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
(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)
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