Philip B. Bedient
Rice University

Lake Travis
Mansfield Dam, Hill Country of Texas

Barker Reservoir Watershed

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.

River vs. Reservoir Routing

Reservoir Routing
~ Reservoir acts to store water and release through control structure later
Max Storage = A = C
~ Inflow hydrograph
~ Outflow hydrograph
~ S - Q Relationship
~ Outflow peaks are reduced
~ Outflow timing is delayed

I
−
Q
= ds dt

Numerical Equivalent
Assume I
1
= Q
1 initially
I
1
+ I
2
– Q
1
+ Q
2
2 2
=
S
2
– S
1
Δ t

Numerical Progression
1.
I
1
+ I
2
– Q
1
+ Q
2
2 2
=
S
2
– S
1
Δ t
2.
I
2
+ I
3
– Q
2
+ Q
3
2 2
=
S
3
– S
2
Δ t
3.
I
3
+ I
4
– Q
3
+ Q
4
2 2
=
S
4
– S
3
Δ t
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 Equation
~ Orifices - Orifice Equation
~ Weirs or combination outflow structures - Weir Equation
Weir Flow
Orifice/pipe

Determining Outflow
Q
=
CA
gH
Q
=
CLH
3/2
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
Pipe
Q (cfs)

1. LHS of Equation is known
2. Know S as function of Q
I
1
+
I
2
+
⎛
⎝
2 S
1 dt
−
Q
1
⎞
⎠ =
⎛
⎝
2 S
2 dt
+
Q
2
⎞
⎠
3. Solve Equation for RHS
4. Solve for Q
2 from S
2
5. Repeat each time step

Storage Indication Method
STEPS
1. Storage - Indication
2. Develop Q (orifice) vs h
3. Develop Q (weir) vs h
4. Develop A and Vol vs h
5. 2S/dt + Q vs Q where Q is sum of weir and orifice flow rates.
NOTES
~ Outlet consists of weir and orifice
~ Weir crest at h = 5.0 ft
~ Orifice at h = 0 ft
~ Area (6000 to 17,416 ft 2 )
~ Volume ranges from 6772 to 84006 ft 3

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
0
Area
10 2 ft
6
Cum Vol
10 3 ft
0
1
2
7.5
9.2
6.8
15.1
3 11.0
25.3
4 13.0
37.4
5 15.1
51.5
7 17.4
84.0
Q total cfs
0
13
18
22
26
29
159
Storage-Indication
2S/dt +Q n cfs
0
35
69
106
150
200
473

Storage Indication Tabulation
Time
40
50
60
0
10
20
30
I n
0
20
40
60
50
I n
+ I n+1
0
20
60
100
110
40 90
30 70
(2S/dt - Q) n
0
0
5.6
30.4
82.4
136.3
145.5
(2S/dt +Q) n+1
0
20
65.6
130.4
192.4
226.3
215.5
Q n+1
0
7.2
17.6
24.0
28.1
40.4
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
Equation
River Reaches

River Rating Curves
~ Inflow and outflow are complex
~ Wedge and prism storage occurs
~ Peak flow Q p greater on rise limb than on the falling limb
~ Peak storage occurs later than
Q p

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

Actual Looped Rating Curves

1938
~ Continuity Equation I - Q = dS / dt
~ Storage Equation S = K {x I + (1-x)Q}
~ Parameters are:
~ x = weighting coefficient
~ K = travel time or time between peaks
~ x = ranges from 0.2 to about 0.5 (pure trans)
~ Assume that initial outflow = initial inflow

1938
~ Continuity Equation I - Q = dS / dt
~ Storage Equation S = K {x I + (1-x)Q}
~ Combine 2 equations using finite differences for I,
Q, S
S
2
- S
1
= K
[ x(I
2
- I
1
) + (1 - x)(Q
2
- Q
1
)
]
~ Solve for Q2 as function of all other parameters

Q
2
=
C
0
I
2
+
C
1
I
1
Where C
0
= (– Kx + 0.5
Δ t) / D
+
C
2
Q
1
C
1
= (Kx + 0.5
Δ t) / D
C
2
= (K – Kx – 0.5
Δ t) / D
D = (K – Kx + 0.5
Δ t)
Repeat for Q
3
, Q
4
, Q
5 and so on.

Select X from most linear plot
Obtain K from line slope

Manning’s Equation
Manning’s Equation used to estimate flow rates
Q p
= 1.49 A (R 2/3) S 1/2 n
Where Q p
= 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 n