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Review of Flood Routing Philip B. Bedient Rice University

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Lake Travis and Mansfield Dam Lake Travis

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LAKE LIVINGSTON

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LAKE CONROE

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ADDICKS/BARKER RESERVOIRS

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Storage Reservoirs - The Woodlands

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Detention Ponds These ponds store and treat urban runoff and also provide flood control for the overall development. Ponds constructed as amenities for the golf course and other community centers that were built up around them.

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DETENTION POND, AUSTIN, TX

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LAKE CONROE WEIR

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Comparisons: River vs. Reservoir Routing Level pool reservoir River Reach

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Reservoir Routing Reservoir acts to store water and release through control structure later. Inflow hydrograph Outflow hydrograph S - Q Relationship Outflow peaks are reduced Outflow timing is delayed Max Storage

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Inflow and Outflow

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Numerical Equivalent Assume I 1 = Q 1 initially I 1 + I 2 – Q 1 + Q 2 S 2 – S 1 2 tt 2 =

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Numerical Progression I 1 + I 2 – Q 1 + Q 2 S 2 – S 1 2 tt 2 = I 2 + I 3 – Q 2 + Q 3 S 3 – S 2 I 3 + I 4 – Q 3 + Q 4 S 4 – S 3 tt tt DAY 1 DAY 2 DAY

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Determining Storage Evaluate surface area at several different depths Use available topographic maps or GIS based DEM sources (digital elevation map) Storage and area vary directly with depth of pond Volume Elev Dam

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Determining Outflow Evaluate area & storage at several different depths Outflow Q can be computed as function of depth for Pipes - Manning’s Eqn Orifices - Orifice Eqn Weirs or combination outflow structures - Weir Eqn Weir Flow Orifice/pipe

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Determining Outflow Weir Orifice H measured above Center of the orifice/pipe H

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Typical Storage -Outflow Plot of Storage in acre-ft vs. Outflow in cfs Storage is largely a function of topography Outflows can be computed as function of elevation for either pipes or weirs S Q Pipe/Weir Pipe

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Reservoir Routing 1. LHS of Eqn is known 2. Know S as fcn of Q 3. Solve Eqn for RHS 4. Solve for Q 2 from S 2 Repeat each time step

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Example Reservoir Routing Storage Indication

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Storage Indication Method STEPS Storage - Indication Develop Q (orifice) vs h Develop Q (weir) vs h Develop A and Vol vs h 2S/dt + Q vs Q where Q is sum of weir and orifice flow rates. Note that outlet consists of weir and orifice. Weir crest at h = 5.0 ft Orifice at h = 0 ft Area (6000 to 17,416 ft 2 ) Volume ranges from 6772 to ft 3

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Storage Indication Curve Relates Q and storage indication, (2S / dt + Q) Developed from topography and outlet data Pipe flow + weir flow combine to produce Q (out) Weir Flow Begins Only Pipe Flow

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Storage Indication Inputs height h - ft h - ftArea 10 2 ft Cum Vol 10 3 ft Q total cfs 2S/dt +Q n cfs Storage-Indication

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Storage Indication Tabulation Time InInInIn I n + I n+1 (2S/dt - Q) n (2S/dt +Q) n+1 Q n Time 2 Note that (7.2) = 5.6 and is repeated for each one

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S-I Routing Results I > Q Q > I See Excel Spreadsheet on the course web site

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S-I Routing Results I > Q Q > I Increased S

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RIVER FLOOD ROUTING

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CALIFORNIA FLASH FLOOD

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River Routing River Reaches Manning’s Eqn

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River Rating Curves Inflow and outflow are complex Wedge and prism storage occurs Peak flow Q p greater on rise limb than on the falling limb Peak storage occurs later than Q p

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Wedge and Prism Storage Positive wedge I > Q Maximum S when I = Q Negative wedge I < Q

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Actual Looped Rating Curves

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Muskingum Method Continuity Equation I - Q = dS / dt Storage Eqn S = K {x I + (1-x)Q} Parameters are x = weighting Coeff K = travel time or time between peaks x = ranges from 0.2 to about 0.5 (pure trans) and assume that initial outflow = initial inflow

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Muskingum Method Continuity Equation I - Q = dS / dt Storage Eqn S = K {x I + (1-x)Q} Combine 2 eqns using finite differences for I, Q, S S 2 - S 1 = K [ x(I 2 - I 1 ) + (1 - x)(Q 2 - Q 1 ) ] Solve for Q2 as fcn of all other parameters

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Muskingum Equations Where C 0 = (– Kx t) / D C 1 = (Kx t) / D C 2 = (K – Kx – 0.5 t) / D WhereD = (K – Kx t) Repeat for Q 3, Q 4, Q 5 and so on.

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Muskingum River X Obtain K from line slope Select X from most linear plot

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Manning’s Equation used to estimate flow rates Q p = 1.49 A (R 2/3) S 1/2 Where Q p = flow rate n = roughness A = cross sect A R = A / P S = Bed Slope Manning’s Equation n

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Circular pipe diameter D Rectangular culvert Trapezoidal channel Triangular channel Hydraulic Shapes

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