d Model Cvl and Surveyng Soware Dranage Analyss Module Deenon/Reenon Basns Owen Thornon BE (Mech), d Model Programmer owen.hornon@d.com 4 January 007 Revsed: 04 Aprl 007 9 February 008 (8Cp) Ths documen descrbes he approxmae mehod or szng deenon basns va he Raonal Mehod, as mplemened n he Dranage Analyss module o d Model. Page o 5
d Model Dranage Analyss Module Deenon/Reenon Basns An Approxmae Mehod or Szng Basns when usng he Raonal Mehod For he desgn o sormwaer deenon and reenon basns, a varey o smple and approxmae mehods may be adoped when usng he Raonal Mehod. These mehods do no requre dealed nlow hydrographs (derved rom unseady low smulaons), nor an accurae sorage-dscharge relaonshp, as would oherwse be requred or he more complex and sophscaed mehod o solvng he Sorage Equaon. For easbly sudes and prelmnary desgn, hese approxmae mehods should generally prove adequae. And or relavely small basns, or larger basns wh low reducon raos (r) large enough o lessen he eec o sorm emporal paerns, some approxmae mehods may even prove adequae or nal desgn hough he Sorage Equaon may sll need o be solved or vercaon o hs. An approxmae mehod, arbued o Boyd, has been presened n boh he ARR (987) and he QUDM (007), and hree more, arbued o Basha, Carroll and Culp, n he QUDM (007) only. All our mehods are based on an assumed rangular nlow hydrograph wh peak Q, and an assumed oulow hydrograph wh a lesser peak Q o, lyng somewhere on he allng lmb o he nlow hydrograph. Wh reerence o he nlow and oulow hydrographs shown n he gure above, he oal basn nlow volume s gven by he area below he nlow hydrograph: area ABCA Q () Page o 5
d Model Dranage Analyss Module Deenon/Reenon Basns And he requred basn sorage volume s gven by he area conaned beween he nlow and oulow hydrographs: s area ADEA area ADFA r r ( Q Qo ) + r ( Qo Qo ) ( Q Q ) + o area FDEF where he acor, beween zero and one, denes he rao o he nal oulow rae (wh an empy basn), o he peak oulow rae, Q o (wh a basn ull o capacy). For dry basns wh a low-level oule nver below he mnmum basn waer level, he oule may begn dschargng a some consderable rae, almos mmedaely as he basn begns o ll hereby reducng he requred sze o he basn. I s or hs ype o oule desgn where should be se o an approprae value greaer han zero, and as such, has been ermed he drop p acor. The rao o equaons () and () may be expressed n erms o r and, as: s ([ ] + r ) r (3) Subsuon o deren values or no equaon (3), yelds he our mehods reerred o above: s 0 r arbued o Boyd (4) () s / 3 r ( + r ) / 3 arbued o Basha (5) s 5 /8 r ( 3 + 5r ) / 8 arbued o Carroll (6) s / 3 r ( + r ) / 3 arbued o Culp (7) I should be noed ha resuls obaned rom equaon (3) are ndependen o he me a whch he nlow peaks ( ). So, whle he Sorage Equaon can accoun or he derences caused by an early nlow peak, or a lae nlow peak, or nsance, equaon (3) canno. In mos cases, however, such concerns are secondary. I s more mporan o esmae adequaely, he desgn values or Q and. The Raonal Mehod s normally only consdered adequae or deermnng he maxmum peak nlow rae (Q max ) when he sorm duraon ( d ) s equal o he me o concenraon ( c ) o he cachmen eedng he basn. I s ar more common, however, or he crcal d he sorm duraon requrng he greaes basn sorage volume o be consderably longer han he c o he cachmen. To correc or hs, some have suggesed ha Q max be used or Q and ha (4 c Q max / 3) be used or, bu hs oen under-predcs he basn sze sgncanly, and here s lle heorecal bass o suppor. Insead, o ollow he (ARR preerred) sascal nerpreaon o he Raonal Mehod whch or he same average recurrence nerval, apples he same runo coecens o sorms o deren duraons he desgn values or Q and should be deermned or longer sorms as ollows: I L L (8) d d + c d Q max Q I c Page 3 o 5
d Model Dranage Analyss Module Deenon/Reenon Basns where I c and I d are he average ranall nenses or sorms o duraon c and d, respecvely (as deermned rom IFD daa) and d c. The mporan hng o noe abou hs ormulaon s ha, or he same average recurrence nerval, sorm duraon and runo/nlraon model, wll always be he same as ha o a hydrograph derved rom a varable-nensy sorm wh any orm o emporal paern. Also noe ha Q s derved rom a rangular hydrograph o volume and base me, o beer represen he peak low rae o a sorm wh an average emporal paern. Implemenaon n d Model In d Model, npu values or and eher Q o or s may be speced a he oules o he dranage nework va he P > Man ab o he Dranage Nework Edor. The Sorm Analyss process hen uses equaons (8) and (3) o solve or eher s or Q o, or a range o up o 5 deren d values beween 5 and 430 mnues, ncludng bu no less han he ull-area c o he cachmen eedng he basn, and only hose whch yeld an r beween zero and one. For each basn, a range o resuls s hus obaned, where he sorm duraon yeldng eher he greaes s or Q o s seleced as he crcal d. The ollowng p arbues are se on he dranage srng oules, upsream o each basn: Inpus: "basn drop p acor" "basn dscharge" or "basn volume" Oupus: "calculaed basn nlow" "calculaed basn nlow volume" "calculaed basn c" "calculaed basn sorm duraon" "calculaed basn sorm nensy" Q o or s "calculaed basn volume" or "calculaed basn dscharge" s or Q o crcal Q crcal ull-area c o cachmen crcal d crcal I d In addon, a dealed desgn repor or each basn s repored n CS orma o he Oupu Wndow, whch may be pased no a spreadshee or audng and o produce desgn graphs. An example repor wh correspondng graphs s shown on he las page. Reerences ARR (987) "Ausralan Ranall and Runo : A Gude o Flood Esmaon", ol., Secon 7.5.6, Insn. Engrs. Aus. QUDM (007) "Queensland Urban Dranage Manual", ol., Secon 5.05., Queensland Gov. Dep. o NR&W, Brsbane. Page 4 o 5
d Model Dranage Analyss Module Deenon/Reenon Basns Example o a Basn Desgn Repor creaed by d Model, showng he resuls or each sorm duraon esed, along wh he nlow and oulow hydrographs o he crcal sorm duraon. The correspondng graph on he rgh hand sde shows each duraon as a do on he Q curve, and conrms ha or he requred 50Yr peak Q o o 530 L/s, he sorage volume requred reaches a maxmum o 6909 cubc meres, durng he sorm o 50 mnues duraon. Page 5 o 5