HECRAS Basic Principles of Water Surface Profile Computations HECRAS wylis zedapiris profilis agebis ZiriTadi principebi by G. Parodi WRS – ITC – The.

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

(conservation of mass)
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 Equation uwyvetobis gantoleba 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

It loses energy with friction and obstructions.
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 Flow erTgvari da normuli dineba
The gravitational forces that are pushing the flow along are in balance with the frictional forces exerted by the wetted perimeter that are retarding the flow. gravitaciuli Zalebi, romlebic aCqareben dinebas imyofebian wonasworobaSi xaxunis ZalebTan, daZabulobis mateba xdeba sveli perimetris zegavleniT, rac anelebs dinebas Uniform or Normal Flow erTgvari da normuli dineba Water flowing gains kinetic energy (higher elevation to a lower). It looses energy with friction and obstructions. When in balance it is under uniform flow (Manning) 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 EGL Y So WS V Hydrostatic pressure distribution hidravlikuri wnevis gadanawileba 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

“n” igulisxmeba saSualo ‘s’ stands for critical
Normal Depth Applies to Different Types of Slopes saSualo siRrme ukavSirdeba ferdobis sxvadasxva tipis daqanebas. cvalebadi nakadi cvalebadi nakadi erTgvari nakadi ‘n’ stands for normal “n” igulisxmeba saSualo ‘s’ stands for critical “s” igulisxmeba kritikuli Yn Yc Cvalebadi nakadi erTgvari nakadi Mild Slope sustad daxrili ferdobi Mild Slope - most natural channels. Steep slope - mountain streams and constructed armored channels Critical slope - rare. 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 where sadac Gravity Friction
Newton's second law niutonis meore kanoni If velocity is constant, then acceleration is zero. So use a simple force balance. Tu siCqare aris mudmivi, maSin aCqareba nulis tolia. Sesabamisad SegviZlia gamoviyenoT martivi Zalebis balansi where sadac Gravity Friction rearrange equation gadavaTamaSoT gantoleba Gravity gravitacia Friction xaxuni small mcire Antoine Chezy (18th century) antoni Cezi (18 saukune)

Manning’s equation maningis gantoleba
dineba koeficienti farTobi ferdobis daxra dasvelebis perimetri One of the most widely used to account for friction losses erT erTi yvelaze farTod gavrcelebuli meTodi xaxunis danakargis dasaTvlelad

Manning’s Equation - ‘n’ units maningis gantoleba - ‘n’ erTeuli
L = length (feet, meters, inches, etc) L = sigrZe (futi, metri, inCi d.a.S. T = time (seconds, minutes, hours, etc) T = dro (wami, wuTi, saaTi, a.S.)

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=0.060 n=0.080 n=0.110 n=0.125 n=0.150 n=0.050 n=0.018 n=0.014 n=0.016 n=0.020

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) Mannings n is a bulk term

Can compute many of the parameters that we are interested in:
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
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% S=0.003 to 0.005 12% to 13% 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 is more for prismatic channels. Varied is more real life. HEC-RAS models steady, gradually varied flow. Uniform Flow ucvleli dineba Depth and velocity are constant with distance along the channel. siRrme da siCqare aris mudmivi arxis gaswvriv mTel sigrZeze Varied Flow cvalebadi dineba Depth and velocity vary with distance along the channel. siRrme da siCqare cvalebadia arxis gaswvriv mTel sigrZeze B. Uniform versus Varied Flow b. ucvleli dineba cvalebadis winaaRmdeg

Both man made and natural channels
Tim McCabe, IA NRCS Subcritical subkritikuli Critical kritikuli Both man made and natural channels orive, xelovnuri da bunebrivi nakadebi Supercritical superkritikuli Hydraulic Jump hidravlikuri naxtomi Hydraulic Jump hidravlikuri naxtomi Critical kritikuli Subcritical subkritikuli Supercritical superkritikuli Subcritical subkritikuli Subcritical subkritikuli Lynn Betts , IA NRCS

