Flow Routing
 Learning Objectives
 Calculate outflow hydrographs for reservoirs using the storage
indication method
 Calculate outflow hydrographs for stream reaches using the
Muskingum method
 Reading:
 8.5 and 8.6 in text
 9-3 in EM 1110-2-1417
Flow Routing
 Flow, or flood, routing – process of
determining the outflow hydrograph from a
reservoir or stream reach for a particular inflow
hydrograph
 Streamflow Routing – technique to compute
the effect of channel storage on the shape and
movement of a flood wave
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Inflow and outflow from a reservoir
Inflow exceeds outflow
and the reservoir is filling
Inflow and outflow are
equal and maximum
storage is reached
Outflow exceeds
inflow and the
reservoir empties
Reservoir Routing – process of determining the
outflow rate from a reservoir for a particular inflow
hydrograph
Level Pool Routing – process for calculating outflow
from a reservoir assuming horizontal water surface
when given inflow and storage-outflow characteristics
Based on the Continuity Equation:
I1  I 2
O1  O2
S 2  S1 
t 
t
2
2
I1  I 2
O1  O2
S 2  S1 
t 
t
2
2
 Values for I1 and I2 are specified by the inflow
hydrograph. Equation 1 contains two
unknowns, O2 and S2.
 Get a relationship between water surface
elevation and reservoir storage by topographic
maps or field surveys.
 Get a elevation-discharge relation from hydraulic
equations relating head and discharge for the
type of outlet.
 t is the time interval of the inflow hydrograph
Step 1 – Develop a stage-storage relationship
for the pond
Central Branch
Webb Branch
1000 ft.
1002 ft.
1004 ft.
1006 ft.
Contour
Elevation Contour
(ft)
Area (ft2)
1000
20000
1002
32000
1004
38000
1006
42000
Average
Contour
Storage
Volume
Area (ft2)
(ft3)
26000
35000
40000
0
52000
122000
202000
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Step 2 – Develop a stage-discharge relationship
for the outflow structure
Water
Elevation
(ft)
1000.0
1004.0
1004.5
1005.0
1005.5
1006.0
Hydraulic
Head
Over
Dam (ft)
0.0
0.0
0.5
1.0
1.5
2.0
Outflow
(cfs)
0.00
0.00
2.56
7.24
13.30
20.48
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Step 3 – Plot outflow (O) as a function of
S/t+O/2 = Storage-indication curve
Water
Storage
Elevation Outflow
S/t + O/2
3
(ft)
(cfs)
Volume (ft )
(cfs)
1000.0
0.00
0
0.00
1002.0
0.00
52000
28.89
1004.0
0.00
122000
67.78
1004.5
2.56
141000
79.61
1005.0
7.24
161000
93.06
1005.5
13.30
181000
107.21
1006.0
20.48
202000
122.46
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Step 4 – Route flow through structure, assuming
initial outflow equals initial inflow
Time (min)
0.0
30.0
60.0
90.0
120
150
180
210
240
Inflow
Average
S/t + O/2 Outflow
(cfs)
Inflow (cfs)
(cfs)
(cfs)
1.1
74
1.1
3
4.9
75.90
1.6
6.7
8.5
81.00
3.2
11
13.5
88.80
5.9
11.4
9.3
94.30
7.8
7.25
5.2
93.75
7.7
4.3
3.4
90.35
6.6
2.75
2.1
86.50
5.1
1.6
1.1
83.00
3.8
Storage
S/t
(cfs) Volume (ft3 )
73.45
132210
75.10
135180
79.40
142920
85.85
154530
90.40
162720
89.90
161820
87.05
156690
83.95
151110
81.10
145980
Inflows for the storm are given. Assume inflow = outflow for the first time step. Using the assumed outflow, find S 1/t - O1 /2
for the first time step ONLY from the storage-indication graph and solve for the initial storage volume. For the second and
remaining time steps, calculate Si/t - Oi /2 and add it to the average inflow (Ii + Ii+1)/2 to determine Si+1/t + Oi+1/2. Use
chart to get Oi+1 and then calculate Si+1.
Start again at next time step.
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Step 5 – Plot inflow and outflow hydrographs
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Flow Routing
 Learning Objectives
 Calculate outflow hydrographs for reservoirs using the storage
indication method
 Calculate outflow hydrographs for stream reaches using the
Muskingum method
 Reading:
 8.5 and 8.6 in text
 9-3 in EM 1110-2-1417