Attentionisto bepaid to the e GERMAN ATV-DVWK RULES AND STANDARDS ATV-DVWK STANDARD ATV-DVWK-A 110E HydraulicDimensioningandPerformanceVerification of Sewers and Drains September 2001 ISBN 3-936514-30-5 Distribution: GFA Publishing Company of ATV-DVWK Water, Wastewater and WasteTheodor-Heu-Allee 17 D-53773 Hennef Postfach 11 65 D-53758 Hennef Telephone: +49-2242/872-120 Telefax: +49-2242/872-100 E-mail: vertrieb@gfa-verlag.de Internet: http://www.gfa-verlag.de ATV-DVWK-A 110E September 2001 2 Die Deutsche Bibliothek [The German Library] CIP-Einheitsaufnahme ATV-DVWK, German Association for Water, Wastewater and Waste: ATV-DVWK Set of Rules and /ATV-DVWK, Water, Wastewater, Waste.- Hennef: GFA Publishing Company of ATV-DVWK. Previously under the title: German Association for Water Pollution Control (ATV): ATV Set of Rules and Standards Standard A 110E. Hydraulic Dimensioning and Performance Verification of Sewers and Drains - 2001 ISBN 3-934984-03-7 All rights, in particular those of translation into other languages, are reserved. No part of thisStandardmaybereproducedinanyform-byphotocopy,microfilmoranyother process - or transferred into a language usable in machines, in particular data processing machines, without the written approval of the publisher. Publisher:ATV-DVWK German Association for Water, Wastewater and Waste, Theodor-Heuss-Allee 17, D-53773 Hennef, Germany Marketing:GFA - Publishing Company of ATV-DVWK, Hennef Original German version set and printed by: DCM, Meckenheim, Germany GFA Gesellschaft zur Frderung der Abwassertechnik e.V. Hennef 2001 ATV-DVWK-A 110E September 2001 3Preamble to the August 1988 Edition TherevisionofATVStandardA110hadtogive consideration to a host of suggestions frompractice,torealisethefirmideasoftheATVAdvisoryBoardandtodealwith fundamentalrelationships.Thequestionsrelatingtotherecalculationofexistingsewer networks(performanceverification),inparticular,madeitnecessarytoexpandthe theoretical part of the draft of the new version to a greater extent than is customary in a standard, which is not meant to be a manual. Consequently,theWorkingGroupfirstdevisedacomprehensivedraft-theOctober 1985 version - which contained more information, explanations and source material than wasnecessaryforthisStandard.Thefinalprintisanabbreviatedversionwhichis essentially limited to describing the procedure in individual practical cases and no longer contains any explanatory information or justifications. Thefollowingaccompanyingpublicationsto this ATV Standard appeared in Vol. 1/1989 of the Korrespondenz Abwasser: Howe, H.O.:Grundzge des neuen ATV-Arbeitsblattes A 110 [Main features of the new ATV Standard A 110.] Haendel, H.: AuswirkungenderNeufassungdesATV-ArbeitsblattesA110aufdie hydraulischeNachrechnungvonAbwasserkanlen[Effectsofthenew edition of ATV Standard A 110 on the hydraulic recalculation of sewers]. Knauf. D.:FlietiefenundDurchflssefrgegliederteQuerschnitte[Flowdepthsand throughflows for structured cross-sections]. Ueker, K.J.:AbfuberechnunginAbwasserkanlenunterBercksichtigungseitlicher Zuflsse [Flow calculation in sewers taking into account lateral inflows]. Unger, P.:Grundlagenderkb-wert-FestlegungimArbeitsblattA110[Basesofthe determination of the kb value in Standard A110]. Preamble to the present Edition Duetosuggestionsreceived,amendmentsandcorrectionswhichhavebecome necessaryandduetohavingtotakeintoaccounttheEuropeanStandardDINEN752 Drain and sewer systems outside buildings, Part 4 Hydraulic design and environmental considerations,ithasbecomenecessarytorevisetheAugust1988editionofATVA 110. ATV Standard ATV-A 110 is, within the framework of European standardisation, a source for additional information in accordance with DIN EN 752, Part 4, Section 4, and thus a component part of this European Standard. TheresultsofvariousATVresearchprojectshaveflownintotherevisededition. Fortunately the following were available for this: ATV-DVWK-A 110E September 2001 4-BeeinflussungderLeistungsfhigkeitvonKanalstreckendurchkonstruktive VernderungenimBereichderSchchte[Influencingoftheefficiencyofsewer reachesthroughdesignchangesintheareaofshafts](ATV/Deutsche Bundesstiftung Umwelt [German Federal Foundation of the Environment] -SIMK - Simulation von Teilfllungenskurven [Simulation of partially filled curves] (ATV 25/97 and ATV 31/99) -Schieender Abflu in Krmmerschchten [Supercritical outflow in shafts for change of flow direction] (ATV 09/98). Important amendments in comparison with the August 1988 edition are: -separation of the procedure with dimensioning and with performance verification -revised,expandedrepresentationofflowlossesinshaftswithandwithout impounding -newtypeoftreatmentofflowinshaftstructureswithsupercriticaldischargewith simultaneous flow diversion -analytical treatment of flow in noncircular profiles and with partial filling conditions -dropping taking into account the form coefficient f -generalisationofthetreatmentofdiscontinuousflowbytheintroductionofthe factor m -calculation of the energy conversion in the outlet area of steep sections -expanded new version of the treatment of flat reaches and deposits -revision of the calculation for open channels and structured cross-sections. Withthecalculationofsurfacecurvestheuninterruptedtransferfrompartialfillingvia completefillingtopressuredischarge(impounding)alsotakingintoaccountthe impounding of shafts, is possible. Simplified mathematical models require model-specific approaches, which would lie outside the scope of ATV Standard A 110.ForreasonsofeasierreadingandcomparabilitywiththeAugust1988editionofATV-A 110,theuseofnew[German]spellingrulesintroducedinsomeFederalGerman States has been dispensed with. Dr.-Ing H. O. Howe, Chairman ATV-DVWK-A 110E September 2001 5Authors ThisStandardhasbeenrevisedbytheATV-DVWKWorkingGroup"Hydraulic Calculation of Sewers and Drains within the ATV-DVWK Specialist Committee Planning of Drainage Systems. The Working Group has/had the following members: Prof. Dr.-Ing. E. Billmeier, Kln Dr.-Ing. P. Drewniok, Leipzig Dr.-Ing. N. Engel, Berlin (from 1998) Dipl.-Ing. K-H. Flick, Kln (Chairman from 10/2000) Dipl.-Ing. H. Haendel, Mnchen, r.i.p.s. Prof. Dr. sc. techn. W. H. Hager, Zrich Dr.-Ing. Harald O. Howe, Kln (Chairman to 9/2000) BD Dr.-Ing. H. Krier, Frankfurt Dipl.-Ing. G. Milkov, Hamburg Obering. H. Schmidt, Erkrath Dipl.-Ing. F. Schweinebraten, Kassel (from 1996) Prof. Dr.-Ing. W. Tiedt, Darmstadt Dr.-Ing. P. Unger, Lich Prof Dr.-Ing. F. Valentin, Mnchen Dipl.-Ing. D. Wengler, Rheinfelden (from 1996) Dipl.-Ing. G. Zanker, Mnchen (to 1996) ATV-DVWK-A 110E September 2001 6ContentsPage Preamble to the August 1988 edition3 Preamble to the present edition3 Authors 5 Notes for users8 1Scope8 2Hydraulic principles8 2.1Forms of discharge and discharge processes8 2.2Defining equations9 2.3Drag coefficient12 2.4Loading assumptions and limiting values15 3Formulas for calculation in the standard case15 3.1Closed channels15 3.1.1Complete filling15 3.1.2Partial filling16 3.1.3Special profiles with dry weather channel20 3.2Open channel20 3.2.1Calculation of flow depths20 3.2.1.1Normal water depth hn20 3.2.1.2Critical depth hcrit21 3.2.1.3General flow depth h(x)21 3.2.2Calculation of flows22 3.2.2.1Normal discharge Qn22 3.2.2.2Critical discharge Qcrit22 3.2.2.3Discharge curve Q = f(h)23 3.2.3Flow depths and flows for structured cross-sections24 4Dimensioning and performance verification26 4.1Determination of roughness26 4.1.1General measure of roughness k26 4.1.2Operational roughness kb 27 4.2Calculation of individual losses28 4.2.1Loss coefficients as a result of positional inaccuracies and changes (Pi)29 4.2.2Loss coefficients for pipe connections (PC)29 4.2.3Loss coefficients at inlet fixtures (in)29 4.2.4Loss coefficients for control shafts (C)30 4.2.5Loss coefficients for special shafts (S)32 4.2.6Loss coefficients (fd) and verifications for flow diversion33 4.2.6.1Subcritical flow34 4.2.6.2Supercritical flow34 4.2.7Loss coefficients for combining structures (CS) and verification for flow merging36 4.2.7.1Subcritical discharge36 4.2.7.2Supercritical discharge38 ATV-DVWK-A 110E September 2001 74.2.8Other loss coefficients38 4.3Dimensioning38 4.4Performance verification39 5Flow with lateral inflow (discontinuous flow)40 5.1Effect of lateral inflow41 5.2Simplified procedure41 5.2.1Dimensioning (selection of a constant replacement flow)41 5.2.2Performance verification42 6Flat stretches and depositing42 7Steep stretches and air transfer45 7.1Steep stretches - inflow46 7.2Steep stretches - throughflow46 7.3Steep stretches - outflow47 8Special structures49 9Pressure and vacuum drainage, compressed air flushed wastewater transport pipelines, wastewater pumping stations with pressure pipelines50 10Private property drainage51 11Cost aspects52 12Literature53 13Symbols, units and definitions56 Appendix59 