Environmental Engineering Reference
In-Depth Information
The design steps include:
•
Assume a value for an initial Strickler
k
s
according to the maintenance
condition and find a first approximation of
y
and
b
;
•
Next re-compute the design values to obtain the proper values of
b
and
k
s
;
•
Next fine-tune the design in view of a small adjustment of the design
width
b
des
, i.e. a value that can be constructed (e.g. width on a half or
whole meter). This fine-tuning has a minor impact on the final results,
unless a completely different value from the originally suggested
b
is used.
When using the de Chézy equation in stead of the Strickler equation,
the approach is the same as before.
The discharge for uniform flow is:
R
0
.
5
S
0
.
5
o
Q
=
A
∗
C
∗
∗
de Chézy
(C.15)
12
R
C
=
18 log
White-Colebrook
(C.16)
k
+
δ/
3
.
5
11
.
6
ν
v
∗
δ
=
(C.17)
g
v
∗
=
∗
R
∗
S
(C.18)
where:
C
de Chézy's coefficient (m
2
s
−
1
)
=
=
=
k
length characterizing the roughness
1/2
a
(Nikuradse)
=
δ
thickness of the laminar sub-layer
v
∗
=
shear velocity
Re-writing the Chézy equation gives:
R
0
.
5
S
0
.
5
o
Q
=
A
∗
C
∗
∗
m
)
y
2
=
+
=
+
A
(
b
my
)
y
(
b/y
(C.19)
b
y
+
m
2
y
2
1
P
=
+
m
)
3
/
2
y
3
(
b/y
+
CS
0
.
5
o
Q
=
2
(1
(
b/y
+
+
m
2
)
y
)
1
/
2
(C.20)
m
)
3
/
2
y
3
(
n
+
CS
0
.
5
o
for
n
=
b/y
:
Q
=
2
(1
(
n
+
+
m
2
)
y
)
1
/
2
2
(1
m
2
))
1
/
2
Q
(
n
+
+
Q
y
5
/
2
=
=
(C.21)
S
0
.
5
CS
0
.
5
o
(
n
+
m
)
3
/
2
∗
∗
C
f
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