A_watersurface_Georg..

HECRAS
wylis zedapiris
profilis agebis ZiriTadi principebi
g. parodi
WRS-ITC- niderlandebi
wylis Sesaxeb . . .
 ukumSvadi siTxe
 siCqare da siRrme icvleba, matulobs an klebulobs raTa moergos kalapotis formas.
 maRali gaWimulobis Zala
 SesaZleblobas aZlevs gluvad gaiWimos aCqarebisas
 ar xasiaTdeba gamWoli simtkiciT
 ar neldeba Seuferxebliv, Sedegad warmoiSveba mdgari (stacionaruli) talRebi, kargia kanoeTi curvisas, haeris
CaTreva, a.S.
Ria kalapotis dineba . . .
 Tavisufali zedapiri
 siTxis zedapiri urTierTqmedebs atmosferosTan
 sazRvrebi araa dadgenili fizikuri sazRvriT, daxuruli wyalsadenis saxiT
vinaidan dineba ukumSvadia, aCqarebis da ganivi kveTis farTobis warmoebuli aris mudmivi. Sesabamisad
dinebis siCqare da siRrme cvalebadia, matulobs an klebulobs raTa moergos kalapotis formas.
uwyvetobis gantoleba
(მასის შენახვის principi)
A = mudmiva
xarji gamoixateba rogorc Q = VA
 Q aris dineba Q
 V aris siCqare V
 A aris ganivi kveTis farTobi A
Ria kalapotis dineba - kontroli
gansazRvreba: kontroli aris dinebis nebismieri maxasiaTebeli, romlisTvisac yalibdeba
erTaderTi (unikaluri) siRrme-xarjis damokidebuleba.
wyalgadasaSvebi
uecari cvlileba dinebis daxris
kuTxeSi an siganeSi.
xaxuni – garkveul distanciaze
wyali miedineba damrecad. ras niSnavs es CvenTvis?
 wylis dineba Ria kalapotSi rogorc wesi matebs energias (kinetikur
energias) vinaidan is miedineba maRali wertilidan dabali wertilisken.
 xaxunTan da obstruqciasTan (dabrkoleba) erTad xdeba energiis dakargva.
gravitaciuli Zalebi, romlebic aCqareben dinebas imyofebian wonasworobaSi xaxunis ZalebTan, daZabulobis mateba
xdeba sveli perimetris zegavleniT, rac anelebs dinebas
erTgvari da normuli dineba
Gravity
Friction
mdinaris mTel sigrZeze...
saSualo siCqare: aris funqcia (ferdobis daxra da winaRoba, romelic
amuxruWebs dinebas zRurblis gaswvriv)
W
F
ras niSnavs es?
warmovidginoT hipoTeturi kalapoti
grZeli prizmuli (erTi da igive seqcia did manZilze) kalapoti
ar gvaqvs cvlileba dinebis daqanebSi, seqciebSi, xarjSi
V2/2g
V
hidravlikuri wnevis
gadanawileba
EGL
Y
WS
So
kalapotis fskeri wylis zedapiris paraleluria da energiis xarisxis wrfis paraleluria. veqtoruli wrfeebi paraleluria.
ucvleli dineba warmoSveba maSin, rodesac xdeba winaRobis Zalebis mier gravitaciuli Zalebis
kompensireba.
erTgvari dineba warmoSveba roca:



saSualo siCqare aris ucvleli seqciidan seqciamde
dinebis siRrme aris ucvleli seqciidan seqciamde
dinebis farTobi aris ucvleli seqciidan seqciamde
Sesabamisad: es SeiZleba moxdes mxolod Zalian grZel, swor, prizmul
kalapotSi, sadac dineba aRwevs zRvrul siCqares
saSualo siRrme ukavSirdeba ferdobis sxvadasxva tipis daqanebas.
cvalebadi
nakadi
cvalebadi
nakadi
erTgvari nakadi
“n” igulisxmeba saSualo
“s” igulisxmeba kritikuli
Yn
Yc
Cvalebadi
nakadi
sustad daxrili ferdobi
Cvalebadi
nakadi
erTgvari nakadi
kritikuli ferdobi
Yc
Yn
cicabo ferdobi
erTgvari nakadi
Tu dineba aris funqcia ferdobis daxrisa da xaxunis
Zalis, rogor SegviZlia gamoviangariSoT is?
 F  ma
niutonis meore kanoni
0
Tu siCqare aris mudmivi, maSin aCqareba nulis tolia. Sesabamisad SegviZlia gamoviyenoT martivi Zalebis balansi
 0 PL  W sin   0
where
sadac
 0  KV 2
rearrange equation
gadavaTamaSoT gantoleba
KV 2 PL  AL sin 
mcire
small
 sin   S 0
V