ATV-DVWK-A 110E September 2001 8Notes for Users ThisATVStandardistheresultofhonorary,technical-scientific/economiccollaboration whichhasbeenachievedinaccordancewiththeprinciplesapplicableforthisactivity (statutes,rulesofprocedureoftheATVandATVStandardATV-A400).Forthis, accordingtoprecedents,thereexistsanactualpresumptionthatitistextuallyand technically correct and also generally recognised. EveryoneisatlibertytoapplythisStandard.However,anobligationforapplicationcan arise from legal or administrative regulations, a contract or other legal reason. ThisStandardisanimportant,however,notthesolesourceofinformationforcorrect solutions.Withitsapplicationnooneavoidsresponsibilityforhisownactionorforthe correctapplicationinspecificcases;thisappliesinparticularforthecorrecthandlingof the margins described in the Standard.1Scope ATVStandardA110Guidelinesforthehydrauliccalculationofsewersinitsoriginal version (October 1965) [not translated into English] had presented the calculation of the dischargecapacityandflowrateontheoreticallybetterassuredbases.Buildingonthe resultsfromPrandtlandColebrook,thedischargecondition,whichisbasedona dimensioning,canbebetterdescribed.Furthermore,theeverincreasinglyimportant subsequentcalculationsofexistingnetworks,withoutapplicationofthebases,would contain considerable uncertainties. Thefirstrevision(August1988)updatedthisStandardATV-A110[translatedinto EnglishasATVStandardATV-A110E]asStandardsfortheHydraulicDimensioning and Performance Verification of Sewers and Drains. This second revision builds further on this. A summary of the rules due to European standardisation and their adoption through DIN EN752-4servesforcurrentorientation.Thesymbolsandtermsusedare-asfaras possible-inagreementwithDIN4044Hydromechanicsinhydraulics;definitions,DIN 4045 Wastewater engineering; vocabulary and DIN EN 752 Drain and sewer systems outside buildings, Part1 Generalities and definitions. 2Hydraulic Principles 2.1Forms of Discharge and Discharge Processes Thedischargeinsewersanddrainsischaracterisedbyagreatnumberof simultaneouslypossibleformsofdischarge,themostimportantofwhichintheareaof sewersystemsarecompiledinTable1below.Alldetailsrefertoparametersinthe direction of flow. Underthegivenprerequisitesandignoringfurthertermsofthecompletedifferential equationthereresultgraduallysimplifiedcalculationstatements,whichareputtogether in Table 2 with their associated designations. The equations in Line (0) describe in detail the discharge process in sewers and drains in a generally valid form. Line (1) applies for transport pipelines without lateral in- or outflows along the calculated stretch. ATV-DVWK-A 110E September 2001 9Further simplifications to Line (2) to Line (6) result through random omission of individual influencing elements. Neglecting the elementsxvgvandtvg1errors occur which can have the opposite tendency. FortransportpipelinestheapplicationoftheequationsinLine(4)shouldtherefore definitely be given preference over the calculation methods according to Line (2) or Line (3).Amoreextensiveassessmentofthecorrectnessofthevarioussimplified assumptions has to date not been possible, instead one is reliant on control calculations in individual cases. Thenecessarynumericalassumptions(incrementsx,t;theirratio;convergence criteria) are to be observed for solutions based on the complete statements in Lines (0) or(1).SimplificationaccordingtoLine(7)isappliedforthecalculationofpartialfilling conditions (see Sect. 3.1.2), butdescribes a discharge form which - with the exception of very long transport pipelines - does not occur in the practical operation of sewers and drains.Neverthelesstheuseofthisrelationship,representsausefulestimationon whoseaccuracynoexaggerateddemandsshouldbeplacedandwhoselimitsare redefined in this standard. 2.2Defining Equations The defining equation for the mean flow rate is AQv = (1) In which the following apply vthe mean velocity in thedirection of flow [m/s] Qthe flow also known as discharge or volume flow1) [m3/s] AThe flow cross-section, in the case of the completely filled circular pipe [m2]: with4dA2 =das the actual internal diameter of the circular pipe (clear width) [m]. Theresistanceformula2)forthefrictionlosses,takenasbeingevenlydistributedalong the flow stretch in the direction of flow, is g 2vr 4lh2hyf = (2) In which the following apply: __________________ 1)In wastewater engineering the flow is usually expressed in l/s; for general considerations m3/s is selected for reasons of dimensioning. 2)This resistance formula was developed by DAubuisson de Voisin (1834) and Weisbach (1845); it is often erroneously attributed to Darcy and also incorrectly referred to as the Darcy-Wiesbach Equation ATV-DVWK-A 110E September 2001 10hfenergy fall a non-dimensional resistance coefficient [1] rhythe hydraulic radius [m], defined as ) filling half / complete with pipe circular the for (4dl perimeter wettedA tion sec cross flowrPhy==lthe length [m] of the drain or sewer section. Converted Eqn. (2): g 2vh 41lhJ2ryfE = = (3) Here, JE is the designation for the gradient of the energy curve. Inthecaseofsteady-state,uniformdischarge(Line7ofTable2),theso-callednormal discharge, the gradient of the energy curve JE is equal to the sole gradient Jso. This can, in general, be formed with the projection length of the pipeline. Up to a gradient of some 200 the inherent error is less than 2 %. On the other hand, with steep stretches, the actual pipeline length is to be applied. Table 1: Forms of discharge in sewers and drains DesignationCriteriaDesignationCriteria steady-state 0t()= unsteady 0t() uniform 0x()= non-uniform 0t() continuousq = 0discontinuousq 0 subcriticalFr < 1supercriticalFr > 1 laminarRe< 2320turbulentRe > 2320 single-phasewastewatermulti-phasewastewater + air Withthehydraulicdimensioningandcalculationtaskswithinwastewaterengineering, therearenotonlycontinuouslyactiveinfluencessuchaswallfrictiontobetakeninto accountbutalsotheeffectsoflocallyoccurringindividuallossestobeincludedinthe calculation. In this the following apply (assuming one-dimensional streamtube theory): t()the variability of a flow value (), e.g. Q, h, v with time t x()the variability of a flow value (), e.g. Q, h, v with flow path x ATV-DVWK-A 110E September 2001 11qthe lateral inflow per unit of length in the direction of flow [m3/(s m)] Fr Froude Number [1] ReReynolds Number [1] Table 2: Calculation formulations for flow processes in sewers and drains LineType of motionMotion equationContinuity equation 0unsteady non-uniform discontinuous F SoJ JxhA gq vmxvgvtvg1 =+ + + qtAxQ=+ 1unsteady non-uniform F SoJ Jxhxvgvtvg1 =+ + 0tAxQ=+ 2unsteady simplified non-uniform F SoJ Jxhtvg1 =+0tAxQ=+ 3simplified unsteady non-uniformF SoJ Jxhxvgv =+ 0tAxQ=+ 4simplified unsteady simplified non-uniformF SoJ Jxh = 0tAxQ=+ 5steady-state non-uniformF SoJ Jxhxvgv =+ 0xQ= 6steady-state simplified non-uniformF SoJ Jxh = 0xQ= 7steady-state uniform (normal discharge) 0xh= 0xQ= In which the following apply Qthroughflow [m3/s] qlateral inflow per unit of length in the direction of flow (assumed steady-state) [m3/(s m)] Aflow cross-section perpendicular to the sole [m2] Jsosole gradient (with open channel possibly not constant) [1] JFfriction gradient3) [1] xpath co-ordinate in direction of flow [m] ttime co-ordinate [s] hfilling height in profile or depth of water (perpendicular to sole) or the pressure head in completely filled drains at the sole of the pipe or profile [m] vmean velocity [m/s] in a cross-section in direction of flow gacceleration due to gravity [m/s2] mfactor with inclusion of additional losses [1] (see also Eqn. 52) Inthegeneral,comprehensiveformwhichincludestheseindividuallosses,Eqn.2becomes: g 2v)r 4l( h2hyf + = (4a) _________________ 3)The friction gradient JF, with sufficient accuracy, may be replaced by the energy gradient JE (see also Eqn. 3) ATV-DVWK-A 110E September 2001 12or for the circular pipe g 2v)dl( h2f + = (4b) Here designates a non-dimensional coefficient (see Sect. 4), through which the size of the individual losses hf,i, referred to the velocity head v/2g, is determined g 2vh2i , f = (4c) With the inclusion of Eqn. 1 one obtains the general flow formula E hyhyJ r 4 g 2lr 41A v A Q + = = (5a) and thus for the circular pipe E2J d g 2ld14dv A Q + = = (5b) Forsimplifiedhandling,thecombinationofthevariouslosscoefficientsintoone operational drag coefficient b is proposed. This is defined as + = lr 4hyb(6) With this Eqns. 5a and 5b become E hybJ r 4 g 21A Q = (7a) and thus for the circular pipe Eb2J d g 214dQ = (7b) 2.3Drag Coefficient In connection with the resistance coefficient, a distinction is made between the following cases and ranges for turbulent flow (laws of resistance): 1)Ideal or hydraulically smooth behaviour (smooth curve) according to Prandtl: ATV-DVWK-A 110E September 2001 13||.|

