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

1. HECRAS Basic Principles of Water Surface Profile ComputationsHECRAS wylis zedapiris profilis agebis ZiriTadi principebi by G. Parodi WRS – ITC – The Netherlands g. parodi WRS-ITC- niderlandebi

2. Incompressible fluid ukumSvadisiTxe 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 water...wylis Sesaxeb . . .

3. 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

4. Continuity Equation uwyvetobisgantoleba (conservation of mass) (მასის შენახვის principi) 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. VA = constant A = mudmiva Discharge is expressed as Q = VA xarji gamoixateba rogorc Q = VA • Q is flow Q - Q arisdineba Q • V is velocity V - V arissiCqare V • A is cross section area A – • A arisganivi kveTis farTobi A

5. Open Channel Flow – ControlsRia kalapotis dineba - kontroli Definition: A control is any feature of a channel for which a unique depth - discharge relationship occurs. gansazRvreba: kontroliarisdinebisnebismierimaxasiaTebeli, romlisTvisacyalibdebaerTaderTi (unikaluri) siRrme-xarjisdamokidebuleba. Weirs / Spillways wyalgadasaSvebi Abrupt changes in slope or width uecaricvlilebadinebisdaxris kuTxeSi an siganeSi. Friction - over a distance xaxuni – garkveul distanciaze

6. 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.

7. Gravity Friction Uniform or Normal FlowerTgvari da normulidineba 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. gravitaciuliZalebi, romlebicaCqarebendinebasimyofebianwonasworobaSixaxunisZalebTan, daZabulobismatebaxdebasveliperimetriszegavleniT, racanelebsdinebas

8. W F Over a long stretch of a river...mdinaris mTel sigrZeze... Average velocity: is a function (slope and the resistance to drag along the boundaries) saSualosiCqare: arisfunqcia (ferdobisdaxra da winaRoba, romelicamuxruWebsdinebaszRurblisgaswvriv)

9. What does that mean?ras niSnavs es? V2/2g V EGL Y WS Hydrostatic pressure distribution hidravlikuri wnevis gadanawileba So 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 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.

10. 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. • Mean velocity is constant from section to section • saSualosiCqarearisucvleliseqciidanseqciamde • Depth of flow is constant from section to section • dinebissiRrmearisucvleliseqciidanseqciamde • Area of flow is constant from section to section • dinebisfarTobiarisucvleliseqciidanseqciamde 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 achieved Sesabamisad: es SeiZleba moxdes mxolod Zalian grZel, swor, prizmul kalapotSi, sadac dineba aRwevs zRvrul siCqares

11. Normal Depth Applies to Different Types of SlopessaSualo siRrme ukavSirdeba ferdobis sxvadasxva tipis daqanebas. cvalebadi nakadi cvalebadi nakadi ‘n’ stands for normal “n”igulisxmebasaSualo ‘s’ stands for critical “s”igulisxmebakritikuli erTgvarinakadi Yn Yc Cvalebadi nakadi erTgvarinakadi Mild Slope sustad daxrili ferdobi Cvalebadi nakadi erTgvarinakadi Critical Slope kritikuli ferdobi Yc Yn Steep Slope cicabo ferdobi

12. 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?

13. 0 Gravity Friction Newton's second law niutonismeorekanoni 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 rearrange equation gadavaTamaSoTgantoleba Gravity gravitacia Friction xaxuni small mcire Antoine Chezy (18th century) antoni Cezi (18 saukune)

14. Manning’s equationmaningisgantoleba dineba koeficienti farTobi ferdobisdaxra dasvelebisperimetri One of the most widely used to account for friction losses erTerTiyvelazefarTodgavrcelebulimeTodixaxunisdanakargisdasaTvlelad

15. Manning’s Equation - ‘n’ unitsmaningisgantoleba - ‘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.)

16. Manning’s nmaningisn 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)

17. Manning’s nmaningisn 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)

18. Guidance Available: seek bibliography and the WEBsaxelmZRvaneloebi: moZebneTbibliografia da internet saitebi n=0.110 n=0.050 n=0.060 n=0.125 n=0.080 n=0.150 n=0.018 NRCS - Fasken, 1963 n=0.018 n=0.014 n=0.016 n=0.020

19. Manning’s n in Steep Channelmaningisn cicaboddaxrilkalapotSi • Streams may appear to be super critical but are just fast subcritical • nakadiSeiZlebaCandes super kritikuli, magramiyosmxolodswrafisubkritikuli • Jarret’sEqn (ASCE J. of HydEng, Vol. 110(11)) ( R = hydraulic radius in feet) • jaretisgantoleba (ASCE J. of HydEng, Vol. 110(11)) ( R = hidravlikuriradiusifutebSi)

20. 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: SegviZliagamoviTvaloTCvenTvissaWirosxvadasxvaparametri Velocity siCqare Trial and error for depth, width, area, etc siRrmis, siganis, farTobis da sxvaparametrebisgadamowmeba da cdomilebisdadgena

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

22. 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% 40% to 70% S=0.003 to 0.005 All How sensitive is the equation? ramdenad mgrZnobiarea gantoleba? W=100’ d=5’ S=0.004 n=0.035 Q=3700 cfs

23. How often do we see normal depth in real channels? ramdenadxSiradvxvdebiTsaSualosiRrmesbunebrivnakadebSi? 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.

24. Limitations of a Normal Depth Computation:SezRudvebisaSualosiRrmisgaTvlebSi: • 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.

