Geoscience Reference
In-Depth Information
and afterward:
Q
h
i
u
0
¼
(28)
1
þe
1
1
þe
2
HB
1
þ
B
2
The aim of this chapter is to define the river banks influence on tachoida at the
meridian. We have:
3
2
y
1
B
1
þ
ln
y
1
B
1
u
x
y
1
;
ð
z
Þ¼u
01
1
þ
2
e
1
3
2
z
H
þ
ln
z
H
e
3
1
þ
2
(29)
and putting
y
1
¼
B
1
we get:
2
Q
BH
ð
1
þ e
1
Þ
ð
1
þ e
2
Þ
3
2
z
H
þ
ln
z
H
u
x
z
ð
;
B
1
Þ¼
Þ
1
þ
e
3
(30)
B
1
B
2
B
ð
1
þ e
2
Þþ
B
ð
1
þ e
1
Similar relationships will be obtained when area (2) is considered and
y
2
¼
B
2
is assumed. The terms that appear in formula (
30
) have the following
meaning:
Q
BH
¼ u
0
(31)
is the average velocity in the riverbed cross section. In the further analysis, we
implement a coefficient
k
in the following form:
ð
1
þ e
1
Þ
ð
1
þ e
2
Þ
k
¼
(32)
B
B
B
B
ð
1
þ e
2
Þþ
ð
1
þ e
1
Þ
k
(
z
), if
n
1
and
n
2
, the Manning roughness
coefficients of the river banks, vary with depth and the cross section is not
rectangular:
In this way, it is possible to obtain
k
¼
u
x
ð
Þ
u
0
¼
z
3
2
z
H
þ
ln
z
H
k
ð
z
Þ
1
þ
(33)
n
2
, values of
B
1
and
B
2
must be first calculated in order to determine the
location of the river meridian. This division will be found on the basis of the
relationship:
If
n
1
6¼
e
3
=
2
2
4
3
5
0
;
75
U
2
n
2
ln
B
1
B
2
¼
e
3
=
2
and
B
1
þ
B
2
¼
B
(34)
U
1
n
1
ln
