Review of Flood Routing

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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 I1 Q1 initially
I1 I2 Q1 Q2 S2 S1

2
2
Dt
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Numerical Progression
I1 I2 Q1 Q2 S2 S1
1.

DAY 1
2
2
Dt
I2 I3 Q2 Q3 S3 S2
2.
DAY 2
Dt
2
2
I3 I4 Q3 Q4 S4 S3
3.
DAY 3
Dt
2
2
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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 - Mannings 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 84006 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
Storage-Indication
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Storage Indication Tabulation
Time 2 Note that 20 - 2(7.2) 5.6 and is
repeated for each one
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S-I Routing Results
I gt Q
Q gt I
See Excel Spreadsheet on the course web site
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S-I Routing Results
I gt Q
Q gt I
Increased S
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RIVER FLOOD ROUTING
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CALIFORNIA FLASH FLOOD
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River Routing
Mannings 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 gt Q
• Maximum S when I Q
• Negative wedge I lt Q

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Actual Looped Rating Curves
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Muskingum Method - 1938

• 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

• 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 C1 (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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Mannings Equation
Mannings 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