Post on 16-Dec-2015
transcript
Review of Flood Routing
Philip B. BedientPhilip B. Bedient
Rice UniversityRice University
Lake Travis and Mansfield Dam
Lake Travis
LAKE LIVINGSTON
LAKE CONROE
ADDICKS/BARKER RESERVOIRS
Storage Reservoirs - The Woodlands
Detention Ponds
These ponds store and treat urban runoff and also These ponds store and treat urban runoff and also provide flood control for the overall development. provide flood control for the overall development.
Ponds constructed as amenities for the golf course Ponds constructed as amenities for the golf course and other community centers that were built up and other community centers that were built up around them.around them.
DETENTION POND, AUSTIN, TX
LAKE CONROE WEIR
Comparisons:River vs. ReservoirRouting
Level pool reservoir
River Reach
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
Inflow and Outflow
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I − Q =dSdt
Numerical EquivalentAssume I1 = Q1 initially
I1 + I2 – Q1 + Q2 S2 – S1
2 t2=
Numerical Progression
I1 + I2 – Q1 + Q2 S2 – S1
2 t2=
I2 + I3 – Q2 + Q3 S3 – S2
I3 + I4 – Q3 + Q4 S4 – S3
t
t2
22
2
DAY 1
DAY 2
DAY 3
1.
2.
3.
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
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
Determining Outflow
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Q = CA 2gH for orifice flow
Q = CLH 3/2 for weir flow
Weir
Orifice H measured above
Center of the orifice/pipe
H
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
Reservoir Routing
1. LHS of Eqn is known
2. Know S as fcn of Q
3. Solve Eqn for RHS
4. Solve for Q2 from S2
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I1 + I2 +2S1
dt− Q1
⎛ ⎝
⎞ ⎠ =
2S2
dt+ Q2
⎛ ⎝
⎞ ⎠
Repeat each time step
Example
Reservoir
Routing
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Storage
Indication
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
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
Storage Indication Storage Indication InputsInputs
heighheightt
h - fth - ft
AreaArea
101022 ft ftCum Cum
Vol 10Vol 1033 ftft
Q totalQ total
cfscfs2S/dt 2S/dt +Q+Qnn
cfscfs
00 66 00 00 00
11 7.57.5 6.86.8 1313 3535
22 9.29.2 15.115.1 1818 6969
33 11.011.0 25.325.3 2222 106106
44 13.013.0 37.437.4 2626 150150
55 15.115.1 51.551.5 2929 200200
77 17.417.4 84.084.0 159159 473473Storage-Indication
Storage Indication Storage Indication TabulationTabulation
TimeTime IInn IInn + I + In+1n+1 (2S/dt - Q)(2S/dt - Q)nn (2S/dt (2S/dt +Q)+Q)n+1n+1
QQn+1n+1
00 00 00 00 00 00
1010 2020 2020 00 2020 7.27.2
2020 4040 6060 5.65.6 65.665.6 17.617.6
3030 6060 100100 30.430.4 130.4130.4 24.024.0
4040 5050 110110 82.482.4 192.4192.4 28.128.1
5050 40 40 9090 136.3136.3 226.3226.3 40.440.4
6060 3030 7070 145.5145.5 215.5215.5 35.535.5
Time 2 Note that 20 - 2(7.2) = 5.6 and is repeated for each one
S-I Routing Results
I > Q
Q > I
See Excel Spreadsheet on the course web site
S-I Routing Results
I > Q
Q > I
Increased S
RIVER FLOOD ROUTING
CALIFORNIA FLASH FLOOD
River Routing
River Reaches
Manning’s Eqn
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
Wedge and Prism
Storage
• Positive wedge I > Q
• Maximum S when I = Q
• Negative wedge I < Q
Actual Looped Rating Curves
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
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
Muskingum Equations
Where C0 = (– Kx + 0.5t) / D
C1 = (Kx + 0.5t) / D
C2 = (K – Kx – 0.5t) / D
Where D = (K – Kx + 0.5t)
Repeat for Q3, Q4, Q5 and so on.
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Q2 = C0I2 + C1I1 + C2Q1
Muskingum River X
Obtain K from line slope
Select X from most linear plot
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
Manning’s Equation
n
• Circular pipe diameter D
• Rectangular culvert
• Trapezoidal channel
• Triangular channel
Hydraulic Shapes