K
RS 0
xaxuni
gravitacia
Gravity
Friction
antoni Cezi (18 saukune)
V  C RS o
maningis gantoleba
2
1
1.49
2
Q
AS R 3
n
dineba (cfs)
Q  flow
koeficienti
n  coeff
A  area
farTobi
ferdobis daxra
S  slope
dasvelebis perimetri
P  wetted
perimeter
RA
P
erT erTi yvelaze farTod gavrcelebuli meTodi xaxunis danakargis dasaTvlelad
dineba
koeficienti
farTobi
ferdobis daxra
dasvelebis perimetri
maningis gantoleba - ‘n’ erTeuli
2
1
1.49
2
Q
AS R 3
n
2
A
L
R
LL
P
2
2
3
(
L
)(
L
)
L /T 
3
n
L = sigrZe (futi, metri, inCi d.a.S.
T = dro (wami, wuTi, saaTi, a.S.)
maningis n
niadagis zRvari aris funqcia marcvlis zomis, xorklianobis (simqisis), araerTgvarovnebis, a.S.
sidide SemoRebuli iyo gasuli saukunis dasawyisSi (kingi 1918)
saxelmZRvaneloebi: moZebneT bibliografia da internet saitebi
n=0.018
NRCS - Fasken, 1963
n=0.110
n=0.050
n=0.018
n=0.014
n=0.060
n=0.125
n=0.016
n=0.080
n=0.020
n=0.150
maningis n cicabod daxril kalapotSi


nakadi SeiZleba Candes super kritikuli, magram iyos mxolod swrafi subkritikuli
jaretis gantoleba (ASCE J. of Hyd Eng, Vol. 110(11)) ( R = hidravlikuri radiusi futebSi)
n  0.39S
0.38
R
0.16
ra SesaZlebloba aqvs maningis gantolebas praqtikaSi?
 SegviZlia gamoviTvaloT CvenTvis saWiro sxvadasxva parametri
 siCqare
 siRrmis, siganis, farTobis da sxva parametrebis gadamowmeba da cdomilebis dadgena
1.49 1 2 2 3
V
S R
n
2
1
1.49
2
Q
AS R 3
n
Sesabamisad... ratom gavarTuloT saqme?
ramdenad mgrZnobiarea gantoleba?
W=100’
d=5’
S=0.004
n=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%
12% to 13%
S=0.003 to 0.005
All
40% to 70%
ramdenad xSirad vxvdebiT saSualo siRrmes
bunebriv nakadebSi?
cicabo ferdobi: saSualo siRrme kritikulze naklebia
nakadebi miiswrafian saSualo siRrmisken
magram iSviaTad aRweven mas
sustad daxrili ferdobi: saSualo siRrme kritikulze metia.
SezRudvebi saSualo siRrmis gaTvlebSi:


mudmivi seqcia – bunebrivi arxi?
ucvleli xorklianoba (simqise) – wylis napirebze gadasvla?