\| = = Re51 . 2lg 2 8 . 0 ) lg(Re 21(8) 2)Completelyorhydraulicallyroughbehaviour(completelyrougharea)accordingto Prandtl ||.|

\| = +||.|

\| =hyhyr 4k71 . 31lg 2 14 . 1kr 4lg 21(9) 3)Technically rough behaviour (transitional area) according to Colebrook (((

+ =hyr 4k71 . 31Re51 . 2lg 21(10) OnlyEqn.10isofpracticalimportanceforuseinsewersanddrains.Itisgenerally designated as the Prandtl-Colebrook equation. Here the following apply: drag coefficient [1] ReReynolds Number ||.|

\|=hyr 4 v[1] kthe hydraulically effective roughness of the internal pipe wall, defined by the Prandtl-Colebrook Equation and to be determined precisely through hydraulic trials only [mm; m]. rhythe hydraulic radius, calculated from the clear dimensions of the flow- in the case of circular pipes it is 4rhy = d [m].cross-section. Intheso-calledMoodydiagram,Fig.1,therelationshipsexpressedintheabove formulas are represented in graphic form. A detail of the part of this diagram interesting for the most frequent cases in practice is contained in Appendix A5. TheapplicationoftherelationshipsaccordingtoEqns8,9and10ispermittedforboth circular cross-sections and non-circular cross-sections and that is for closed profiles and also open channels. Even in the case of cross-sections, which are far from circular, the takingintoaccountofaformcoefficientfisdispensedwithforthecorrectionofthe hydraulic radius rhy 4). The kinematic viscosity is defined as ] s / m [ v2= (11) Here the following apply: dynamic viscosity [kg/(m s)] density [kg/m3] The dependence of kinematic viscosity on the temperature is shown in Table 3. _________________ 4)For this see also the report of ATV Research Projects 25/97 and 31/99 ATV-DVWK-A 110E September 2001 14 Fig. 1:Moody diagram for completely filled circular pipes Table 3: Kinematic viscosity for various temperatures (values for pure water) T[C]51015202530 106 ((

sm2 1.521.311.151.010.90 0.80 With the calculation of sewers and drains as a rule the following is set: ATV-DVWK-A 110E September 2001 15((

