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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Mansfield Dam, built in 1937
Lake Travis
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Brays Bayou High Flow
6 to 7 inches of Rainfall
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T.S. Allison June 2001
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Houston
Galveston Bay
Hurricane Rita Landed on Sabine, TX On Sep 24,
2006
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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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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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Inflow and Outflow
I1 I2 Q1 Q2 S2 S1

2
2
Dt
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Inflow Outflow Day 3
change in storage / time Re Repeat for
each day in progression
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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)
• Outflow Q can be computed as function of depth
  for either pipes, orifices, or weirs or
  combinations

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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

Combined
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 Pond Routing

• 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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Example Pond Routing
Develop Q (orifice) vs h Develop Q (weir) vs
h Develop A and Vol vs h Storage - Indication
2S/dt Q vs Q where Q is sum of weir and
orifice flow rates.
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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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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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Comparisons River vs. Reservoir Routing
Level pool reservoir
River Reach
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River Routing
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
• Peak storage occurs later than Qp

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Looped Rating Curves

• Due to complex hydraulics
• Higher peak Qp on inflow
• Lower peak Qp on outflow
• Due to prism and wedge
• Red River results shown

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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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Muskingum Equations

• Continuity Equation I - Q dS / dt
• S K xI (1-x)Q
• Parameters are x weighting and K travel
  time - x ranges from 0.2 to about 0.5
• where Cs are functions of x, K, Dt and sum to
  1.0

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Muskingum Equations
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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Hydraulic Shapes

• Circular pipe diameter D
• Rectangular culvert
• Trapezoidal channel
• Triangular channel

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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 3 - Note that 65.6 - 2(17.6) 30.4 and is
repeated for each one