Environmental Engineering Reference
In-Depth Information
R
i
=
hydraulic radius for the subsection i;
R
e
=
equivalent hydraulic radius;
h
i
=
water depth of subsection i;
k
si
=
hydraulic roughness in each subsection i;
k
se
=
equivalent or equivalent hydraulic roughness;
d
y
=
width of subsection i;
total number of subsections.
Method 5.
Méndez (1998) proposed to divide the discharge into discharges
through the central part and side slope parts and the total discharge is
the sum of subsection discharges.
Q
N
=
Q
lat
(see Figure 5.11).
Neglecting the effect of the momentum transfer, the discharge through
a stream column of width d
y
and water depth
h
i
, with a local roughness
height
k
si
can be calculated as:
=
Q
cen
+
C
i
h
i
d
y
h
i
S
f
Q
i
=
(5.31)
where
18 log
12
h
i
k
si
C
i
=
(5.32)
T
Lateral discharge
Central discharge
Lateral discharge
dy
k
sl
h
i
l
h
m
k
sb
Figure 5.11. Schematization of
flow through a trapezoidal canal.
B
The discharge through each of the subsections is the summation of
the flow in each stream tube and can be written as:
mh
B
C
i
h
i
h
i
S
f
d
y
C
i
h
hS
f
d
y
Q
=
Q
lat
+
Q
cen
=
2
+
(5.33)
0
0
Solving the equation gives:
4
5
mh
ln
18
S
1
/
f
h
3
/
2
2
.
3
12
h
k
sl
−
2
5
12
h
k
sb
Q
=
+
B
ln
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