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**Review of Flood Routing**

Philip B. Bedient Rice University

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**Lake Travis and Mansfield Dam**

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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 I1 + I2 – Q1 + Q2 S2 – S1**

Assume I1 = Q1 initially I1 + I2 – Q1 + Q S2 – S1 = 2 2 Dt

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**Numerical Progression**

I1 + I2 – Q1 + Q S2 – S1 1. = DAY 1 2 2 Dt I2 + I3 – Q2 + Q S3 – S2 2. DAY 2 2 2 Dt I3 + I4 – Q3 + Q S4 – S3 3. DAY 3 2 2 Dt

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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 Elev Volume 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 H Orifice H measured above**

Center of the orifice/pipe

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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 Pipe/Weir S Pipe Q

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**Reservoir Routing LHS of Eqn is known Know S as fcn of Q**

Solve Eqn for RHS Solve for Q2 from S2 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 ft2) Volume ranges from 6772 to ft3

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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) Only Pipe Flow Weir Flow Begins

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**Storage Indication Inputs**

height h - ft Area 102 ft Cum Vol 103 ft Q total cfs 2S/dt +Qn 6 1 7.5 6.8 13 35 2 9.2 15.1 18 69 3 11.0 25.3 22 106 4 13.0 37.4 26 150 5 51.5 29 200 7 17.4 84.0 159 473 Storage-Indication

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**Storage Indication Tabulation**

Time In In + In+1 (2S/dt - Q)n (2S/dt +Q)n+1 Qn+1 10 20 7.2 40 60 5.6 65.6 17.6 30 100 30.4 130.4 24.0 50 110 82.4 192.4 28.1 90 136.3 226.3 40.4 70 145.5 215.5 35.5 Time Note that (7.2) = 5.6 and is repeated for each one

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

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 Manning’s Eqn River Reaches

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**River Rating Curves Inflow and outflow are complex**

Wedge and prism storage occurs Peak flow Qp greater on rise limb than on the falling limb Peak storage occurs later than Qp

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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 - 1938 Storage Eqn S = K {x I + (1-x)Q}**

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 - 1938 Storage Eqn S = K {x I + (1-x)Q}**

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 S2 - S1 = K [x(I2 - I1) + (1 - x)(Q2 - Q1)] Solve for Q2 as fcn of all other parameters

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**Muskingum Equations Where C0 = (– Kx + 0.5Dt) / D**

C2 = (K – Kx – 0.5Dt) / D Where D = (K – Kx + 0.5Dt) Repeat for Q3, Q4, Q5 and so on.

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**Muskingum River X Select X from most linear plot Obtain K from**

line slope

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**Manning’s Equation Qp = 1.49 A (R2/3) S1/2 n**

Manning’s Equation used to estimate flow rates Qp = 1.49 A (R2/3) S1/2 Where Qp = flow rate n = roughness A = cross sect A R = A / P S = Bed Slope n

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**Hydraulic Shapes Circular pipe diameter D Rectangular culvert**

Trapezoidal channel Triangular channel

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