Environmental Engineering Reference
In-Depth Information
Initiation of motion
10
0
10
-1
Motion
No motion
10
-2
10
-1
10
0
10
1
10
2
10
3
Figure 5.16. Shields' diagram
for initiation of motion (after
van Rijn, 1993).
Re
*
u
∗
cr
d
50
v
Re
∗
=
(5.71)
u
2
∗
τ
θ
=
1)
gd
50
=
(5.72)
(
s
−
(
s
−
1)
ρgd
50
ghS
o
u
∗
=
(5.73)
The use of the Shields' diagram is not very practical, since the
u
∗
value
appears in both parameters and in both axes of the diagram, and can only
be solved by trial and error. This imperfection of the Shields' diagram is
eliminated by introducing the particle parameter
D
∗
which is represented
by (Yalin, 1977):
(
s
1
/
3
Re
2
∗
−
1)
g
D
∗
=
=
d
50
(5.74)
v
2
θ
In this way the critical mobility parameter
θ
cr
will be expressed as a
function of
D
∗
. Once
D
∗
is known the Van Rijn (1993) relationships can be
used to determine the value of
cr
and to solve the equation for
τ
cr
.
According to van Rijn the relationships between
θ
cr
and
D
∗
are:
0
.
24
D
−
1
∗
θ
cr
=
for 1
< D
∗
≤
4
(5.75)
0
.
14
D
−
0
.
64
∗
θ
cr
=
for 4
< D
∗
≤
10
(5.76)
0
.
04
D
−
0
.
1
∗
θ
cr
=
for 10
≤
D
∗
≤
20
(5.77)
0
.
013
D
0
.
29
∗
θ
cr
=
for 20
≤
D
∗
≤
150
(5.78)
θ
cr
=
0
.
055
for
D
∗
>
20
(5.79)
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