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

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.

nino.kheladze

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

So…why make things any more complicated?Sesabamisad... ratom gavarTuloT saqme?

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


Hydraulic Jumphidravlikuri naxtomi




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.


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.


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


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


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


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.



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



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

M

S

M

Sluice gateარხის გასასვლელი

dc dn

dn

General Shape Of Profileprofilis zogadi forma

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

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

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Transcript of by G. Parodi WRS – ITC – The Netherlands g. parodi WRS-ITC- niderlandebi