ferdobis ucvleli daqaneba
wylis gamavlobis SenarCuneba – xidebi, jebirebi, a.S.
Ria arxis dineba xasiaTdeba cvalebadobiT
b. ucvleli cvalebadis winaaRmdeg
ucvleli dineba
cvalebadi dineba
siRrme da siCqare aris mudmivi
arxis gaswvriv mTel sigrZeze
siRrme da siCqare cvalebadia
arxis gaswvriv mTel sigrZeze
b. ucvleli dineba cvalebadis winaaRmdeg
subkritikuli
kritikuli
superkritikuli
orive, xelovnuri da bunebrivi nakadebi
hidravlikuri naxtomi
subkritikuli
Tim McCabe, IA NRCS
subkritikuli
kritikuli
superkritikuli
hidravlikuri naxtomi
subkritikuli
Lynn Betts , IA NRCS
bunebriv, TandaTanobiT cvalebad dinebebSi:
siCqare da siRrme icvleba seqciidan seqciamde.
Tumca, energia da masa SenarCunebulia.
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 - 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.
energiis gantolebis Sesaxeb:
 Termodinamikis pirveli kanoni
bernulis gantoleba:
(V2/2g)2
+ P2/w + Z2
=
(V2/2g)1 + P1/w + Z1
•kinetikuri energia + wnevis energia + potenciuri energia aris SenarCunebuli
+ he
daimaxsovreT – es aris Ria nakadi da hidrostatikuli wnevis ganawileba:
Y2
(V2/2g)2
+ P2/w + Z2
Y1
=
(V2/2g)1 + P1/w + Z1 + he
mCqarebluri wneva SeiZleba warmodgenili iyos vertikalurad gazomili wylis doniT (SesaZlebelia
problemuri iyos, cicabo daqanebis SemTxvevaSi – nakadis xazi Tavsdeba an gadaixreba uecrad)
energiis gantoleba
(V2/2g)2
he
Y2
(V2/2g)1
Y1
Z2
Z1
datumi
(V2/2g)2 + Y2 + Z2 = (V2/2g)1 + Y1 + Z1 + he
energiis danakargi
he  L S f  C
V22
2g

V12
2g
standartuli nabijis meTodi
(V2/2g)2
he
Y2
(V2/2g)1
Y1
Z2
Z1
datumi
1
2
2
WS 2  WS1  (1V1   2V2 )  he
2g



daiwyeT nacnobi wertilidan
ramdeni ramea ucnobi?
Semowmeba da cdomileba
HEC-RAS - gamoTvlebis procedurebi
1.
savaraudo wylis zedapiris simaRle zeda/qveda dinebis gaswvriv.
2.
savaraudo wylis zedapiris simaRleze dayrdnobiT, gansazRvreT Sesabamisi xarji da zewolis
siCqare.
3.
meore safexuris Sedegad miRebuli sididis gamoyenebiT iTvlis da xsnis gantolebas “misTvis”
4.
meore da mesame bijis Sedegad miRebuli sididiT ixsneba energiis gantoleba WS2-sTvis.
5.
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.
energiis danakargi – mniSvnelovani faqtori

gamoyenebuli danakargis koeficienti
 maningis sidide xaxunis danakargi
 Zalian mniSvnelovania gaangariSebuli profilis sizustisTvis
 daakalibreT (SeamowmeT) rogorc ki monacemebi xelmisawvdomia
 kumSvis da gafarTovebis koeficienti X seqciisTvis
 danakargis gamo, romelic dakavSirebulia X seqciaSi farTobis da siCqaris cvlilebasTan.
 SekumSva, roodesac siCqare matulobs qveda dinebaSi
 gafarToveba, rodesac siCqare klebulobs qveda dinebaSi
 xidi da wyalsadenis SekumSvis da gafarTovebis danakargis koeficientebi
 igivea, rac X seqciisTvis, magram rogorc wesi sidide ufro didia.
 xaxunis danakargi fasdeba, rogorc xaxunis kuTxis da gawvdomis xarjis wonis mTeli
sigrZis warmoebuli
he  L S f  C
V
2
2
2g

V
2
1
2g
Llob Qlob  Lch Qch  Lrob Qrob
L
Qlob  Qch  Qrob
xaxunis danakargi fasdeba, rogorc xaxunis kuTxis da gawvdomis xarjis
wonis mTeli sigrZis warmoebuli.
he  L S f  C
V22 V12
2g

