Environmental Engineering Reference
In-Depth Information
u
B
u
h
u
z
y
Figure 2.7. Distribution of
the velocity in a rectangular
channel.
x
The velocity profile in the vertical direction for a rectangular cross
section can be approximated by the logarithmic equation as given by
van Rijn (1984):
u
κ
ln
z
v
z
=
(2.21)
z
0
where:
u
∗
=
shear velocity (m/s)
v
z
=
the velocity at a point
z
(m/s)
κ
=
constant of von Karman (from measurements
κ
=
0.4)
z
0
=
level of the zero velocity (m)
the level of a point above a datum (m)
By definition the shear velocity
u
∗
=
√
τ/ρ
and it can be expressed as:
z
=
τ
ρ
=
gRS
o
u
∗
=
(2.22)
By using
κ
=
0.4 the relationship for
v
z
becomes:
2
.
5
u
∗
ln
z
z
0
v
z
=
(2.23)
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