Geoscience Reference
In-Depth Information
Inserting Eqs. (5.17)-(5.19) into Eq. (5.16) yields
⎛
⎞
2
/
3
M
j
n
3
/
2
j
⎝
⎠
n
=
1
χ
/χ
(5.20)
j
=
Division of energy slope
The method based on the division of energy slope originated from Engelund (1966) is
another option for determining the composite hydraulic properties for the cross-section
with rough vertical sidewalls or steep bank slopes. This method gives
τ
j
=
γ
RS
f
,
j
(5.21)
and applies the equal velocity assumption and the Manning equation in the entire
cross-section and each panel:
R
2
/
3
2
,
R
2
/
3
2
=
(
/
)
S
f
,
j
=
(
/
)
S
f
nU
n
j
U
(5.22)
Inserting Eqs. (5.17), (5.21), and (5.22) into Eq. (5.16) yields the following equation
for the composite Manning
n
:
⎛
⎞
1
/
2
M
⎝
j
n
j
/χ
⎠
n
=
1
χ
(5.23)
j
=
Conveyance method
The assumption of equal velocity used in the previous methods, based on the division
of either hydraulic radius or energy slope, is only applicable in simple channels. For
compound channels with floodplains, the flow velocities in the main channel and
floodplains may be significantly different. A more adequate method for determining
the composite hydraulic properties in compound channels is the conveyance method.
The conveyance method divides the cross-section into subsections in such a way that
the equal velocity assumption can be approximately valid in each subsection. Each
subsection can be further divided into panels. The flow area, wetted perimeter, and
conveyance of each subsection can be calculated in the normal way. The conveyances
of all subsections are then summed to provide the total conveyance for the entire cross-
section. For example, the compound cross-section shown in Fig. 5.4 can be divided
into three subsections: main channel, left floodplain, and right floodplain, and the
total conveyance is determined by
A
5
/
3
LF
n
LF
χ
A
5
/
3
MC
n
MC
χ
A
5
/
3
RF
n
RF
χ
K
=
LF
+
MC
+
(5.24)
2
/
3
2
/
3
2
/
3
RF
