3.2.3 Fall Velocity
The prime indicator of the interaction of sediments in suspension within the flow is the fall
velocity of sediment particles. The fall velocity of a particle is defined as the velocity of that
particle falling alone in quiescent, distilled water of infinite extent. In most cases, the particle
is not falling alone, and the water is not distilled or quiescent. Measurement techniques are
available for determining the fall velocity of groups of particles in a finite field in fluid other
than distilled water. However, little is known about the effect of turbulence on fall velocity.
A particle falling at terminal velocity in a fluid is under the action of a driving force due to its
buoyant weight and a resisting force due to the fluid drag. Fluid drag is the result of either
the tangential shear stress on the surface of the particle, or a pressure difference on the
particle or a combination of the two forces. The fluid drag on the falling particle FD is given
by the drag equation
FD = CD A s ρ ω2 / 2
(3.2)
The buoyant weight of the particle Ws is:
Ws = (ρ s - ρ) gVp
(3.3)
where:
CD
Coefficient of drag
=
Terminal fall velocity of the particle
=
ω
As
Projected area of the particle normal to the direction of flow
=
Fluid density
=
ρ
Particle density
=
ρs
g
Acceleration due to gravity
=
Vp
Volume of the particle
=
The area and volume can be written in terms of the characteristic diameter of the particle Ds
or:
A s = K1 D2
(3.4)
s
and
Vp = K 2 D3
(3.5)
s
Where the coefficients K1 and K2 depend on the shape of sediment particles. For example,
K1 = π/4 and K2 = π/6 for spherical particles. If the particle is falling at its terminal velocity, FD
= Ws
(ρ s - ρ) gVp = CD A s ρ ω2 / 2
(3.6)
3.4
Previous Page
