EM 1110-2-1100 (Part III)
30 Apr 02
pieces on a wave-washed shingle beach are apt to have greater strength than the bulk strength of the rock from
which the gravel was derived.
III-1-4. Fall Velocity
When a particle falls through water (or air), it accelerates until it reaches its fall or settling velocity. This is
the terminal velocity that a particle reaches when the (retarding) drag force on the particle just equals the
(downward) gravitational force. This quantity figures prominently in many coastal engineering problems.
While simple in concept, its precise calculation is usually not. A particle's fall velocity is a function of its
size, shape, and density; as well as the fluid density, and viscosity, and several other parameters.
a. General equation.
(1) For a single sphere falling in an infinite still fluid, the balance between the drag force and the
gravitational force is:
2
π D 2 ρ Wf
π D3
(III-1-6)
(ρs & ρ) g
CD
'
4
2
6
or, solving for the velocity:
1
4 g D ρs
2
(III-1-7)
&1
Wf '
3 CD ρ
where
Wf = fall velocity
CD = dimensionless drag coefficient
D = grain diameter
ρ = density of water
ρs = density of the sediment
(2) The units of the fall velocity will be the same as the units of (gD). The problem now usually
becomes one of determining the appropriate drag coefficient. Figure III-1-5, which is based upon extensive
laboratory data of Rouse and many others, shows how the drag coefficient CD varies as a function of the
Reynolds number (Re = Wf D/ν, where ν is the kinematic viscosity) for spherical particles. Re is
dimensionless, but Wf , D, and ν must have common units of length and time.
(3) The plot in Figure III-1-5 can be divided into three regions. In the first region, Re is less than about
0.5, and the drag coefficient decreases linearly with Reynolds number. This is the region of small, light
grains gently falling at slow velocities. The drag on the grain is dominated by viscous forces, rather than
inertia forces, and the fluid flow past the particle is entirely laminar. The intermediate range is from about
Coastal Sediment Properties
III-1-21
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