Review of Flood Routing
Philip B. Bedient
Rice 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
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.
DETENTION POND, AUSTIN, TX
LAKE CONROE WEIR
Comparisons:
River vs.
Reservoir
Routing
Level pool reservoir
River Reach
Reservoir Routing
• Reservoir acts to
store
water and release
through control structure
later.
Max Storage
• Inflow hydrograph
• Outflow hydrograph
• S - Q Relationship
• Outflow peaks are
reduced
• Outflow timing is delayed
Inflow and Outflow
dS
IQ
dt
Numerical Equivalent
Assume I1 = Q1 initially
I1 + I2 – Q1 + Q2
2
2
=
S2 – S1
Dt
Numerical Progression
1.
I1 + I2 – Q1 + Q2
2
2.
2
I2 + I3 – Q2 + Q3
2
3.
=
2
I3 + I4 – Q3 + Q4
2
2
S2 – S1
Dt
S3 – S2
Dt
S4 – S3
Dt
DAY 1
DAY 2
DAY 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
Elev
Volume
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
Q  CA 2gH for orifice flow
Q  CLH
3/2
for weir flow
Weir
H
Orifice H measured above
Center of the orifice/pipe
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
Reservoir Routing
2S1
 2S2

I1  I 2 
 Q1 
 Q2
 dt
  dt

1. LHS of Eqn is known
2. Know S as fcn of Q
3. Solve Eqn for RHS
4. Solve for Q2 from S2
Repeat each time step
Example
Reservoir
Routing
----------
Storage
Indication
Storage Indication Method
Note that outlet consists
of weir and orifice.
STEPS
Storage - Indication
Weir crest at h = 5.0 ft
Develop Q (orifice) vs h
Orifice at h = 0 ft
Develop Q (weir) vs h
Area (6000 to 17,416 ft2)
Develop A and Vol vs h
Volume ranges from 6772
to 84006 ft3
2S/dt + Q vs Q where Q is
sum of weir and orifice
flow rates.
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
Storage Indication Inputs
height
h - ft
Area
102 ft
Cum Vol
103 ft
Q total
cfs
2S/dt +Qn
cfs
0
6
0
0
0
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
15.1
51.5
29
200
7
17.4
84.0
159
473
Storage-Indication
Storage Indication Tabulation
Time
In
In + In+1
(2S/dt - Q)n
(2S/dt +Q)n+1
Qn+1
0
0
0
0
0
0
10
20
20
0
20
7.2
20
40
60
5.6
65.6
17.6
30
60
100
30.4
130.4
24.0
40
50
110
82.4
192.4
28.1
50
40
90
136.3
226.3
40.4
60
30
70
145.5
215.5
35.5
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
Manning’s Eqn
River Reaches
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
Q2  C0I2  C1I1  C2Q1
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.
Muskingum River X
Select X from most linear plot
Obtain K from
line slope
Manning’s Equation
Manning’s Equation used to
estimate flow rates
Qp = 1.49 A (R2/3) S1/2
n
Where Qp = flow rate
n = roughness
A = cross sect A
R=A/P
S = Bed Slope
Hydraulic Shapes
• Circular pipe diameter D
• Rectangular culvert
• Trapezoidal channel
• Triangular channel