Environmental Engineering Reference
In-Depth Information
Lower flow regime
Upper flow
regime
Figure 5.14. Total shear stress
due to skin resistance and bed
forms as a function of the mean
velocity (Jansen, 1994).
V (m/s)
configuration takes place. For velocities that are slightly larger then the
threshold value small disturbances in the form of ripples will develop.
Higher velocities will produce dunes and at this stage, the total bed shear
stress consists of the two above-mentioned components, namely the skin
and the form resistance. The total shear stress is:
τ
=
τ
+
τ
(5.54)
The definition of the Darcy-Weisbach friction factor gives:
τ
=
ρgRS
(5.55)
fρv
2
8
τ
=
(5.56)
8
gRS
v
2
f
=
(5.57)
In the same way, the total friction factor
f
can be considered to have two
components:
f
+
f
f
=
(5.58)
8
g/C
2
Using
f
=
results in:
1
C
2
=
1
(
C
)
2
+
1
(
C
)
2
(5.59)
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