25. Open ChannelFlow is typically variedRiaarxisdinebaxasiaTdebacvalebadobiT B. Uniform vs. Varied b. ucvlelicvalebadiswinaaRmdeg Uniform Flow ucvlelidineba Depth and velocity are constant with distance along the channel. siRrme da siCqarearismudmivi arxisgaswvrivmTelsigrZeze Varied Flow cvalebadidineba Depth and velocity vary with distance along the channel. siRrme da siCqarecvalebadia arxisgaswvrivmTelsigrZeze B. Uniform versus Varied Flow b. ucvlelidinebacvalebadiswinaaRmdeg

26. Subcritical subkritikuli Critical kritikuli Supercritical superkritikuli Tim McCabe, IA NRCS Hydraulic Jump hidravlikurinaxtomi Subcritical subkritikuli Critical kritikuli Both man made and natural channels orive, xelovnuri da bunebrivinakadebi Supercritical superkritikuli Hydraulic Jump hidravlikurinaxtomi Subcritical subkritikuli Subcritical subkritikuli Lynn Betts , IA NRCS

27. In natural gradually varied flow channels:bunebriv, TandaTanobiTcvalebaddinebebSi: 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.

28. 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)SegiZliaTgamoiyenoTenergiisda uwyvetobisgantolebebiwyliszedapirissimaRliserTimonakveTidanwyliszedapirissimaRlismeoremonakveTzegadasasvlelad, romelicTavisTavadariszedadinebisTvis(subkritikuli) an qvedadinebisTvis(superkritikuli)mocemulimanZili.

29. 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.

30. How about that energy equation?energiisgantolebisSesaxeb: First law of thermodynamics Termodinamikis pirveli kanoni Bernoulli ‘s Equation bernulisgantoleba: + = + P1/w + (V2/2g)2 P2/w + Z2 (V2/2g)1 Z1 + he • Kinetic energy + pressure energy + potential energy is conserved • kinetikuri energia + wnevis energia + potenciuri energia aris SenarCunebuli

31. + = + P1/w + (V2/2g)2 P2/w + Z2 (V2/2g)1 Z1 + he Remember - it’s an open channel and a hydrostatic pressure distributiondaimaxsovreT – es aris Ria nakadi da hidrostatikuli wnevis ganawileba 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)

32. Energy Equationenergiis gantoleba (V2/2g)2 Energy Grade Line energiisxarisxisgrafiki he Water Surface wyliszedapiri Y2 (V2/2g)1 Channel Bottom kalapotisfskeri Y1 Z2 Z1 Datum datumi + = (V2/2g)2 Y2 + Z2 (V2/2g)1 + Y1 Z1 + he + Energy Losses energiisdanakargi

33. Standard Step Methodstandartuli nabijis meTodi Start at a known point. daiwyeTnacnobiwertilidan How many unknowns? ramdenirameaucnobi? Trial and error Semowmeba da cdomileba (V2/2g)2 he Y2 (V2/2g)1 Y1 Z2 Z1 Energy Grade Line energiisxarisxisgrafiki Water Surface wyliszedapiri Channel Bottom kalapotisfskeri Datum datumi

34. 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. HEC-RAS - Computation ProcedureHEC-RAS - gamoTvlebis procedurebi

35. Energy Loss - important stuffenergiis 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.

36. Friction loss is evaluated as the product of the friction slope and the discharge weighted reach length xaxunisdanakargifasdeba, rogorcxaxuniskuTxisda gawvdomisxarjiswonismTelisigrZiswarmoebuli

37. Friction loss is evaluated as the product of the friction slope and the discharge weighted reach lengthxaxunisdanakargifasdeba, rogorcxaxuniskuTxisda gawvdomisxarjiswonismTelisigrZiswarmoebuli. Channel Conveyance Senakadis gadazidva

38. Friction Slopes in HEC-RASxaxunis 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, დაsxva.) 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

39. FlowClassificationdinebis 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

40. Friction Slopes in HEC-RASxaxunis 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. gamoyenebuli gantoleba aris Tu ara xaxunis kuTxe mocemuli ganivi kveTisTvis meti vidre xaxunis kuTxe Semdeg ganiv kveTSi? profilis tipi ki ara ki ara saSualo xaxunis kuTxe harmoniuli saSualo saSualo xaxunis kuTxe geometriuli saSualo სubkritikuli სubkritikuli სuperkritikuli superkritikuli

41. Friction Slopes in HEC-RASxaxunis 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.

42. HEC-RASHEC-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

43. 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

44. Other losses include:sxva danakargebi: • Contraction losses • SekumSvis danakargi • Expansion losses • gafarToebis danakargi C = contraction or expansion coefficient C = SekumSvis an gafarToebis koeficienti

45. 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.

46. 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.

47. Specific Energyspecifikuri energia y b 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 width SeniSnva: hidravlikuri siRrme (y) aris ganivi kveTis farTobi gayofili udides siganeze

48. Specific Energyspecifikuri energia 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: mcireferdobisTviskuTxearis 45. or y Y2 or E

49. Specific Energyspecifikuri 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. Minimum specific energy minimaluri specifikuri energia Y1 Y2

50. Specific Energyspecifikuri energia Q: What is that minimum? A: Critical flow!! kiTxva: ra aris minimumi? pasuxi: kritikuli dineba Minimum specific energy minimaluri specifikuri energia