napiris dineba wertilis gaswvriv
Secondary circulation pattern at a river bed cross section meoradi cirkulaciis magaliTi mdinaris fskeris ganiv seqciaSi
Other assumptions in HEC-RASHEC-RAS – is sxva daSvebebi– is sxva daSvebebi
HEC-RAS is a fixed bed model HEC-RAS aris fiqsirebuli kalapotis modeliaris fiqsirebuli kalapotis modeli
The cross section is static ganivi kveTi statikuria HEC-6 allows for changes in the bed. saSualebas iZleva SevcvaloT kalapotis modelisaSualebas iZleva SevcvaloT kalapotis modeli
HEC-RAS can not by itself reflect upstream watershed changes. HEC-RAS –s ar aqvs funqcia, rom Tavad gaiTvaliswinos zeda s ar aqvs funqcia, rom Tavad gaiTvaliswinos zeda
dinebis wyalgasayaris cvlileba.dinebis wyalgasayaris cvlileba.
HEC-RAS is a simplification of the HEC-RAS is a simplification of the natural systemnatural systemHEC-RAS – HEC-RAS – i aris bunebrivi sistemis gamartivebuli i aris bunebrivi sistemis gamartivebuli modelimodeli