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 (V2/2g)2 + P2/w + Z2 = (V2/2g)1 P1/w + Z1 he Bernoulli ‘s Equation bernulis 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 Y2 Y1 (V2/2g)2 + P2/w + Z2 = (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 daqanebis SemTxvevaSi – nakadis xazi Tavsdeba an gadaixreba uecrad)

Energy Equation energiis gantoleba
Water Surface wylis zedapiri Energy Grade Line energiis xarisxis grafiki Y2 Y1 he (V2/2g)1 (V2/2g)2 Z2 Z1 Datum datumi Channel Bottom kalapotis fskeri Energy loss is friction loss plus contraction/expansion loss friction loss is friction slope times length contraction/expansion is loss coeff times absolute value of change in vel head (V2/2g)2 + Y2 Z2 = (V2/2g)1 Y1 Z1 he Energy Losses energiis danakargi

Standard Step Method standartuli nabijis meTodi
Y2 Y1 he (V2/2g)1 (V2/2g)2 Z2 Z1 Energy Grade Line energiis xarisxis grafiki Water Surface wylis zedapiri Channel Bottom kalapotis fskeri Datum datumi Start at a known point. daiwyeT nacnobi wertilidan How many unknowns? ramdeni ramea ucnobi? Trial and error Semowmeba da cdomileba

HEC-RAS - Computation Procedure HEC-RAS - gamoTvlebis procedurebi
Assume water surface elevation at upstream/ downstream cross-section. savaraudo wylis zedapiris simaRle zeda/qveda dinebis gaswvriv. Based on the assumed water surface elevation, determine the corresponding total conveyance and velocity head. savaraudo wylis zedapiris simaRleze dayrdnobiT, gansazRvreT Sesabamisi xarji da zewolis siCqare. With values from step 2, compute and solve equation for ‘he’. meore safexuris Sedegad miRebuli sididis gamoyenebiT iTvlis da xsnis gantolebas “misTvis” With values from steps 2 and 3, solve energy equation for WS2. meore da mesame bijis Sedegad miRebuli sididiT ixsneba energiis gantoleba WS2-sTvis. 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. 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. Pages 3-13 thru 3-15 of Hydraulic Ref Man. gives table of Manning's 'n' values. Very subjective in nature. Lot of times it depends on what time of year you assume. We typically use 0.35 for aged channels in good hydraulic condition and work up from there.

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 length xaxunis danakargi fasdeba, rogorc xaxunis kuTxis da gawvdomis xarjis wonis mTeli sigrZis warmoebuli. 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.) Average Friction Slope - best results for M1 profiles saSualo xaxunis kuTxe - saukeTeso Sedegi M1 tipis profilebisTvis. Geometric Mean Friction Slope - used in USGS/FHWA WSPRO model geometriuli saSualo xaxunis kuTxe – gamoiyeneba USGS/FHWA WSPRO modelisTvis Harmonic Mean Friction Slope - best results for M2 profiles harmoniuli saSualo xaxunis kuTxe – saukeTeso Sedegi M2 tipis profilebisTvis

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

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. aris Tu ara xaxunis kuTxe mocemuli ganivi kveTisTvis meti vidre xaxunis kuTxe Semdeg ganiv kveTSi? gamoyenebuli gantoleba profilis tipi ki ara სubkritikuli სuperkritikuli superkritikuli saSualo xaxunis kuTxe harmoniuli saSualo geometriuli 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.

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 C = contraction or expansion coefficient C = SekumSvis an gafarToebis koeficienti

Contraction and Expansion Energy Loss Coefficients SekumSvis 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.

Expansion and Contraction Coefficients SekumSvis da gafarToebis koeficientebi
gafarToveba Contraction SekumSva No transition loss ar aris gadasvlis danakargi Gradual transitions TandaTanobiTi gadasva 0.3 0.1 Typical bridge sections ტიპიური xidis seqcia 0.5 Abrupt transitions wyvetili gadasvla 0.8 0.6 Notes: maximum values are 1. Losses due to expansion are usually much greater than contraction. Losses from short abrupt transitions are larger than those from gradual changes. SeniSvna: maqsimaluri sidide aris 1. gafarToebiT gamowveuli danakargi aris rogorc wesi bevrad didi sidide, vidre SekumSviT gamowveuli danakargi. mokle, wyvetili gadasvlis Sedegad miRebuli danakargi aris ufro didi vidre TandaTanobiTi gadasvlis Sedegad miRebuli danakargi.