= sm10 31 . 126 Withinthisthenormallyhighertemperaturesandtheothercompositionofwastewater compared with pure water are taken into account. 2.4Loading Assumptions and Critical Values The load assumptions for determining the flow and water surface profiles can be found in ATV Standard ATV-A 118E. Information concerning the surface run-off (e.g. percolation, pit losses and flow times) is given in ATV-A 118E and ATV-M 165. DIN1986,Part2appliestogetherwithDINEN12056forprivatepropertydrainswithin buildings; outside of buildings the standard series DIN EN 752 applies. With the dimensioning of sewers and drains, for reasons of correct operation, attention is to be paid to the observance of critical values for flow velocities. Flat stretches (see Sect. 6) are characterised by operation in the vicinity of the minimum velocity, steep stretches (see Sect. 7) by operation with relatively high velocities. Globalcriticalvaluesforbothrangesarenolongersuitable.Therecommended procedure is dealt with in detail in Sects. 6 and 7. 3Formulas for Calculation in the Standard Case 3.1Closed Channels Thedimensioningofnewconstructionandrenovationofsewersanddrainsisnormally orientedtowardscompletefilling (Index: V), whereby this should not be exploited to the full.Ifthedimensioningdischargereaches90%ofthedischargecapacityQv,itis recommended to select the next largest cross-section. This gives global consideration to the following: -undercuttingofnominaldimensionswithinthepermissibleframeworkinaccordance with DIN 4263, Sect. 2.1, -reductionsofcross-sectionduetounavoidabledepositsofupto3%ofthetotal cross-sectional area even if sewers and drains are maintained regularly, -equation of the actual sewer length l with its projection l. Withperformanceverificationofsewersanddrainstherespectivepermittedback-up heightsortheoverdammingfrequencyarerelevant(seeDINEN752-2).Procedurefor dimensioning is presented in Sect. 4 of this standard. 3.1.1Complete Filling For circular profiles the general discharge formula is: ATV-DVWK-A 110E September 2001 16||.|

\| (((

+ =EE2J d g 2d 71 . 3kJ d g 2 d51 . 2lg 24dQ (12) For non-circular profiles the general discharge formula is: ||.|

\| (((

+ =E hyhyE hy hyJ r 4 g 2r 84 . 14kJ r 4 g 2 r 451 . 2lg 2 A Q (13) A mathematical consideration of the deviation of any profile (form coefficient f) from the circularprofileisdispensedwith,asforallnormalcross-sectionshapesinsewer systems, f can be set = 1. Eqn. 13 applies for all profile shapes used in sewer systems such as, for example, oval, taperingandchannelcross-sections,alsowithconsiderabledeviationfromacircular shape. In the case of steady-state, uniform discharge in pipes filled to the top, Eqns. 12 and 13 the energy gradient JE is replaced by the sole slope JSo. InkeepingwiththedetailsgiveninSect.4.1,theroughnesskcanbereplacedbythe operationalroughnesskb.Inallcases-circularprofileaswellasnon-circularprofile- DIN 4263, Sect. 3.2 (clear width) is valid without restriction and must be observed5). 3.1.2Partial Filling Simplifiedassumptionscanbemadeforthecalculationofdischargeprocesseswith partial filling. For steady-state, uniform discharge (normal discharge) the energy gradient andwatersurfaceprofilerunparalleltothesole(Fig.2).Withpartialfillingcurvesthe partial filling values are referred to complete filling. Watersurfaceprofilecalculationsareabsolutelyessentialwithnon-uniformdischarge (see also Sect. A3.) Degree of filling h/H and the therefrom calculated geometrical parameters (see Table 14) arenon-dimensional;withcircularpipesH=d.TheprofileHisalwaysmeasured perpendiculartothepipeaxisThefillingheighthmustthereforealsobemeasured perpendiculartothepipeaxis.Thefillingheightisthusnotthesameasthedepthof water h, but rather linked with this parameter h by the relationship ' h cos / h = (14) and therefore with cleaned sewers is always somewhat smaller than the depth of water6). ____________________ 5)Clearwidthsaretheactualdimensionsofthecross-sections.Thedimensionoftheclearwidthshouldcorrespondwiththe characteristicvalueofthenominalwidth.Forthepurposeofhydraulicdimensioninginwastewaterengineeringandingeneral hydraulic engineering may only be assumed to be equal to the nominal width if the undercutting of the cross-section, referred to thenumericalvalueofthenominalwidth,doesnotexceed5%.Inthiscasetheaveragecleardiameterundercutsthe characteristic value of the nominal width by ca. 2.5 %. 6)With gradient values 200 (0.200; 1:5) h = h and l = l can be set; the resultant error is 2 %. Eqns 14 and 15 are to be used for calculation with larger sole gradients For the length the following applies ATV-DVWK-A 110E September 2001 17 = cos / ' l l (15) Forthecalculationofpartialfillingconditionsinallformsofcross-sectiontheform coefficient f = 1 is also applied. Fig. 2:Normal discharge with partially filled sewers The partial filling curves - see also 7)8)9) - the following applies for flow velocities 625 . 0V , hyT , hyVTrrvv||.|

\|= (16) and for discharges 625 . 0V , hyT , hyVTVTrrAAQQ||.|

\| = (17) _________________ 7)Franke, P.: Die Rauhigkeitsverhltnisse im teilgefllten Rohr [Roughness conditions in the partially filled pipe]. 8)Tiedt,W.:HydrodynamischeUntersuchungendesTeilfllungsproblems[Hydrodynamicinvestigationsofthepartialfilling problem]. 9)Sauerbrey,M.:AbfluinEntwsserungsleitungenunterbesondererBercksichtigungderFlievorgngeinteilgeflltenRohren [Discharge in drainage pipelines under special consideration of flow procedures in partially filled pipes]. Investigations have shown that the unrestricted application of Eqns. 16 and 17 is justified forallformsofcross-section10).Inadditiontothis,thepossibilityispointedoutof ATV-DVWK-A 110E September 2001 18calculatingthenormaldepthofwaterinpartiallyfilledcross-sectionsdirectlyusing iterative evaluation of Eqn. 13. ThetheoreticalinvestigationsbyTiedt8)haveconfirmedthepracticalexperimentsby Sauerbrey9) insofar as the influence of air friction on the discharge behaviour of partially filled,closedcross-sectionscanbeneglected.Thepartialfillingcurvesthushavea reverse bending part with a discharge maximum with partial filling, to which the greatest possible stable normal depth of water is to be assigned. Due to the problems of aeration or air entrainment in sewer pipelines, combined with the resultantriskofthesurchargingofthepipelines,thepartialfillingcurvesfordischarges are terminated at 0 . 1QQVT=With profiles with a flat roof it is recommended that the partial filling curves for discharges areterminated,dependentonthewidthofthecross-sections,10to20cmbelowthe crown, whereby the following is possible in these cases: 0 . 1QQVT> Fig.3:Partial filling curves for circular, oval and tapering profiles __________________ 10)ATV:SIMK-SimulationvonTeilfllungskurven,.AbschluberichtdesForschungsvorhabens(ATV25/97andATV31/99) [Simulation of partial filling curves, final report of the research project (ATV 25/97 and ATV 31/99)]. In Fig. 3 is shown the plot of the partial filling curves for the forms shown in Fig. 4 (oval profile) and Fig. 5 (tapering profile), whereby the curve for the oval profile lies above the ATV-DVWK-A 110E September 2001 19middlecurveforthecircularprofile(Fig.3)andbelowitforthetaperingcross-section. Profileswithsimilarhydraulicbehaviourcanbegroupedtogetherforthepractical calculationof the partial filling values (for this see also Appendix A2). The partial filling curves for the flow velocities are also terminatedand that is at the point hT/d at which QT/QV = 1.0 is reached. For profiles with flat roofs this also takes place at 10 to 20 cm below the crown. Fig. 4:Oval profile witha) full filling and b) partial filling Fig. 5:Tapering profile witha) full filling and b) partial filling ATV-DVWK-A 110E September 2001 203.1.3Special Profiles with Dry Weather Channel The calculations with complete filling for this type of profile are carried out using Eqn. 13 over the complete cross-section, without hydraulic structuring in the partial profile. The calculation for partial filling is in accordance with Sect. 3.2.3. 3.2Open Channel Sewers in the form of open channels pose questions with the hydraulic dimensioning as wellaswithlaterperformanceverification,whichinpartdeviatefromthetreatmentof closedprofiles.Nevertheless,itshouldbenotedthat,inthecaseofthecalculationof watersurfaceprofiles,theconditionsinpartiallyfilled,closedprofilescorrespondwith those, which are dealt with here for open channels. In this respect the statements of this section are also valid for general solutions for sewers and drains in the operational state of partial filling.Under normal conditions of operating open, natural channels the Reynolds No. is so high that,inthesenseofthedefinitioninaccordancewithEqn.9,onehas,asarule,to reckon with flow in the completely rough range.Therefore it is possible in this case also to apply other relationships for the determination of the energy gradient. As an alternative to the treatment according to Prandt-Colebrook the relationships according to Manning-Strickler can be recommended here. For the flow formula these are 2 / 1E3 / 2hy StJ r k v = (18) and for the discharge formula 2 / 1E3 / 2hy StJ r k A Q = (19) using the coefficient ((

