Page 131 - Fundamentals of Physical Volcanology

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108 CHAPTER 8

the terminal velocities of clasts of various densities, ditions the drag coefficient is not a constant but
sizes, and shapes by dropping them and filming instead is inversely proportional to a dimensionless
their motion with high-speed cameras. For very number called the Reynolds number, Re. This num-
small clasts, normal laboratories were high enough ber represents the ratio between the inertial forces
to allow clasts to reach their terminal velocity, but and the viscous forces acting on the clast and is
larger clasts required the use of the stairwells or tall defined by
buildings!
The experiments showed that the normal rules of Re = (dU ρ )/η a (8.2)
a
fluid mechanics applied to volcanic particles pro-
vided due account was taken of their often very where U is the speed of the clast through the gas
irregular shapes. We already used the relevant rela- and η is the viscosity of the gas. What is observed is
a
tionships in eqns 6.8 and 6.9 in Chapter 6 to de- that for spheres, C is equal to 24/Re, and combin-
D
scribe how pyroclasts of a given size, density, and ing this with eqn 8.2 shows that in laminar flow
shape are suspended in the gas stream inside an conditions eqn 8.1 has to be replaced by
eruption column. For a clast falling through air,
2
the equivalent of eqn 6.9, now written in terms of U = (d σ g)/(18 η ) (8.3)
a
T
the average diameter, d, of the clast instead of the
radius, is For irregularly shaped particles the constants dif-
fer from 24 and 18, and again have to be determined
U = 4 d σ g (8.1) from experiments, but the basic relationships
3 C ρ
T
D a are the same. Some examples of the experimental
determinations of clast terminal fall speeds consis-
where U is still the terminal velocity of a clast of tent with these theoretical equations are shown
T
density σ, but now it is the density of the atmo- in Fig. 8.4. These values all correspond to condi-
spheric air, ρ , that controls the clast fall speed. The tions at ground level under average temperature
a
influence of the shape of the clast is represented by and pressure conditions. Equation 8.1 shows that
the value of the drag coefficient C , which has to be the terminal velocities of large clasts depend on the
D
determined from experiments on actual volcanic reciprocal of the density of the atmosphere, and
particles. Furthermore the value of C for a given the density, like the pressure, of the atmosphere
D
clast shape will depend on how its “average” dia- decreases with height. This means that the terminal

meter d is defined: d could be the arithmetic mean velocity of a large clast must be greater when it is
of the longest dimension of the clast and the two high in the atmosphere than when it nears the
dimensions at right angles to this, or it could be ground. Similarly eqn 8.3 shows that the terminal
defined as the diameter of a sphere with the same velocities of small clasts depend on the reciprocal
volume as the clast, and so on – various alternates of the viscosity of the atmospheric gas. The viscosi-
have been used, and care must be taken to use con- ties of gases are mainly a function of temperature,
sistent values of C . decreasing as the temperature decreases, and since
D
In describing the support of clasts inside an erup- the atmospheric temperature generally decreases
tion column, Chapter 6 was mainly concerned with with height under normal conditions, the terminal
the relatively large clasts in the lower part of the velocities of small clasts, like those of large clasts,
column. The gas flow around these pyroclasts is are greatest when they are high in the atmosphere.
turbulent, and so it was possible to assume that the
drag coefficient, C , in eqn 8.1 was nearly constant
D 8.2.4 Other factors affecting fallout from
for a given clast shape. Here we also need to be con-
eruption columns
cerned about the fall of very small particles released
from the upper part of the column and the umbrella The physical processes described above and in
cloud. The air flow past these pyroclasts is laminar, Chapter 6, which determine how clasts are carried
i.e., smooth, not turbulent, and under these con- up in an eruption column and how they fall from