Geoscience Reference
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from each other. However, the empirical equations estimate the approximate values
of
t
c
, and their use cannot be recommended for the precise estimations.
5.2 Semitheoretical Analyses
Shields (
1936
) was the pioneer to propose a semitheoretical theory for the
entrainment threshold of sediments. The threshold of particle motion is governed
by balancing the driving force (as drag force) and the stabilizing resistance. At
the threshold condition, when the sediment particle is about to move,
u
!
u
c
(i.e., the threshold shear velocity) that has led to the following functional
representation:
Y
c
¼
f
ð
R
Þ
(9)
threshold Shields parameter,
u
c
2
/
Dgd
or
where
Y
c
¼
gd
. Figure
1
that shows
the Shields' experimental results, which relate
Y
c
and
R
, is known as
Shields
diagram
. Figure
1
depicts three distinct flow zones: (1) Smooth flow for
R
t
c
/
Dr
2: in
this case,
d
is much smaller than the thickness of viscous sublayer, and it is linearly
varying that
Y
c
¼
500: the viscous sublayer does
not exist. The threshold Shields parameter
Y
c
is invariant of the fluid viscosity and
has a constant value of 0.056. (3) Transitional flow for 2
0.1/
R
. (2) Rough flow for
R
500: sediment
particles are of the order of the thickness of viscous sublayer. There is a minimum
value of
Y
c
¼
R
10.
The shortcoming of the Shields diagram is that the viscous parameter does not
have any effect for
R
0.032 corresponding to
R
¼
70, but
Y
c
still varies with
R
in this range. Furthermore,
the
t
c
and
u
c
that are interchangeable are shown as dependent and independent
1
Laminar
flow at bed
Turbulent
flow at bed
Sediment motion
0.1
τ
0
= τ
c
No sediment motion
0.01
1
10
100
1000
R
*
Fig. 1 Shields parameter
Y
c
as a function of
R
*