2g
2
1
1
1.49
3
Q
AR S f 2  KS f 2
n
1
Q
Q
2
2
Sf 
,Sf  (
)
K
K
Senakadis
gadazidva
xaxunis kuTxe HEC-RAS-Si
saSualo gadazidva (HEC-RAS-is winapiroba) –saukeTeso Sedegi
yvela tipis profilisTvis (M1, M2, და sxva.)
saSualo xaxunis kuTxe - saukeTeso Sedegi M1 tipis profilebisTvis.
geometriuli saSualo xaxunis kuTxe – gamoiyeneba USGS/FHWA
WSPRO modelisTvis
harmoniuli saSualo xaxunis kuTxe – saukeTeso Sedegi M2 tipis
profilebisTvis
 Q1  Q 2 

S f  
 K1  K 2 
Sf 
S f1  S f2
2
S f  S f1  S f2
Sf 
2Sf1  S f2
S f1  S f2
2
dinebis klasifikacia
cicabo ferdobi: saSualo siRrme kritikul siRrmeze
naklebia
susti daxra: saSualo siRrme kritikulze metia
xaxunis kuTxe HEC-RAS-Si
HEC-RAS –s aqvs parametri, romelic saSualebas aZlevs programas SearCiios da gamoiyenos saukeTeso xaxunis kuTxis
funqcia profilebis tipebis mixedviT.
aris Tu ara xaxunis kuTxe
mocemuli ganivi kveTisTvis meti vidre xaxunis
kuTxe Semdeg ganiv kveTSi?
gamoyenebuli gantoleba
profilis tipi
სubkritikuli (M1, S1)
სubkritikuli (M2)
სuperkritikuli(S2)
superkritikuli(M3, S3)
ki
ara
ki
ara
saSualo xaxunis kuTxe (2-14)
harmoniuli saSualo (2-16)
saSualo xaxunis kuTxe (2-14)
geometriuli saSualo (2-15)
xaxunis kuTxe HEC-RAS-Si
HEC-RAS–s aqvs parametri, romelic saSualebas aZlevs programas SearCiios da gamoiyenos saukeTeso xaxunis kuTxis funqcia profilebis
tipebis mixedviT.
HEC-RAS
suraTi 2.2 HEC-RAS წინაპირობითი გადაზიდვების ქვედანაყოფი
gadazidvebis (gadatanis) qvedanayofis, winapirobiT miRebuli meTodi warmoadgens maningis N sidides
HEC-2 stili
suraTi 2.3 ალტერნატიული გადაზიდვების ქვედანაყოფის მეთოდი
(HEC-RAS–2 სტილი)
SemoTavazebuli meTodi romელსაც iyenebs HEC-2 – hyofs datborvis zonas yovel individualur zedapiris
wertilSi.
SniSnva: SesaZlebelia mogvces mniSvnelovani gansxvaveba, rodesac gvaqvs didi cvlileba datborvaSi
sxva danakargebi:
 SekumSvis danakargi
 gafarToebis danakargi
V V
he  L S f  C

2g 2g
2
2
C = SekumSvis an gafarToebis koeficienti
2
1
SekumSvis da gafarToebis energiis danakargis koeficientebi
V V
he  L S f  C

2g 2g
2
2

2
1
SeniSnva 1: WSP2 iyenebs zeda dinebis seqcias, mis qveviT arsebuli mTeli gawvdomisTvis, maSin roca
HEC-RAS-i asaSualoebs or X seqcias Soris arsebul koeficientebs.