smk3 / 1St in accordance with Manning-Strickler, which, in the fully rough range, is dependent on wall roughness only (see Appendix A7). 3.2.1Calculation of Flow Depths 3.2.1.1Normal Water Depth hn In special cases, for example in the case of long, disturbance-free flow sections, normal discharge prevails. Under this term are gathered those discharge processes with which, intheflowdirectionx,noneoftheflowparametersinvolvedchangesorwithwhichthe assumptionofthisidealisedflowconditionisnecessaryforreasonsofconvenience (estimation, analytical simplification). Under these circumstances the friction gradient JF, theenergygradientJE,thewaterprofilegradientJWandthesolegradientJSoare, mathematically, equal to each other:Thus the following applies ATV-DVWK-A 110E September 2001 21JF = JE = JW = JSo(20) The depth of water with which the condition in accordance with Eqn. 20 is met, is called the normal water depth hn, whose calculation takes place with the aid of Eqns. 13 and 20 or 19 and 20. If Q, JSo, d, kb and v are specified in Eqn. 13, or Q, KSt, and JSo, and the form functions A = f(h) and rhy = f(h) in Eqn. 19, then the flow depth sought, the normal water depth hn can be determined mathematically by iteration. Whicheverformulaisselectedforthecalculationofthenormaldepthofwaterthe associateddischargecanresultassub-critical(Fr1)oralsoin thetransitioncondition(FR=1)(seeTable1)Thuswhethersubcriticalorsupercritical normal discharge is present is decided by the size of the Froude number.3.2.1.2Critical Depth hcrit Initialrelationshipforeachdealingwithflowcharacteristicsintheboundaryarea,with velocity distribution assumed to be uniform, is the relationship1A gb QFr322== (21a) where FrFroude Number [1] bwater level width [m]. For partially filled circular sections the following approximation applies 422h d gQFr = (21b) Attention is drawn to ATV Standard ATV-A 111 (Sect. 3.2) for oval and tapering profiles. WarningisgivenonthesimplifieddefinitionoftheFroudeNumberh g / v Fr = ash signifies the actual flow depth in the special case of the rectangular cross-section only. Thecriticaldepthalwaysappearswithtransitionbetweensubcriticalandsupercritical discharge.Withinwastewaterengineeringitistobeobservedwithlargedifferencesin thesolegradientofneighbouringreaches(e.g.drops,changeofcross-section).Places at which the critical depth appears mark a decoupling of parts of the wastewater network, which is to be noted when dealing with the subject mathematically. 3.2.1.3General Flow Depth h(x) Dischargetakesplaceunevenly,unsteadilyanddiscontinuously.Theusualformofthe approximationoriginatesfromLine5ofTable2andusestherelationshipsforthe unsteady,unevendischargeonly,i.e.thewaterdepthrises(backwatercurve)orfalls (decline curve) in the direction of flow with the result that neither the friction gradient nor ATV-DVWK-A 110E September 2001 22the energy gradient nor, as a result of this, the water surface profile are known from the outset. Under these conditions the flow depth sought h varies from place to place, that is h = f(x) andcanonlybefoundbyintegrationofthedifferentialequationofthewatersurface gradient.Thisresultsfromtherelationshipsrelevantinthecaseunderconsiderationin accordance with Line 5 of the tables is 2F SoFr 1J Jdxdh = (22) whose integration delivers the desired result. ax2F Soh dxFr 1J J) x ( h + = (23) As both JF and Fr2 represent functions of h this also succeeds only by iteration. The initial waterdepthhi,tobeaccountedforasadditiveconstant,iseitherspecified(e.g.as designretentionlevel)oristobecalculatedfromtheflowparametersofdesignated positions, so-called monitoring cross-sections, for example in the form of a critical depth hl.Ifthedischargeissupercritical(Fr>1),integrationistobedownstream.;ifthereis sub-criticaldischargepresentintheintegrationzone(Fr1.Withthiswaterdepthsand discharges are to be determined only with involvement of the energy curve. A calculation of normal flow over the sole gradient is excluded. Withcross-sectionalshapeswithdiscontinuousincreaseofthewettedperimeterand with only small change to the water depth (as, for example, with profiles with dry weather channel and double-sided benching) the different flow velocities cannot be ignored. The influence of non-uniform distribution of velocities can be neglected if the flow depth above the benching exceeds the depth of the channel (hB > HCh). Intheregionofsmallerflowdepthsoverthelateralbenching(hBHCH)thefollowing simplifiedapproximationprocedureisrecommendedforthecalculationofthehydraulic efficiency and the associated characteristic values of the flow conditions: -separationofthestructuredcross-sectioninthepartialflowregionsuchthatthe variationsinvelocityintheindividualpartialcross-sectionareinsignificant.Inthis case the delineation can be by imaginary, perpendicular interfaces. -IncreaseofthegeometricallywettedperimeterIp,Choftheflowchannelthroughthe correctionfactorlp*tothehydraulicallyeffectivewettedperimeter.Forthe calculation of , with hB HCh, the following applies as approximation: ||.|

