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Steady vs.Unsteady FlowlSteadylUnsteadyUnsteady flow through channels and reservoirslAffect of channel or reservoir storage on flow hydrographsReduce peak flowsProlong hydrograph base timesRouting ExamplelAffected bySlopeShapeRoughnessStorageAB?Flow RoutingInflow HydrographOutflow HydrographChannel reach orReservoirFlow Routing Used To:lDetermine impacts of Channel modificationsReservoir spillway modificationslDesign structures toControl storm waterMitigate flood flowsTrap sedimentStorage Routing MethodslBased on the continuity equationlAlso known as hydrologic routinglMethods include:Basic storage routingMuskingum routingConvex RoutingKinematic RoutingHydraulic Flow RoutinglBased on momentum and continuity equationslUsually done by a numerical solution of the governing equations or by the method of characteristics.Continuity and Momentum Equations:A ReviewArea=Avq(x,t)dxI=O+D DSContinuity EquationVolume of the control elementInflowOutflowContinuity equationMomentum EquationStorage RoutingStorage RoutinglStorage based on:Channel geometryDepth of flowFlow rate lcan be related to depth of flow through Mannings equation assuming steady,uniform flowStorage can be based on the average cross-sectional area of the reach for a given flow rateStoragelStorage can be based on the average cross-sectional area of the reach for a given flow rate.lLength of the channel section multiplied by the average cross-sectional area of the channel at a given flow rate would give the storage in the reach at that flow rate.Other inflows(or outflows)lTributary inflowslOverland flowslGround water contributionsChannel routinglChannel usually divided into several reaches where outflow from one become inflow to the next.lReaches should have fairly uniform hydraulic properties.lRouting interval should not exceed 1/5 to 1/3 of the time to peak of the hydrograph being routed.lRouting interval should not exceed travel time through the reach.lCommon method to solve is to plot characteristic curves(S+ODt/2 and S-ODt/2 versus discharge or depth.ExamplelA channel is 2500 ft long,has a slope of 0.09%and is clean with straight banks and no rifts or deep pools.The appropriate Mannings n is 0.030.A typical cross section is shown in the figure on the next page.Along the length of the channel there is no lateral inflow.The inflow hydrograph to the reach is triangular in shape with a base time of 3 hr,a time to peak of 1 hour and a peak flow rate of 360 cfs.Route the hydrograph through the channel reach using the storage routing procedure.Muskingum Methody2SStorage RoutingMuskingum RoutingMuskingum RoutinglStorage in reach is a linear function of both the inflow and outflow rate.lx and k must be determined from channel characteristics(For best results based on observed hydrographs).lx of zero corresponds to reservoir storage routing;x of makes the storage a function of the average flow rate in the reach.Muskingum Routing(no streamflow records)lIn the absence of streamflow records,k may be estimated as the flow travel time in the reach and x may be taken as about 0.25.Muskingum-Cunge MethodlProcedure to get better estimates for k and x.lc represents a flood wave celeritylm comes from the uniform flow equation and may be taken as 5/3.lv is the velocity at bankful dischargeMuskingum-Cungelqo is the flow per unit width generally calculated at the peak flow rate.lSo is the slope of the channel.Example:Muskingum-Cunge MethodlRepeat storage routing example using the Muskingum-Cunge method.Convex RoutinglInvolves only inflow-outflow hydrograph relationships i.e.continuity equation is not directly involved.lC is a parameter between 0 and 1.0 and can be estimated from:Convex RoutinglTravel time is calculated by Dt=CK where K can be approximated by the travel time through the reach.lMay result in an inconvenient time interval.lThe C value of C*for a more convenient time interval can be calculated from where Dt is from the equation above and the ratio of Dt*/Dt is kept close to unity.Example:Convex RoutingRepeat the previous example problem using Convex Routing.Reservoir RoutingReservoir RoutinglSimilar to channel storage routinglOutflow controlled by the principle spillway at a rate depending on the height of water above the inlet.lOutflow is at a maximum where it crosses the inflow hydrographReservoir RoutinglStorage is at a maximum when outflow is at a maximum.lStorage volume required in the reservoir is the area between the inflow and outflow hydrographs prior to the peak outflow.lIf the initial water level is the spillway crest than the volumes under the inflow and outflow hydrographs are equal.Graphical Routing:Puls MethodlGraphically solve the continuity equation using storage characteristic curves.lStage-storage curve is developed from topographic information relative to the reservoir site.lStage-discharge curve is based on the hydraulics of the reservoir outlet.lRouting interval should be 10 to 25%of the time to peak of the inflow 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