Geoscience Reference
In-Depth Information
having diameter
D
, while Brayshaw et al
.
(
1983
) measured the ratio as 1.8 for the
same roughness at
R
¼
10
4
. Aksoy (
1973
) and Bagnold (
1974
) found the
lift to drag ratio on a sphere of about 0.1 and 0.5 at
R
¼
5.2
300 and 800, respectively.
Apperley (
1968
) studied a sphere laid on gravels and found lift to drag ratio as 0.5 at
R
¼
70. Watters and Rao (
1971
) observed negative (downwards) lift force on a
sphere for 20
100. Davies and Samad (
1978
) also reported that the lift
force on a sphere adjacent to the bed becomes negative if significant underflow
takes place beneath the sphere and the flow condition is
R
<
<
R
<
5. However, the lift is
positive for
R
5, although the negative lift force could not be clearly explained.
While the lift forces obviously contribute to the sediment entrainment, the
occurrence of lift on a sediment particle is still unclear. Insufficient experimental
results are available to determine quantitative relationships; as such a critical lift
criterion has so far not been obtained which could have been a ready reference for
the determination of sediment entrainment. The occurrence of negative lift at low
R
has been well established, but its cause and magnitude remain uncertain. It was
understood that besides the lift, the drag is always prevalent to contribute towards
the sediment entrainment. For higher
R
, the correlation between lift and drag is
another uncertain issue, although the lift is definitely positive.
5 Threshold Shear Stress Concept
5.1 Empirical Equations of Threshold Shear Stress
Attempts have been made to correlate the threshold boundary shear stress
t
c
with
sediment properties for experimental and field data. Kramer (
1935
) proposed:
p
ðr
s
rÞ
t
c
¼
29
gd
=
M
(6)
t
c
is in g/m
2
;
M
is the uniformity coefficient of Kramer; and
d
is in mm.
Equation (
6
) is applicable for 0.24
where
d
6.52 mm and 0.265
M
1.
USWES (
1936
) recommended the following formula:
p
Dd
t
c
¼
0
:
285
=
M
(7)
where
t
c
is in Pa; and
d
is in mm. Equation (
7
) is valid for 0.205
d
4.077 mm
and 0.28
0.643.
A simple equation of
M
t
c
is given by Leliavsky (
1966
) as:
t
c
¼
166
d
(8)
t
c
is in g/m
2
; and
d
is in mm. None of the equations take into account the
effect of fluid viscosity. Further, each of these equations produces results that differ
where