\|+ = Ch BBB pH hh 21 h * l (27) The following results from this: R , p*L , p*Ch , pCh , p*l l l l + + = (28) -calculationofthewaterlevelsandlowconditionswhicharetobesetwithspecified discharge with the aid of the generalised Bernoulli Equation. Withknowngeometry,specifieddischargeandprogressoftheenergygradient,the respectivewaterlevelpositioncanbedeterminedonlybyiteration(seeAppendixA3), whereby in the case of structured cross-sections it is additionally complicated in that the relevantvelocityheadandthekineticenergycomponentcanbegivenonlywithknown discharge distribution. Assumingahydrostaticpressuredistributioninallpartialcross-sections(parallelflow) the energy head results from = + = + =n1 I2NN3i NN Eg 2vh dA vQ g 21h h (29) In this n is the number of partial cross-sections.ATV-DVWK-A 110E September 2001 25As characteristic value for the degree of irregularity of the distribution of the velocity the correction value in Eqn. 29 can be estimated in a simplified form from= i3i2A vv Q1(30) With single cross-sections = 1, with structured cross-sections can lie between 1 and 2. With cross-sections normally used in wastewater engineering = 1 may be set. Takingdifferentpartialdischargecross-sectionsintoaccountleadstothefollowing discharge equation 11) =2 / 1E iJ c Q (31) with chydraulic control value of a partial cross-section i JEenergy gradient For the calculation of the flow process, the hydraulic control values are to be determined separatelyforthepartialdischargecross-sections(seealsoFig.6).Dependingonthe selection of resistance law or flow formula you obtain the following conditional equations: Fig. 6:Designations in the structured flow cross-sections Calculation in accordance with Prandtl-Manning, Eqn. 9 - completely rough area ( )i i , hy i , hy i ik / r 84 . 14 lg 2 r 4 g 2 A c = (32) Calculation in accordance with Manning-Strickler, Eqn. 18 3 / 2i , hy i , St i ir k A c = (33) ATV-DVWK-A 110E September 2001 26For three-part structured profile cross-sections (left - Index L; middle, channel - Index Ch; right - Index R) the following discharge equation is, for example, to be derived from Eqns. 31 and 33 ( )2 / 1E3 / 2R , hy R , St R3 / 2Ch , hy Ri , St Ch3 / 2L , hy L , St LJ r k A r k A r k A Q + + = (34) Theiterativesolutionofthisequationproducesthedischargedistributioninthree-part structured flow cross-sections. 4Dimensioning and Performance Verification Thecalculationsfordimensioningandforperformanceverificationtakeplaceusingthe same hydraulic bases which, with regard to flow losses (roughness, individual losses) are describedbelowindetailin4.1and4.2.Theprocedureforthecalculationrangeare described in 4.3 and 4.4. 4.1Determination of Roughness 4.1.1General Measure of Roughness k EverycalculationwhichmakesuseofthePrandtl-Colebrookresistancelawrequires knowledge of the equivalent sand roughness or the natural roughness of the inner wall of the channel in question. This degree of roughness is to be determined beforehand, as a rule on the basis of experimental data, if required, however, also through an appropriate estimation or determination on the basis of operational experience. The same applies for theroughnesscoefficientsofeachtypeofflowformulathus,forexample,alsoforthe coefficient kSt of the Manning-Strickler flow formula, whose arithmetic value corresponds withthedegreeofroughnesskofthePrandtl-Colebrookresistancelaw(seeAppendix A7).Thespecialcasesofdeviatingtypesofroughness(sandroughness,ripple roughness) are dealt with in Appendix A6. IfonesolvesthePrandtl-Colebrookresistancelawfortechnicalroughnessbehaviour (transitional region) ||.|

\|+ =hyr 84 . 14kRe51 . 2lg 21(10) for k, you obtain ||.|

\| = Re51 . 210 r 84 . 14 k) 2 /( 1hy(35) as determining equation for the degree of roughness k with =hyr 4 vRe (36) 2F hyvJ r 4 g 2 = (37) ATV-DVWK-A 110E September 2001 27||.|

\| =b / A gv1dxdhJ J2So F(38) Therelationshipistobeevaluatedusinglocalmeasureddataand,withk,providesa local,theoreticallyfoundeddegreeofroughnessofthewettedchannelsides.Ifthe channel sides display technical roughness as assumed based on the Prandtl-Colebrook resistance law, then a sufficiently constant k value is to be expected independent of the experimental data used. 4.1.2Operational Roughness kb Iflocalflowresistancesorenergyheadlossestogetherwithlossesasaresultofwall friction are to be reflected in an augmented coefficient of roughness, together with losses resultingfromwallfriction,i.e.ifdiscontinuousflowresistancesorlossesaretobe included in an operational roughness kb, this can be done in the manner shown in Sect. 2.2, Eqn. (5a) ff. If the loss coefficients of all disturbance sources located in the area of achannelreachlareknown,andifisusedtorepresenttheresistancecoefficient resultingfromnaturalroughnessandbthatresultingfromoperationalroughness,the following definition equation applies: + = lr 4hyb(6) If the operational coefficient of resistance b is calculated, knowing Re, k, rhy and , and if and Re are introduced into the resistance law, then kb/4rhy and from this the degree of roughnesskb soughtcanbeobtained.Thisincreaseddegreeofroughnessproduces mathematically the same total falls in energy as if one had applied continuous and local energy falls separately and then combined these. This operational degree of roughness kbisnotdependentaloneontheactualwallfrictionkandtheincorporatedindividual resistances , but additionally on rhy,l as well as normally on the Reynolds Number Re. Global determination for kb must take this situation into account. Underthesepreconditionsitispossibleandpermitted,fordimensioning,forcertain combinations of types of loss to function with a global value kb for operational roughness. ClassificationandjustificationareaccordingtoTable4dependentonthevarioustypes of sewer. Attention is drawn to Sect. 4.3 for preconditions and limitations. Table 4: Global values for operational roughness kb [mm] Type of sewerDesign of shaft Control shafts Shaped shafts Special shafts ATV-DVWK-A 110E September 2001 28Transport sewer Main sewers DN 1000 Main sewers > DN 1000 Brickwork sewers, on-site concrete sewers, sewers made from non-standard pipes without special verification of roughness0.50 0.75 - 1.50 0.50 0.75 0.75 1.50 0.75 1.50 1.50 1.50 Throttle lengths (1), pressure pipelines (1,2,3), siphons (1) and relining lengths without shafts 0.25 1) Excluding inlet, outlet and bend loses 2) Excluding pressure network (see also Sect. 9) 3) Effects on pumping stations see Sect. 9 4.2Calculation of Individual Losses ThemethodpresentedinSect.4.1fordealingwithquestionsassociatedwiththeso-calledoperationalroughnesscontainsandetailedanalysisofallindividualinfluences from which those variables arise which can be combined mathematically into a kb value. Withknowledgeoftheindividualinfluencesitisofcoursepossibletocollatedeviating preconditionsintoanindividualandjustifiedtreatment.Forthispurposethefollowing evaluation of available details and documents serves for individual losses as a result of -positional inaccuracies and modifications, -pipe conditions, -inlet fittings, -shaft structures of standard design (straight passage)(12), -shaft structures of special design (straight passage), -curved structures and -conjunction structures. The loss coefficients for this refer to g 2vh2i , f = (4c) __________________ 12)ATV Arbeitsblatt [Standard]-A 157 4.2.1Loss Coefficients as a Result of Positional Inaccuracies and Changes (Pi) ThelosscoefficientsPiaretobetakenfromTable5.Theyapplyforthepossible positionalinaccuraciesandchangesforeachpipeconnection.Withnpointsof connection the loss coefficient Pi is to be applied n times. Table 5: Loss coefficients Pi ATV-DVWK-A 110E September 2001 29DNPi 100 125 150 200 250 300 400 500 600 - 1000 > 1000 0.023 0.022 0.020 0.017 0.015 0.014 0.012 0.010 0.005 0 4.2.2Loss Coefficients for Pipe Connections (PC) ThelosscoefficientsPCaretobetakenfromTable6.Theyapplyforthepossible positionalinaccuraciesandchangesforeachpipeconnection.Withnpointsof connection the loss coefficient PC is to be applied n times. Table 5: Loss coefficients PC DNPC 100 125 150 200 250 300 400 500 600 - 1000 > 1000 0.020 0.016 0.012 0.009 0.007 0.006 0.004 0.003 0.0015 0.001 4.2.3Loss Coefficients at Inlet Fixtures (in) ThelosscoefficientsinaretobetakenfromTable7.Theyapplyforeverypositionat whichaninletfixtureinthemainsewerisplannedorispresent.Withnsuchpointsof inletdomesticconnections,road gullies) the loss coefficient in is to be applied n times. Theselosscoefficientscoveronlytheeffectsofthegeometryoftheinletfittings;the hydraulic effects of the inlet flow on the flow in the main sewer are covered in Sect. 5 Table 7: Loss coefficients in HdZ in ATV-DVWK-A 110E September 2001 300.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.000 0.002 0.004 0.007 0.011 0.016 0.022 0.029 0.036 0.045 2ininHd045 . 0 |.|

