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
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
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.
Continuity Equation
uwyvetobis gantoleba
(conservation of mass)
(მასის შენახვის principi)
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
Open Channel Flow – Controls
Ria 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
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.
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
Uniform or Normal Flow
erTgvari da normuli dineba
Gravity
Friction
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
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
V2/2g
V
Hydrostatic pressure
distribution
hidravlikuri wnevis
gadanawileba
EGL
Y
WS
So
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.
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
Normal Depth Applies to Different Types of Slopes
saSualo siRrme ukavSirdeba ferdobis sxvadasxva tipis daqanebas .
cvalebadi
nakadi
cvalebadi
nakadi
erTgvari nakadi
Yn
Yc
‘n’ stands for normal
“n” igulisxmeba saSualo
‘s’ stands for critical
“s” igulisxmeba kritikuli
Cvalebadi nakadi
erTgvari nakadi
Mild Slope
sustad daxrili ferdobi
Cvalebadi nakadi
erTgvari nakadi
Critical Slope
kritikuli ferdobi
Yc
Yn
Steep Slope
cicabo ferdobi
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?
Newton's second law
niutonis meore kanoni
 F  ma
0
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
 0 PL  W sin   0
where
where
sadac
 0  KV 2
rearrange equation
rearrange
equation
gadavaTamaSoT gantoleba
KV 2 PL  AL sin 
small
mcire all
sm
 sin   S 0
V

K
RS0
Gravity
gravitacia
Gravity
Friction
xaxuni
Friction
Antoine Chezy (18th century)
antoni Cezi (18 saukune)
V  C RSo
Manning’s equation
maningis gantoleba
2
1
1.49
2
Q
AS R 3
n
Q  flow(cfs)
dineba
n  coeff
koeficienti
A  area
farTobi
S  slope
ferdobis daxra
P  wetted perim eter
RA
dasvelebis perimetri
P
One of the most widely used to account for friction losses
erT erTi yvelaze farTod gavrcelebuli meTodi xaxunis danakargis dasaTvlelad
Manning’s Equation - ‘n’ units
maningis gantoleba - ‘n’ erTeuli
2
1
1.49
2
Q
AS R 3
n
2
A
L
R
P
LL
2
2
3
(
L
)(
L
)
L /T 
3
n
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.)
Manning’s n
maningis 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)
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 brush
Mountain 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)
Manning’s n
maningis 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)
Guidance Available: seek bibliography and the WEB
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
Manning’s n in Steep Channel
maningis 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


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)
n  0.39S
0.38
R
0.16
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
1.49 12 2 3
V
S R
n
2
1
1.49
2
Q
AS R 3
n
So…why make things any more complicated?
Sesabamisad... ratom gavarTuloT saqme?
How sensitive is the equation?
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%
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.
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 varied
Ria 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
B. Uniform versus Varied Flow
b. ucvleli dineba cvalebadis winaaRmdeg
Varied Flow
cvalebadi dineba
Depth and velocity vary with
distance along the channel.
siRrme da siCqare cvalebadia
arxis gaswvriv mTel sigrZeze
Subcritical
subkritikuli
Critical
kritikuli
Both man made and natural
channels
orive, xelovnuri da bunebrivi nakadebi
Supercritical
superkritikuli
Hydraulic Jump
hidravlikuri naxtomi
Tim McCabe, IA NRCS
Subcritical
subkritikuli
Critical
kritikuli
Supercritical
superkritikuli
Hydraulic Jump
hidravlikuri naxtomi
Subcritical
subkritikuli
Lynn Betts , IA NRCS
Subcritical
subkritikuli
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 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.
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
Bernoulli ‘s Equation
bernulis gantoleba:
(V2/2g)2
•
+ P2/w + Z2
=
(V2/2g)1 + P1/w + Z1
Kinetic energy + pressure energy + potential energy is conserved
• kinetikuri energia + wnevis energia + potenciuri energia aris SenarCunebuli
+ he
Remember - it’s an open channel and a hydrostatic pressure
distribution
daimaxsovreT – es aris Ria nakadi da hidrostatikuli wnevis ganawileba
Y2
(V2/2g)2
+ P2/w + Z2
Y1
=
(V2/2g)1 + P1/w + Z1 + he
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 daqanebi s SemTxvevaSi
– nakadis xazi Tavsdeba an gadaixreba uecrad)
Energy Equation
energiis gantoleba
(V2/2g)2
he
Y2
(V2/2g)1
Y1
Z2
Z1
Datum
datumi
(V2/2g)2 + Y2 + Z2 = (V2/2g)1 + Y1 + Z1 + he
Energy Losses
energiis danakargi
he  L S f  C
V22
2g

