Review of Flood Routing
Philip B. Bedient
Rice University
Lake Travis and
Mansfield Dam
Lake Travis
Mansfield Dam, built
in 1937
Lake Travis
Brays Bayou High Flow
6 to 7 inches of Rainfall
T.S. Allison
June 2001
Houston
Galveston Bay
Hurricane Rita Landed on
Sabine, TX On Sep 24, 2006
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.
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
Inflow and Outflow
I1 + I2 – Q1 + Q2
2
2
=
S2 – S1
Dt
Inflow & Outflow Day 3
= change in storage / time
S3  S2
I 2  I 3 / 2  Q2  Q3 / 2  dt
Re
Repeat for each day in progression
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
Q  CA 2gH for orifice flow
Q  CLH
3/2
for weir flow
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
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 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
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.
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
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
Comparisons:
River vs.
Reservoir
Routing
Level pool reservoir
River Reach
River Routing
River Reaches
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
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
Wedge and
Prism
Storage
• Positive wedge
I>Q
• Maximum S when I = Q
• Negative wedge
I<Q
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
Q2  C0I2  C1I1  C2Q1
where C’s are functions of x, K, Dt and sum to 1.0
Muskingum Equations
C0 = (– Kx + 0.5Dt) / D
C1 = (Kx + 0.5Dt) / D
C2 = (K – Kx – 0.5Dt) / D
Where
D = (K – Kx + 0.5Dt)
Q2  C0I2  C1I1  C2Q1
Repeat for Q3, Q4, Q5 and so on.
Muskingum River X
Select X from most linear plot
Obtain K from
line slope
Hydraulic Shapes
• Circular pipe diameter D
• Rectangular culvert
• Trapezoidal channel
• Triangular channel
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 - Qn
2S/dt +Qn
Qn
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 3 - Note that 65.6 - 2(17.6) = 30.4 and is repeated for each one