1. Review of Flood Routing
Philip B. Bedient
Rice University

2. Lake Travis and Mansfield Dam

3. LAKE LIVINGSTON

4. LAKE CONROE

5. ADDICKS/BARKER RESERVOIRS

6. Storage Reservoirs - The Woodlands

7. 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.

8. DETENTION POND, AUSTIN, TX

9. LAKE CONROE WEIR

10. Comparisons: River vs. Reservoir Routing
Level pool reservoir
River Reach

11. 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

12. Inflow and Outflow

13. Numerical Equivalent I1 + I2 – Q1 + Q2 S2 – S1
Assume I1 = Q1 initially
I1 + I2 – Q1 + Q S2 – S1 = 2 2 Dt

14. Numerical Progression
I1 + I2 – Q1 + Q S2 – S1 1. =
DAY 1 2 2 Dt
I2 + I3 – Q2 + Q S3 – S2 2.
DAY 2 2 2 Dt
I3 + I4 – Q3 + Q S4 – S3 3.
DAY 3 2 2 Dt

15. 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

16. 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

17. Determining Outflow Weir H Orifice H measured above
Center of the orifice/pipe

18. 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

19. 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

20. Example
Reservoir
Routing
Storage
Indication

21. 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 ft3

22. 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

23. Storage Indication Inputs
height
h - ft
Area
102 ft
Cum Vol 103 ft
Q total
cfs
2S/dt +Qn 6 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
51.5 29
200 7
17.4
84.0
159
473
Storage-Indication

24. Storage Indication Tabulation
Time In
In + In+1
(2S/dt - Q)n
(2S/dt +Q)n+1
Qn+1 10 20
7.2 40 60
5.6
65.6
17.6 30
100
30.4
130.4
24.0 50
110
82.4
192.4
28.1 90
136.3
226.3
40.4 70
145.5
215.5
35.5
Time Note that (7.2) = 5.6 and is repeated for each one

25. S-I Routing Results See Excel Spreadsheet on the course web site
I > Q
Q > I
See Excel Spreadsheet on the course web site

26. S-I Routing Results
I > Q
Q > I
Increased S

27. RIVER FLOOD ROUTING

28. CALIFORNIA FLASH FLOOD

29. River Routing
Manning’s Eqn
River Reaches

30. 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

31. Wedge and Prism Storage
Positive wedge I > Q
Maximum S when I = Q
Negative wedge I < Q

32. Actual Looped Rating Curves

33. Muskingum Method - 1938 Storage Eqn S = K {x I + (1-x)Q}
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

34. Muskingum Method - 1938 Storage Eqn S = K {x I + (1-x)Q}
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

35. Muskingum Equations Where C0 = (– Kx + 0.5Dt) / D
C2 = (K – Kx – 0.5Dt) / D
Where D = (K – Kx + 0.5Dt)
Repeat for Q3, Q4, Q5 and so on.

36. Muskingum River X Select X from most linear plot Obtain K from
line slope

37. Manning’s Equation Qp = 1.49 A (R2/3) S1/2 n
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 n

38. Hydraulic Shapes Circular pipe diameter D Rectangular culvert
Trapezoidal channel
Triangular channel