V12
2g
Standard Step Method
standartuli nabijis meTodi
(V2/2g)2
he
Y2
(V2/2g)1
Y1
Z2
Z1
Datum
datumi
1
2
2
WS 2  WS 1  (1V1   2V2 )  he
2g






Start at a known point.
daiwyeT nacnobi wertilidan
How many unknowns?
ramdeni ramea ucnobi?
Trial and error
Semowmeba da cdomileba
HEC-RAS - Computation Procedure
HEC-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.
Energy Loss - important stuff
energiis danakargi – mniSvnelovani faqtori


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.
 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
he  L S f  C
V
2
2
2g

V
2
1
2g
Llob Qlob  Lch Qch  Lrob Qrob
L
Qlob  Qch  Qrob
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.
he  L S f  C
V22
2g

V12
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
Channel
Conveyance
Senakadis
gadazidva
Friction Slopes in HEC-RAS
xaxunis 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, და sxva.)
 Q1  Q2 

S f  
 K1  K 2 
Average Friction Slope - best results for M1 profiles
saSualo xaxunis kuTxe - saukeTeso Sedegi M1 tipis profilebisTvis.
Sf 
Geometric Mean Friction Slope - used in USGS/FHWA
S f1  S f2
2
WSPRO model
geometriuli saSualo xaxunis kuTxe – gamoiyeneba USGS/FHWA WSPRO modelisTvis
S f  S f1  S f2
Harmonic Mean Friction Slope - best results for M2
profiles
harmoniuli saSualo xaxunis kuTxe – saukeTeso Sedegi M2 tipis profilebisTvis
Sf 
2S f1  S f2
S f1  S f2
2
Flow
Classification
dinebis 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
Friction Slopes in HEC-RAS
xaxunis 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 პარამეტრი, romelic saSualebas aZlevs programas SearCiios da gamoiyenos saukeTeso xaxunis kuTxis funqcia profilebis tipebis mixedviT.
profilis tipi
aris Tu ara xaxunis kuTxe
mocemuli ganivi kveTisTvis meti vidre xaxunis
kuTxe Semdeg ganiv kveTSi?
gamoyenebuli gantoleba
ki
ara
ki
ara
სubkritikuli
სubkritikuli
სuperkritikuli
superkritikuli
saSualo xaxunis kuTxe
harmoniuli saSualo
saSualo xaxunis kuTxe
geometriuli saSualo
Friction Slopes in HEC-RAS
xaxunis 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 პარამეტრი, romelic saSualebas aZlevs programas SearCiios da gamoiyenos saukeTeso xaxunis kuTxis funqcia profilebis tipebis mixedviT.
HEC-RAS
HEC-RAS
გრაფა 2.2 HEC-RAS წინაპირობითი გადაზიდვების ქვედანაყოფი
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-2 style
გრაფა 2.3 ალტერნატიული გადაზიდვების ქვედანაყოფის მეთოდი
(HEC-RAS–2 სტილი)
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
Other losses include:
sxva danakargebi:
 Contraction losses
 SekumSvis danakargi
 Expansion losses
 gafarToebis danakargi
V V
he  L S f  C

2g 2g
2
2
C = contraction or expansion coefficient
C = SekumSvis an gafarToebis koeficienti
2
1
Contraction and Expansion Energy Loss Coefficients
SekumSvis da gafarToebis energiis danakargis koeficientebi
V V
he  L S f  C

2g 2g
2
2

2
1
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.
Expansion and Contraction Coefficients
SekumSvis da gafarToebis koeficientebi
gafarToveba
Contraction
SekumSva
0
0
0.3
0.1
0.5
0.3
0.8
0.6
Expansion
No transition loss
ar aris gadasvlis danakargi
Gradual transitions
TandaTanobiTi gadasva
Typical bridge sections
ტიპიური xidis seqcia
Abrupt transitions
wyvetili gadasvla
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.
Specific Energy
specifikuri 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
y
b
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
2
V
E  y
2g
Q
q 
b
V Q
by
V  q
y
2
q
E  y
2
2gy
Specific Energy
specifikuri energia
2
q
( E  y) y 2 
 const.
2g
const.
2
y 
Ey
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
Specific Energy
specifikuri energia
2
q
2
( E  y) y 
 const.
2g
const.
2
y 
Ey
Y1
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
Y2
Specific Energy
specifikuri energia
q2
E  y
2 gy 2
dE
q2
 1
0
3
dy
gy
q2
1
3
gy
Q: What is that minimum?
A: Critical flow!!
kiTxva: ra aris minimumi?
pasuxi: kritikuli dineba
Minimum specific
energy
minimaluri specifikuri
energia
Froude Number
frudes ricxvi
q2
E  y
2 gy 2
dE
q2
2
 1