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 b y 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

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

For any pair of E and q, we have two possible depths that have the same specific energy. One is supercritical, one is subcritical. The curve has a single depth at a minimum specific energy. nebismieri E da q wyvilisTvis, Cven gvaqvs ori SesaZlo siRrme, romelTac aqvT erTnairi specifikuri energia. erTi aris superkritikuli, meore subkritikuli. mruds axasiaTebs erTi siRrme minimaluri specifikuri energiisTvis. Minimum specific energy minimaluri specifikuri energia Y1 Y2

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

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

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 Whenever the water surface passes through critical depth, the energy equation is not considered to be applicable. There are several instances when the transition from subcritical to supercritical flow can occur such as significant changes in channel slope, bridge constrictions, drop structures and weirs, and stream junctions.

Momentum Equation momentis gantoleba
( V / 2g ) Y Z = ( V / 2g) + Y + Z + hm 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. Whenever the water surface passes through critical depth, the energy equation is not considered to be applicable. There are several instances when the transition from subcritical to supercritical flow can occur such as significant changes in channel slope, bridge constrictions, drop structures and weirs, and stream junctions.

Low flow hydraulics at bridges dabali dinebis hidravlika xidTan
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 Lets look at some types of open channel flow. Steady vs Unsteady Unsteady is more real life. Steady is what 1-dimensional flow models simulate. 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 Horizontal vel. Dist. Across a natural channel. 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 top). realuri saSualo V aris daaxloebiT 0.6D (zedapiridan) Vertical vel. Dist. - note ordinates on y-axis are backward. siRrme 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) An Albert Einstein “Thought Experiment” “I begin with a little experiment which anybody can easily repeat. Imagine a flat-bottomed cup full of tea. At the bottom there are some tea leaves, which stay there because they are rather heavier than the liquid they have replaced. If the liquid is made to rotate by a spoon, the leaves will soon collect in the center of the bottom of the cup. The explanation of this phenomenon is as follows: the rotation of the liquid causes a centrifugal force to act on it. This in itself would give rise to no change in the flow of the liquid if the latter rotated like a solid body. But in the neighborhood of the walls of the cup the liquid is restrained by friction, so that the angular velocity with which it rotates is less there than in other places nearer the center. In particular, the angular velocity of rotation, and therefore the centrifugal force, will be smaller near the bottom than higher up. The result of this will be a circular movement [helical flow]of the liquid of the type illustrated in [the figure] which goes on increasing until, under the influence of ground friction, it becomes stationary. The tea leaves are swept into the center by the circular movement and act as proof of its existence. [The tea leaves are homologous to the sediment that comprises point bar deposits.] “ Einstein, A., 1954, The cause of the formation of meanders in the courses of rivers and of the so-called Baer's Law, pp in Ideas and Opinions: New York, Bonanza Books, 337 p. 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) ALBERT EINSTEIN AND MEANDERING RIVERS, Kent A. Bowker Search and Discovery Article #70001 (1999)

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

End of lecture leqciis dasasruli

HECRAS Basic Principles of Water Surface Profile Computations HECRAS wylis zedapiris profilis agebis ZiriTadi principebi by G. Parodi WRS – ITC – The.

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HECRAS Basic Principles of Water Surface Profile Computations HECRAS wylis zedapiris profilis agebis ZiriTadi principebi by G. Parodi WRS – ITC – The.

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Presentation on theme: "HECRAS Basic Principles of Water Surface Profile Computations HECRAS wylis zedapiris profilis agebis ZiriTadi principebi by G. Parodi WRS – ITC – The."— Presentation transcript:

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