SeniSnva 2: WSP2 iyenebs mxolod LSf-s Zvel versiebSi da damatebuli aqvs C uaxles versiebSi, iyenebs ra
“danakargis” baraTs.
SekumSvis da gafarToebis koeficientebi
gafarToveba
SekumSva
0
0
TandaTanobiTi gadasva
0.3
0.1
tipiuri xidis seqcia
0.5
0.3
wyvetili gadasvla
0.8
0.6
ar aris gadasvlis danakargi
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.
specifikuri energia
gansazRvreba: dinebis xelmisawvdomi energia
nakadis fskerTan mimarTebaSi ufro prioritetulia vidre datumTan
mimarTebaSi
y
b
vuSvebT, rom totaluri energia aris ucvleli, mTel seqciaSi, Sesabamisad
Cven vRebulobT 1-D
2
V
E  y
2g
q Q
b
Q
V 
by
q
V 
y
2
SeniSnva: hidravlikuri siRrme (y) aris ganivi kveTis farTobi gayofili
udides siganeze
q
E  y
2 gy 2
specifikuri energia
2
q
( E  y) y 2 
 const .
2g
const .
2
y 
Ey
specifikuri energiis gantoleba SeiZleba gamoviyenoT mrudis asagebad.
kiTxva: ra gamoyeneba aqvs mruds?
pasuxi: is gamoiyeneba maSin, rodesac saWiroa interpretacia gavukeToT Ria dinebis
konkretul aspeqts.
wylis zedapiris
simaRle
Y1
SeniSnva: mcire ferdobisTvis
kuTxe aris 45.
or
y Y2
totaluri energia H an E
or E
specifikuri energia
2
q
( E  y) y 2 
 const .
2g
const .
2
y 
Ey
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.
wylis zedapiris
simaRle
minimaluri specifikuri
energia
Y1
Y2
totaluri energia H
specifikuri energia
q2
E  y
2 gy 2
dE
q2
 1
0
3
dy
gy
2
q
1
3
gy
kiTxva: ra aris minimumi?
pasuxi: kritikuli dineba
wylis zedapiris
simaRle
minimaluri specifikuri
energia
totaluri energia H
frudes ricxvi
q2
E  y
2 gy 2
dE
q2
2
 1

1

Froude
dy
gy 3
q
V
Froude 

gy
gy 3

Tanafardoba nakadis siCqaresa (inerciis Zala) da talRis siCqares Soris (gravitaciuli Zala)
frudes ricxvi

Tanafardoba nakadis siCqaresa (inerciis Zala) da talRis siCqares Soris (gravitaciuli Zala)
inertia
Fr 
gravity
Fr > 1, superkritikuli dineba
Fr < 1, subkritikuli dineba
1: subkritikuli, Rrma, neli dineba, arRvevs, Slis mxolod zeda dinebas
2: superkritikuli, Cqari, zedapiruli dineba, aRreva, aSliloba SeiZleba ar
vrceldebodes zeda dinebaSi.
wylis zedapiris
simaRle
subkritikuli
superkritikuli
totaluri energia H
kritikuli dineba





frude = 1
minimaluri specifikuri energia
cvlileba
mcire cvalebadoba energiaSi (xorklianoba, forma, da sxva) warmoqmnis did cvlilebebs siRrmeSi
xdeba wyalgadasaSvebSi
wylis zedapiris
simaRle
subkritikuli
superkritikuli
totaluri energia H
SeniSvna: kritikuli siRrme araa damokidebuli daxraze da xorklianobaze
kritikuli dinebis gansazRvra
HEC-RAS iTvlis kritikul dinebas X seqciaSi 5 gansxvavebul situaciisTvis:

superkritikuli dinebis reJimi iyo gansazRvruli

kritikuli siRrmis gaangariSeba momxmareblis moTxovniT

kritikuli siRrme ganisazRvreba yvela X seqciis sazRvarze

fraudis ricxvis dadgeniT ganisazRvreba sabalanso simaRlesTan dakavSirebuli dinebis reJimis

gansazRvrisaTvis saWiro kritikuli siRrme.
programul uzrunvelyofas ar SeuZlia gaawonasworos energiis gantoleba mocemuli daSvebis
farglebSi manam ar miaRwevs განმეორებადობის maqsimalur zRvars.
HEC-RAS-Si Cven gvaqvs arCevani
jer kidevs saWiroa zedmiwevniT Semowmdes gadaadgileba
hidravlikuri naxtomi?

wylis zedapiri “daxtis”

rogorc wesi ჯებირების და დაბრკოლების SemTxvevaSi

Zalian maRali energiis danakargi/gaflangva “naxtomis” turbulentur zonaSi
hidravlikuri
H y d r anaxtomi
u l ic
J ump
S u b c dineba
subkritikuli
rit ic
a l F lo
w
superkritikuli
dineba
S upe
r c r it
ic a l F
lo w
dinebaF l
ow
grZivi profilis zogadi forma
dc
არხის გასასვლელი
dn
dn
M
S
M
uecrad cvalebadi dinebis SemTxveva

gadis subkritikulidan superkritikulisken an piriqiT miiReba uecarad cvalebadi dinebis SemTxvevaSi.

