Environmental Engineering Reference
In-Depth Information
in rectangular canals with the selected data is similar to the one given
earlier.
5.2.8
Effect of bed forms on the flow resistance
The hydraulic resistance to flowing water in open channels is affected
by the development of bed forms such as ripples, mega ripples and dunes.
The hydraulic resistance due to the bed roughness is expressed by a
friction factor. Most common friction factors are:
- the Darcy-Weisbach friction factor
f
:
8
gRS
f
v
2
8
g
C
2
f
=
from
f
=
(5.49)
- the de Chézy coefficient:
v
√
S
f
R
C
=
(5.50)
- the Manning (
n
) or Strickler (
k
) roughness coefficient:
R
2
/
3
S
1
/
2
f
n
=
for Manning
(5.51)
v
v
R
2
/
3
S
1
/
2
f
k
=
for Strickler with
n
=
1
/k
(5.52)
For the same conditions the Manning coefficient can be related to the
de Chézy coefficient by:
R
1
/
6
n
C
=
(5.53)
In these lecture notes, mainly the de Chézy coefficient will be used to
describe the friction in irrigation canals. The use of the Darcy-Weisbach
and Manning/Strickler roughness coefficients follows from the equations
described above.
Not only the wall (grain) roughness, but also the bed forms, are ele-
ments that resist the flow and the total resistance in channels with a
movable bed consists of two components:
•
the surface or skin resistance due to the grain roughness; the resistance
has a grain-related shear stress
τ
:
•
the form resistance due to hydrodynamic forces acting on the bed forms
has a form-related shear stress
τ
.
Figure 5.14 presents the total shear stress due to skin and form resis-
tance for different velocities. For low velocities, the bed shear stress is
smaller than the threshold value and no motion of particles occurs: the bed
remains flat and the total bed shear stress is represented by the grain related
shear stress
τ
. For increasing velocity, especially beyond the threshold,
transport of sediment will start, the bed becomes unstable and some bed
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