Geoscience Reference
In-Depth Information
c
axes. This is an important assumption made in the equations used to calculate
theflow velocity responsible for transporting a particle.
The drag force can be described as follows
γ
f
·
V
b
2
F
D
=
C
D
·
d
2
·
(3.2)
Where
C
D
=
drag coefficient,
d
=
diameter of particle (usually the
b
axis),
f
=
specific weight of the fluid (g
−
1
)and
V
b
=
flow velocity at bed.
The drag coefficient (
C
D
)isafunction of the shape of the particle. Sphere
shaped particles are easier to entrain than a cube. The smaller the face being
acted upon by the drag force the higher the velocity required to initiate motion.
Drag coefficients can be defined by a shape factor (SF) expressed as,
SF
=
d
S
/
√
d
I
·
d
L
(3.3)
Where
d
S
=
diameter of
c
axis,
d
I
=
diameter of
b
axis and
d
L
≡
diameter of
a
axis.
The lift force can be expressed as follows,
C
L
d
2
γ
S
·
V
b
2
F
L
=
(3.4)
where
C
L
=
coefficient of lift and
S
=
the specific weight of the sediment.
The lift force can only apply where the fluid flow covers the entire particle
being entrained. Costa (1983)suggests that a lift coefficient of 0.178 be used as
it represents the velocity one-third of the particle diameter above the stream
bed or the point at which lift occurs.
The resisting force can be expressed as follows,
F
R
=
(γ
S
−
γ
f
)
g
µ
(3.5)
where
gravitational constant. Static
friction refers to the friction between the boulder and the channel bed. Costa
(1983)notesthat
=
coefficient of static friction and
g
=
varies between 0.5 and 0.8 with a commonly accepted value
of 0.7.
Simplifying equations (3.2), (3.4)and(3.5) and solving for bed velocity (
V
b
)
gives,
V
b
=
√
[2 (γ
S
−
γ
f
)
d
I
g
µ
/
γ
f
(
C
L
+
C
D
)]
(3.6)
The average flow velocity can be obtained by multiplying the bed velocity (
V
b
)
by 1.2
V
=
1
.
2
V
b
(3.7)
Williams andCosta (1988)andCosta (1983) outline the derivation of these
equations in more detail and Wohl (1995)reviews some of the potential problems
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