Environmental Engineering Reference
In-Depth Information
h
h
z
z
crest
crest
h
h
Manhole
Manhole
Manhole
Manhole
Fig. 13.15
Free weir linkages. h
U
, upstream water level; h
D
, downstream water level; z
cyest
, crest elevation.
is greater than
synchronization (s);
P
i
¼1
D
depth above the crest h
U
z
cyest
t
i
is the total length of
time steps (s) after m steps of calculations in UIM;
T
syn
l
þD
c
o
A
c
w
w
for the submerged weir linkages. The orifice
equation is used for calculating the interacting
discharge:
P
i
¼1
D
t
i
is the time left (s) before the
next (l
þ
1
th
) synchronization.
The above equations were used to successfully
link the 1D SIPSON and the 2D UIM modelling
approaches to create a fully integrated above-
ground surface flows and below-ground drainage
system. Fuller details of the UIM model were
reported by Chen et al. (2007).
T
c
o
A
p
1
2
Q
¼
sign H
h
½
2
g
ð
h
U
h
D
Þ
ð
13
:
24
Þ
where c
o
is the orifice discharge coefficient.
Timing synchronization
The flow dynamics in drainage networks and over-
landsurfacearesolvedbytwoseparatemodelsusing
different time steps. Hence, to correctly link the
models the synchronization of time is extremely
important. This is particularly so as the 2D simu-
lation uses a variable time step. The process of
synchronization is shown in Figure 13.17.
Equations 4.20 and 4.21 provide an estimate of
time step
D
Case Studies
Comparison of 1D/1D and 1D/2D Models
at Keighley
The 1D SIPSON model and the 2D Urban Inun-
dation Model (UIM) were coupled in a study to
compare the performance of the 1D/1Dand 2D/1D
models developed as part of FRMRC. The case
study area shown in Figure 13.18 is located near
Stockbridge in Keighley, West Yorkshire, and was
used to test the applicability of the models and the
modelling process.
The study area had an overall catchment area of
approximately 3.5 km
2
, with the below-ground
drainage system comprising 45 main sewer pipes
t
0
m
þ1
, and the next time at which the
two models are synchronized is given by Equa-
tion 13.25:
n
o
X
m
i
t
0
m
þ1
D
t
m
þ1
¼ max
ð
T
syn
l
þD
T
¼1
D
t
i
Þ; D
ð
13
:
25
Þ
where
D
t
m
þ1
is the time step size (s) used for the
þ1
th
step; T
syn
l
is the time of the previous (l
th
)
m
h
h
crest
h
h
crest
z
z
Manhole
Manhole
Manhole
Manhole
Fig. 13.16
w linkages. A, node area; w, assumed weir width; h
U
,
upstream water level; h
D
, downstream water level; z
cyest
, crest elevation.
Submerged weir h
U
A
=
w or orifice h
U
>
A
=
