Geoscience Reference
In-Depth Information
that were in use in various studies leading discrepancies in the data sets and
introducing difficulties in making comparisons (Paintal
1971
; Buffington and
Montgomery
1997
).
3 Competent Velocity Concept
A competent velocity is a velocity at the particle level (boundary velocity) or the
depth-averaged velocity, which is just adequate to start the particle movement for a
given size. Goncharov (
1964
) used the competent velocity as detachment velocity
U
n
. It was defined as the lowest average velocity at which individual particles
continually detach from the bed. He gave an equation of
U
n
as:
0
:
5
U
n
¼
log
ð
8
:
8
h
=
d
Þð
0
:
57
Dgd
Þ
(1)
where
h
¼
flow depth;
d
¼
representative particle diameter, that is median parti-
cle diameter;
g
¼
acceleration due to gravity;
D ¼
s
1;
s
¼
relative density of
sediment, that is
mass density of fluid.
Carstens (
1966
) proposed an equation of competent velocity
u
cr
at the particle
level by analyzing a large number of experimental data. It is:
r
s
/
r
;
r
s
¼
mass density of sediment; and
r ¼
u
cr
=Dgd
3
:
61
ð
tan
'
cos
y
sin
yÞ
(2)
' ¼
y ¼
where
angle of repose of sediment; and
angle made by the streamwise
sloping bed with the horizontal.
Neill (
1968
) proposed a design curve for the initial movement of coarse uniform
gravels in terms of average-velocity
U
cr
as a competent velocity. It is:
1
=
3
U
cr
=Dgd
¼
2
ð
h
=
d
Þ
(3)
The forces acting on a spherical sediment particle resting on the bed of an open
channel were analyzed by Yang (
1973
) to propose the equations for both smooth
and rough boundaries as follows:
U
cr
w
ss
¼
5
log
R
2
:
06
þ
0
:
66
for 0
<
R
<
70
(4a)
0
:
for
R
r
U
cr
=
w
ss
¼
:
2
05
70
(4b)
where
w
ss
¼
terminal fall velocity;
R
¼
shear Reynolds number, that is
u
d
/
u
;
u
¼
kinematic viscosity of fluid.
Zanke (
1977
) recommended the following equation:
shear velocity; and
u ¼
0
:
5
U
cr
¼
2
:
8
ðDgd
Þ
þ
14
:
7
c
1
ðu=
d
Þ
(5)