1

Froude
dy
gy 3
q
V
Froude 

gy
gy 3


Ratio of stream velocity (inertia force) to wave velocity (gravity force)
Tanafardoba nakadis siCqaresa (inerciis Zala) da talRis siCqares Soris (gravitaciuli Zala)
Froude Number
frudes ricxvi


Ratio of stream velocity (inertia force) to wave velocity (gravity force)
Tanafardoba nakadis siCqaresa (inerciis Zala) da talRis siCqares Soris (gravitaciuli Zala)
inertia
Fr 
gravity
wylis zedapiris
simaRle
Fr > 1, supercritical flow
Fr > 1, superkritikuli dineba
Fr < 1, subcritical flow
Fr < 1, subkritikuli dineba
1: subcritical, deep, slow flow, disturbances only
propagate upstream
1: subkritikuli, Rrma, neli dineba, arRvevs, Slis mxolod zeda dinebas
Subcritical
subkritikuli
Supercritical
superkritikuli
3: supercritical, fast, shallow flow, disturbance can
not propagate upstream
superkritikuli, Cqari, zedapiruli dineba, aRreva, aSliloba SeiZleba ar
vrceldebodes zeda dinebaSi.


Critical Flow
kritikuli 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
wylis zedapiris simaRle
Subcritical
subkritikuli
Supercritical
superkritikuli
Note: Critical depth is independent of roughness and slope
SeniSvna: kritikuli siRrme araa damokidebuli daxraze da xorklianobaze
Critical Depth Determination
kritikuli 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 განმეორებადობის maqsimalur
zRvars.
In HEC-RAS, we have a choice for the calculations
HEC-RAS-Si Cven gvaqvs arCevani gaTvlebisTvis
Still need to examine transitions closely
jer 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
H y d r a u l ic
J ump
S upe
r
c r it i
S ubc
ri
cal F
lo w
F lo w
t ic a l
F lo w
General Shape Of Profile
profilis zogadi forma
dc
dn
Sluice gate
არხის გასასვლელი
dn
M
S
M
A rapidly varying flow situation
uecrad 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
Momentum Equation
momentis gantoleba


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
Difference in pressure + weight of water - external friction = mass x acceleration
gansxvaveba wnevaSi + wylis wona – gare xaxuni = masis X aCqarebas
P2  P1  Wx  Ff  Q  ρ  ΔVx
Momentum Equation
momentis gantoleba
2
( V / 2g )
+ Y
2
+Z =
2
2
2
( V / 2g) + Y + Z + hm
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.
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 zero
vinaidan gadaadgileba moklea, gare energiis danakargi (xaxunis gamo) miCneulia nulad
Classifications of Open Steady versus Unsteady
Ria უცვლელი dinebis klasifikacia ცვალებადი dinebis sapirispirod
a. უცვლელი ცვალებადის საწინააღმდეგოდ
ურყევი (უცვლელი) dineba
siRrme da siCqare mocemul wertilSi ar icvleba drois mixedviT
მერყევი (ცვალებადი) dineba
siRrme da siCqare mocemul wertilSi icvleba drois
mixedviT
Unsteady Examples
ცვალებადი 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
HEC-RAS is a 1-Dimensional Model
HEC-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
Velocity Distribution - It’s 3-D
siCqaris gadanawileba – 3D
Because of free surface and friction, velocity is not uniformly distributed
Tavisufali zedapiris da xaxunis gamo, siCqare ar aris ucvleli sxvadsxva doneebze
V  Vxi  Vy j  Vz k
suraTi 4. magaliTi siCqaris gadanawilebisა 2-D -Si
…but HEC-RAS is 1-D
magram arsebobs 1-D
Velocity Distribution
siCqaris 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

realuri saSualo V aris daaxloebiT 0.6D
(zedapiridan)
siRrme
top).
Teoriuli
realuri
საშუალო
siCqare
Secondary circulation pattern at a river bed cross section
meoradi cirkulaciis magaliTi mdinaris fskeris ganiv seqciaSi
Outward shoaling flow across point bar
gare napiris dineba wertilis gaswvriv
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)
Other assumptions in HEC-RAS
HEC-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