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

2. Lake Travis and Mansfield Dam

3. Mansfield Dam, built in 1937
Lake Travis

4. Brays Bayou High Flow
6 to 7 inches of Rainfall

5. T.S. Allison
June 2001

6. Hurricane Rita Landed on Sabine, TX On Sep 24, 2006
Houston
Galveston Bay
Hurricane Rita Landed on Sabine, TX On Sep 24, 2006

7. Storage Reservoirs - The Woodlands

8. 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.

9. 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

10. Inflow and Outflow

11. Inflow and Outflow
I1 + I2 – Q1 + Q S2 – S1 = 2 2 Dt

12. Inflow & Outflow Day 3 = change in storage / time
Re Repeat for each day in progression

13. 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

14. 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

15. 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

16. 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 ft3

17. 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.

18. 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

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

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

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

22. River Routing
River Reaches

23. 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

24. 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

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

26. Muskingum Equations S = K [xI + (1-x)Q]
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 C’s are functions of x, K, Dt and sum to 1.0

27. 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.

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

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

30. 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

31. 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

32. Storage Indication Tabulation
Time In
In + In+1
2S/dt - Qn
2S/dt +Qn Qn 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 3 - Note that (17.6) = 30.4 and is repeated for each one