\| = (39) with dindiameter of an inlet pipeline Hprofile height of main sewer 4.2.4Loss Coefficients for Control Shafts (C) ControlshaftswithinthemeaningofthisStandardareshaftswhosebenchingreaches up to the crown of the outgoing pipe (see Fig.7). The values listed in Table 8 characterise the losses with subcritical discharge by values gainedexperimentally.Slightimpoundingleadstoconsiderableincreaseofthelosses. Alllossescontaineveryinfluenceasaresultoflosseswithinflow,throughflowand outflow,however,notthepipefrictioncomponentoverthelengthoftheshaft.Theloss for respectively one shaft is to be applied per sewer reach. Thevaluesforshaftswithstraightpassagecanbeapplieduptoachangeofflow direction of maximum 10 within a shaft using C = 0.05 to 0.25 Shaftswithchangeofdirectionof>10to45aretobetakenintoaccountusinga value of C = 0.1 - 0.7. ATV-DVWK-A 110E September 2001 31 Fig. 7:Control shaft with raised benching Table 8: Loss coefficients C C for changes of direction of Discharge situation dh 0 - 10>10 - 45>45 Partial filling< 100.050.10.15 Crown filling1.00.10.20.5 Impounding, complete filling under overpressure> 1.00.250.71.0 Channel with cover plate for all h/d0.050.10.2 ThevaluesinTable8areapplicablefortherelativeshaftdiameterBSh/danddeflection radiir/dcarriedoutwiththisnormalinsewersystems.Intheabsenceofdetailed ATV-DVWK-A 110E September 2001 32investigations the above given values can, until further notice, also be appliedfor shafts in sewers with non-circular profiles (oval profile, tapering profile). 4.2.5Loss Coefficients for Special Shafts (S) Special shafts within the meaning of this Standard are shafts in which the benching does notreachuptothecrownoftheoutgoingpipeandwithwhich,therefore,higherloss coefficients are to be applied mathematically. Fig. 8:Special shafts with low-lying benching The values listed in Table 9 characterise the losses with subcritical discharge by values gainedexperimentally.Slightimpoundingleadstoconsiderableincreaseofthelosses. Alllossescontaineveryinfluenceasaresultoflosseswithinflow,throughflowand outflow,however,notthepipefrictioncomponentoverthelengthoftheshaft.Theloss for respectively one shaft is to be applied per sewer reach. Thevaluesforshaftswithstraightpassagecanbeapplieduptoachangeofflow direction of maximum 10 within a shaft using S = 0.15 to 0.85 Shaftswithchangeofdirectionof>10to45aretobetakenintoaccountusinga value of S = 0.3 - 1.3. ATV-DVWK-A 110E September 2001 33In the absence of detailed investigations the above given values can, until further notice, alsobeappliedforshaftsinsewerswithnon-circularprofiles(ovalprofile,tapering profile). The profile height H appears in the place of the diameter d. Table 9: Loss coefficients S S for changes of direction of Discharge situation dh 0 - 10>10 - 45>45 Partial filling< 100.150.30.5 Crown filling1.00.30.41.0 Impounding, complete filling under overpressure> 1.00.851.32.5 Channel with cover plate for all h/d0.050.10.2 ThevaluesinTable8areapplicablefortherelativeshaftdiameterBSh/danddeflection radii r/d carried out with this normal in sewer systems. The values according to Table 8 for bends of 0 - 10 are to be applied for coupled shafts. 4.2.6Loss Coefficients (fd) and Verifications for Flow Diversion Inthecaseofflowdiversion,withregardtotheverificationtobecarriedout,onemust differentiate strictly between subcritical discharge (Fr < 1) and supercritical discharge (Fr > 1). Forsubcriticaldischargelosscoefficientsfdcanbedeterminedandincludedinthe hydraulic verification (see Sect. 4.2.6.1). Forsupercriticaldischargethisprocedureisnotpossible.Theverificationlossesis replaced by design and operational details, which are to guarantee a disruption-free flow without unwanted effects on operation (see Sect. 4.2.6.2). Transcritical discharge conditions with 0.75 < Fr < 1.5 are hydraulically unstable and therefore are, as far as possible, to be excluded (see also ATV Standard ATV-A 111, Sects. 3.2 and 3.6). 4.2.6.1Subcritical Flow The additional loss as a result of diversion with a bend radius of r referred to the sewer axis can be applied using ATV-DVWK-A 110E September 2001 34 = sinrd32(40) with raverage diversion radius diversion angle. Losscoefficientsasaresultofflowdiversioninshaftsarealreadycontainedinthe values in Tables 8 and 9. 4.2.6.2Supercritical Flow Theflowinshaftswithdiversionwithsupercriticaldischargeischaracterisedlessby resultant additional losses rather much more by wave formation at the outer edge of the bend,wherebytheinneredgeremainsquasidry.Thisinfluenceriseswithincreasing Froude Number. Thewaveheightcanbegreaterthanthediameteroftheexitingpipe.Thewastewater thenstrikesagainsttheshaftoutletwallandcanleadtoacollapseofthesupercritical flow.Thenahydraulicjumpoccursintheshaftwhichcanmoveintotheinletpipeand which places the shaft under pressure discharge. The air inflow in the in the submerged pipe is then cut off; pulsation can then occur which effects a build up of the water level in the shaft and leads, finally, to the familiar phenomena of lifting of the manhole cover and increase of the noise loading. Thefollowingconditions,whicharefundamentallytobeobserved,resultfromdetailed investigations into this13): -the loading of the inlet sewer (QT/QV) may not exceed 50 % -the design of the shaft channel is always to be with raised benching (control shafts in accordance with Sect. 4.2.4. -diversionsof90,withthesamer/dleadtosmallerdisturbancesthanwith45(and shorter layout of the flow path) -diversionsof45canbeheldoperationallymorestablewithanopenstraight extension (l 3do)of the shaft -coversintheareaoftheshaftareofparticularadvantage,especiallywith retrofitting/rehabilitation of existing facilities. __________________ 13)ATV:SchieenderAbfluinKrmmerschachten.AbschluberichtdesForschungsvorhanens(ATV09/98)[Supercritical discharge in elbow shafts. Final Report] For the flow in shaft structures verification of height(hM) and ATV-DVWK-A 110E September 2001 35position() of the wave maximum is to be carried out for Fro. Fig. 9:Unobstructed elbow shaft; a) plan, b) longitudinal section ( )22ooMB 50 . 0 1hh + = (41) 2o M) Fr ( 8 . 2 tan = (42) Here 2 / 1o oFr B = (43) B - Bend Number = r/do(44) - relative bending of the shaft diversion referred to the diameter do of the inlet pipe and r - radius of the elbow axis For verification the following applies: ATV-DVWK-A 110E September 2001 36u Md h 1.0. With the employment of the individual concept the losses as a result of wall roughness k and the individual losses arising are to be verified by reach, whereby k is fundamentally tobeapplied,alsowithregardtothechangeofcharacteristicsofthepipewallinlong-term operation.Withperformanceverificationofexistingnetworks,iftheeffectiveclearwidthinthe individualcaseisnotorcannotbedetermined,oneistoreckonbasicallywith95%of the nominal width in which the cross-section reduction as a result of normal depositing is also covered. Withthis,aspecialgeneralkbvaluetableforimpounding,overdammingandflooding verification is impossible. This procedure converts DIN EN 752-4, Sect. 9.2.3. 