energiis gantoleba gamoiyeneba TandaTanobiT cvalebadi dinebisTvis (saWiroebs Sida energiis danakargis
gadaTvlas)

SesaZlebelia empiriuli gantolebis gamoyeneba

SesaZlebelia momentis gantolebis gamoyeneba
momentis gantoleba


miRebulia niutonis meore kanonidan, F=ma
miusadageT F = ma wylis tans yvelaze axlosmdebare zeda dinebasTan da qvedadinebis X seqcias
gansxvaveba wnevaSi + wylis wona – gare xaxuni = masis X aCqarebas
P2  P1  Wx  Ff  Q  ρ  ΔVx
momentis gantoleba
2
( V / 2g )
+ Y
2
+Z =
2
2
2
( V / 2g) + Y + Z + hm
1
1
1
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.
ucvlel dinebaSi, Sinagani da garegani danakargi identuria. TandaTanobiT cvalebad dinebaSi, isini erTmaneTTan
miaxloebuli sidideebia.
HECRAS SeuZlia gamoiyenos momentis gantoleba:




hidravlikuri naxtomi
hidravlikuri wveTi
dabali dinebis hidravlika xidTan
nakadebis SekavSireba
vinaidan gadaadgileba moklea, gare energiis danakargi (xaxunis
gamo) miCneulia nulad
Ria damyarebuli dinebis klasifikacia daumyarebeli dinebis sapirispirod
a.
damyarebuli da daumyarebeli
dineba
damyarebuli dineba
daumyarebeli dineba
siRrme da siCqare mocemul wertilSi ar icvleba drois
mixedviT
siRrme da siCqare mocemul wertilSi icvleba
drois mixedviT
daumyarebeli dinebis magaliTebi
bunebrivi dineba yovelTvis arastabiluria – rodisaa saWiro arastabilurobis komponentebis
gaTvaliswineba?





kaSxlis garRveva
mdinaris SesarTavebi
yureebi, ubeebi
wyaldidobis talRebi
sxva
HEC-RAS-i aris 1D – ganzomilebiani modeli
 miedineba erTi mimarTulebiT
 es aris qaoturi sistemis gamartiveba
 ar SeuZlia asaxos aratipiuri simaRleebi moxvevis adgilebSi
 ar SeuZlia asaxos meoradi dinebebi
siCqaris gadanawileba – 3D
Tavisufali zedapiris da xaxunis gamo, siCqare ar aris ucvleli sxvadsxva doneebze
V  Vx i  V y j  Vz k
suraTi 4. magaliTi siCqaris gadanawilebisა 2-D -Si
magram arsebobs 1-D
siCqaris gadanawileba
siCqaris gadanawileba kalapotSi

realuri maqsimaluri V aris
daaxloebiT 0.15D
(zedapiridan)
realuri saSualo V aris daaxloebiT
0.6D (zedapiridan)
siRrme

Teoriuli
realuri
საშუალო
siCqare
meoradi cirkulaciis magaliTi mdinaris fskeris ganiv seqciaSi
gare napiris dineba wertilis gaswvriv
erTi ujredis Teoria (tomsoni, 1876; havtorni. 1951; quiki, 1974)
gare napiris dineba wertilis
gaswvriv
cirkulaciuri dinebis dRevandeli Teoria gaRunvis indikatoriT napiris ujredisTvis (hei da tornei, 1975)
HEC-RAS – is sxva daSvebebi
 HEC-RAS aris fiqsirebuli kalapotis modeli
 ganivi kveTi statikuria
 saSualebas iZleva SevcvaloT kalapotis modeli
 HEC-RAS –s ar aqvs funqcia, rom Tavad gaiTvaliswinos zeda dinebis
wyalgasayaris cvlileba.
HEC-RAS – i aris bunebrivi sistemis gamartivebuli
modeli