Environmental Engineering Reference
In-Depth Information
If the roughness height in the bed (
k
sb
) and sides (
k
sl
) is the same and
is equal to
k
se
then the equation can be written as:
4
5
mh
ln
12
h
18
S
1
/
f
h
3
/
2
2
.
3
2
5
B
ln
12
h
k
se
Q
=
k
se
−
+
(5.34)
Comparing the equations gives:
0
.
8ln
k
sl
+
(
B/h
)ln
k
sb
ln
k
se
=
(5.35)
0
.
8
m
+
(
B/h
)
18 log
12
R
k
se
C
e
=
(5.36)
Since the lateral transfer of momentum and its effect on the velocity dis-
tribution across the canal is not included, the equation will over predict
the flow rate. If this equation is to be used for discharge calculation then
a correction factor for the velocity distribution has to be applied. The
modified effective Chézy's roughness coefficient is then
C
é
=
f
e
C
e
, with
f
e
being the correction factor for the effective Chézy coefficient, which
is a function of the
B
/
y
-ratio, side slope
m
and roughness on the bed and
side slopes (Méndez, 1998).
Method 6.
Instead of applying a correction on the basis of the veloc-
ity distribution the equivalent roughness is computed using the previous
equation only. Comparing the equations gives:
0
.
8ln
k
sl
+
(
B/h
)ln
k
sb
ln
k
se
=
(5.37)
0
.
8
m
+
(
B/h
)
18 log
12
R
k
se
C
e
=
(5.38)
where:
m
=
side slope;
h
=
water depth in m;
B
=
bottom width in m;
k
se
=
hydraulic roughness in each stream tube
i
;
k
sl
=
hydraulic roughness along the sides;
k
sb
=
hydraulic roughness along the bottom.
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