5Flow with Lateral Inflow (Discontinuous Flow) In sewer networks calculation is to be carried out along a calculation stretch, for example betweentwoshaftswithaflowincreaseasaresultoflateraldischarges(domestic connections,streetgullies).Anexceptionisformedonlybypuretransportsewers, throttle lengths and pressure pipelines. With collectors with lateral inflow, contrary to the detailsinTable6,onehastoworkwithaformulationfordiscontinuousflow.This requires the following system of equations: Motion equation F SoJ JdxdhA gq vm = + (50) Continuity equation qdxdQ= (51) In the differential equation for the water surface profile to be derived from this, the lateral inflow then has the form that the right-hand side of this equation has to be expanded by an additional term to take into account change of the velocity head withwhichtheenergywhichisrequiredfortheaccelerationofthelaterally discharged volume flow to the velocity of the main stream, is taken into account. Duetothelateralinflowthevelocitydistributionintheflowcross-sectionisalso modifiedsothatthepreviouslyemployedformulationforthefrictionlossesisno longersufficient.Theresistancebehaviour,duetothecomplexflow,uptonow couldonlyberecordedinspecialcases.Withthelackofsufficientlysound ATV-DVWK-A 110E September 2001 41findings the additional loss can, in comparison with continuous flow, be taken into accountapproximatelythroughtherepeatedapproachofthemodificationofthe velocity head. In general this results in 2q F So22F SoFr 1J J JFr 1A gq Q mJ Jdxdh = = (52a) withmasfactorwiththeinclusionofadditionallosses(seeTable2).Duetothe formulation described previously, m = 2 and thus 2q F So2F So22 2F SoFr 1J J JFr 1A gq Q 2J JFr 1A gq QA gq QJ Jdxdh = = = (52b) Theapplicationofthisformulationisnotpermittedforcombining structures! Thefollowingstatementsapplyforthecaseofsteadystate,simplifiednon-uniform discontinuous flow. They can be transferred analogously to other types of calculation in accordance with Table 2. 5.1Effect of Lateral Inflow The flow loss depends on the following factors: -total throughflow Q [m3/s], -size and distribution of the lateral inflow q [m3/(s.m)], -flow cross-section (with all partial influences), -bottom gradient and flow rate. With unfavourable conditions - i.e. in particular if a large lateral inflow is discharged into a relativelysmallmainstreamoverashortsewerlength-thelosselementJqcanreach several times JF. 5.2Simplified Procedure Depending on the tasking, simplified procedures are recommended for the application of Eqn. 52. These are different for the planning stage (dimensioning) and for the verification of existing networks (performance verification).5.2.1Dimensioning (Selection of a Constant Replacement Flow) InordertoavoidthecostlyevaluationofEqn.52theenergyheadlossalonga calculation stretch for a collector sewer, as a rule, is so determined that one determines thefrictionlossforaconstant-thatisnotdiscontinuous-assumedflow(equivalent flow). On the other hand, with the application of the throughflow Qe at the end of the calculation stretchasconstantequivalentflowoverthecompletereach,ahigherfrictionlossis ATV-DVWK-A 110E September 2001 42determinedwithwhichtheusuallyadditionaldischargelossofdiscontinuousflowis recorded. Within the scope of justifiable accuracy, one can calculate using this simplification if, for thecomponentQofthelateralinflowalongareach,thecriteriainaccordancewith Table 11 are met in the various nominal width ranges. Table 11:Limits on the validity of the calculation using Qe. Relative lateral inflow Nominal width rangeQ/Qe DN 200 to DN 500 DN 600 to DN 1000 DN 1100 to DN 2000 DN> 2000 No limitation 0.30 0.10 0.05 Q = Qe - Qi With the exceeding of the validity limits for the equivalent flow the relationships presented using Eqn. 52 are to be investigated17) and, if required, a higher equivalent flow is to be employed. 5.2.2Performance Verification For the performance verification it can be assumed that the inventory of the network for whichtheverificationistobecarriedouthas,inallrespects,beenrecorded.This includes the position and admission of the lateral inflow from private properties and street drainage.Withthisitwouldbepossibletorecordanalyticallytheindividualconditions existing at all discharge points and to deviate from the assumed evenly distributed lateral inflows according to Eqn. 52. This presumes that for each discharge point the geometric and hydraulic conditions are described and taken into account via an additional individual loss which has to be applied. Thecombinationofthedescribedeffectsbyreachandtheapplicationofanequivalent flow remains an option. 6Flat Stretches and Depositing Wastewaterisamixtureofwaterwithmostnon-uniformsubstancesamongstwhich settleablematterisalsotobemet.Itssedimentationwithinthepipelinesystemcanbe prevented through suitable selection of the relevant parameters. A traverse wall stress of =1.0N/m2should,underno circumstances,beundercut.Attentionisdrawntothe Literature for the fundamental detailss18). __________________ 17) Ueker,K.J.:AbflurechnunginAbwasserkanlenunterbercksichtigungseitlicherEinflsse[Flowcalculationinsewerstaking into account lateral inflows]. 18) Macke, E.: ber Feststofftransport bei niedrigen Konzentrationen in teilgefllten Rohrleitungen [On solid matter transport with low concentrations in partially filled pipelines]. Deposits are prevented if a necessary minimum wall traverse stress, which is dependent onthevolumeconcentrationofsettleablesolidmatter,isachievedorexceeded.The ATV-DVWK-A 110E September 2001 43necessary minimum wall traverse stress min in N/m2 , for concentrations of CT = 0.05 for combined wastewater and stormwater and CT = 0.03 for wastewater min = 4.1Q1/3 (for stormwater and combined sewers)(53a) min = 3.4Q1/3 (for normal sewers)(53b) withQinm3/sandthatisindependentofdiameterandgradientofthepipeline considered. The respectively available wall traverse stress avail is calculated from F hy availJ r g = (54) Assuminganoperationalroughnesskb=1.5mmlowercriticalvaluesJcofthesole gradientforthedifferentnominalwidthrangesofovalprofilesanddegreesoffillingof hT/d = 0.1 to 0.5 and for 1.0 N/m2 according to Tables 12a and 12b19). Both tables also contain ranges which are characterised by the maintenance of min = 1.0 N/m2.Thedetailsfortheseareunderlaidingrey.Forfillingheightsofh