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1Chapter 9 Reservoir and Stream Flow RoutingWater Resources Engineering Lays W. MaysJuliane Nogueira de AlbuquerqueLvia Malacarne PinheiroSo Carlos, maio de 2015.University of So PauloSo Carlos School of Engineering

Flow Routing um processo para determinar o tempo e a magnitude de fluxo em um ponto em um curso dagua de, conhecido ou assumido hidrograma, em um ou mais pontos sobre a corrente.Se o fluxo for uma enchente, o procedimento especificamente conhecido como escoamento de cheia (flood routing)2Purpose of Flow Routing3QtQtQtQt(a)Flood prediction, warning(b)Reservoir design(c)Flood plain delineation(d)Watershed simulation(e)Others

Types of flow routingLumped/hydrologic:Flow is calculated as a function of time alone at a particular location;Governed by continuity equation and flow/storage relationship.

Distributed/hydraulic:Flow is calculated as a function of space and time throughout the system;Governed by continuity and momentum equations.

4OrClassifications of Flow RoutingBy Spatial and Temporal Variation:(a) Lumped Flow Routing Flow is calculated as a function of time only at a fixed location in space;(b) Distributed Flow Routing Flow is calculated as a function of time and space in the system.By Governing Equations Used:(a)Hydrologic Routing - Employs continuity equation, along with an analytical or an assumed relationship between storage and discharge within a system, in the calculation.(b)Hydraulic Routing Use both continuity and momentum equations to describe unsteady, non-uniform flow in a flow system.By Watercourse Type(a)River Flow Routing(b) Reservoir Routing(c)Overland Flow Routing5StreamFlowHydrologicRoutingHydraulicRoutingLevel-PoolMethodSaint-VenantEquationContinuityEquationMomentumEquationMuskingumMethod6Hydrologic Routing The hydrologic routing are lumped procedures and compute flow rate as a function of time alone at a downstream location.7Three types:

Level pool method (reservoir routing)Storage is nonlinear function of Q;Muskingum method (river routing)Storage is linear function of I and Q;Series of reservoir modelsStorage is linear function of Q and its time derivatives.O aspecto fsico do problema revelado pela comparao do escoamento permanente uniforme e o escoamento decorrente da passagem da onda pelo mesmo canal.71. Level Pool Routing (reservoir)Its a procedure for calculating the outflow hydrograph from a reservoir assuming a horizontal water surface, given its inflow hydrograph and storage-outflow characteristics.

Eq. 1.18

9PROCURAR EXEMPLOS =pConsidere 2 acres (4046,85642m) de coluna dgua detida na bacia. O hidrograma triangular de entrada de fluxo crescendo linearmente de zero at o pico de 60 csf em 60 min e decresce linearmente para um descarga de zero em 180 min. O hidrograma do escoamento de fluxo atraves da bacia de deteno usando a relao atura-descarga para 5 ft de diametro do cano de vertedouro nas colunas 1 e 2 da tabela. O cano colocado no cho ao nivel da bacia. Assumindo que a bacia esta incialmente vazia, use o procedimento de escoamento d e nivel d e piscina com um tempo de intervalo de 10 min determinar a profundidade mxima na bacia de deteno. (exemplo 9.2.1 do livro)102. Muskingum Method (river)Muskingum Method is a commonly used hydrologic routing method that is based upon a variable discharge-storage relationship. This hydrologic method is based by a combination of wedge and prism storage. During the advance of a flood wave, inflow exceeds outflow, producing a wedge of storage.11Neste modelo, o volume armazenado de escoamento no canal de um rio determinado pela combinao da cunha e do prisma de armazenamento. Durante o avano de uma onda de cheia, a vazo de entrada excede a vazo de sada, resultando em um balano negativo. Alm disso, ocorre um prisma de armazenamento, o qual formado por um volume de seo transversal constante, no decorrer do comprimento do canal prismtico.Este mtodo consiste na utilizao da equao da continuidade e de relaes entre o armazenamento e as vazes de entrada e de sada. Portanto leva em considerao a cunha de armazenamento formada no rio.

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AdvancingFloodWaveI > Q

RecedingFloodWaveQ > I12

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Condicionante para uso da equao:14

Example 2Route the inflow hidrograph below using the Muskingum method; t=1h, X=0,2 , K=0,7 TIME0123456INFLOW080020004200520044003200TIME78910111213INFLOW25002000150010007004000

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Time(h)0123456Q(csf)02721178445548864020300916Hydraulic Routing17tambm conhecido como Escoamento distribudo, se baseia nas equaes de Saint-Venant estabelecidas em 1870 e constituem um sistema de equaes, em derivadas parciais, em x e t, que descrevem, sob hipteses fixadas, os escoamentos no permanentes em canais.17ContinuityEquationMomentumEquationConservationFormNonconservationFormKinematicWaveDiffusionWaveDynamicWave18As equaes de Saint-Venant se dividem em Equaes de Continuidade, que consideram a conservao de massa, e Equaes de Momento (que so um par de equaes diferenciais parciais que descreve a conservao de massa e condies de momento), que contm termos para os processos fsicos que governam o fluxo momentneo, tais como a foras de atrito, de presso e a gravitacional no sentido do escoamento.Cabe ressaltar que ocasionalmente alguns termos da equao de momento podem ser desconsiderados por ter menos relevncia que os termos restantes.

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19Kinematic WaveKinematic waves govern flow when inertial and pressure forces are not important. In this method, the gravity and friction forces are balanced, so the flow does not accelerate appreciably.For a kinematic wave, the energy grade line is parallel to the channel bottom and the flow is steady and uniform (S0=Sf) within the differential length.

20The Kinematic Wave is recommended when the flow variations are small and when the ratio of the discharge phase is not a loopA onda cinemtica recomendada quando as variaes de fluxo so pequenas e quando a relao da fase de descarga no um loop.

20ProgramasHEC-HMSTheHydrologic Modeling System(HEC-HMS) is designed to simulate theprecipitation-runoffprocesses of dendriticdrainage basins. It is designed to be applicable in a wide range of geographic areas for solving the widest possible range of problems.

https://www.youtube.com/watch?v=zfj-V8pfoxs21KinerosThe kinematic runoff and erosion model KINEROS is an event oriented, physically based model describing the processes of interception, infiltration, surface runoff and erosion from small agricultural and urban watersheds. The watershed is represented by a cascade of planes and channels; the partial differential equations describing overland flow, channel flow, erosion and sediment transport are solved by finite difference techniques. The spatial variation of rainfall, infiltration, runoff, and erosion parameters can be accomodated. KINEROS may be used to determine the effects of various artificial features such as urban developments, small detention reservoirs, or lined channels on flood hydrographs and sediment yield.22Modelo Muskingum-CungeTirar do artigo e do livro no lab

23Usar exemplos pratico de toda a apresentaoBibliografia e linksFazer mais exercicios olhar livro do PORTO24Referncias Bibliogrficashttp://pubs.usgs.gov/pp/1302/report.pdfMays, Larry W., 2010 Water Resource Engineering, 2nd Edition.Porto, Rodrigo de Melo, 1999 Hidrulica Bsica, 2nd edition.Bedient, Philip B., 1989 Hydrology and Foodplain Analysis, 1st edition.25