Page 125 - Fundamentals of Physical Volcanology

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102 CHAPTER 7

Ukinrek in Alaska in 1977, when violent explosions these two amounts of heat must be equal, we can
due to interactions between magma and ground- find the final temperature as a function of the vol-
water created two nearby craters with diameters of ume fraction of water in the mixture [V /(V +
w w
170 and 300 m (see Chapter 1). V )]. Assuming that the initial temperatures of
m
We can illustrate the importance of the relative the water and magma are 300 K and 1450 K,
amounts of water and magma in controlling the vio- respectively, that the magma is somewhat vesicu-
−3
lence of a hydromagmatic explosion by calculating lar with a density of 2000 kg m , and taking values
the equilibrium temperature, T , of the resulting of the thermal parameters for water from standard
e
steam and chilled magma fragments when a given tables, the final temperatures are found to vary
mixture of water and hot magma mix together. with the water content as shown in Fig. 7.4. Also
The heat lost by the magma, H , is shown in Fig. 7.4 is the maximum speed of the
m
chilled magma and steam thrown out in the explo-
H = V ρ c (T − T ) (7.6) sion. The speed is calculated using the equivalent of
m
m
m m
e
m
eqn 7.1, with the peak pressure during the explo-
where V , ρ , c , and T are the volume, density, sion being found from the fact that the water is
m m m m
specific heat, and initial temperature, respectively, turned into steam so fast that there is essentially no
of the magma. The heat gained by the water, H , change in volume. Notice that the most energetic
w
consists of the amounts of heat needed to warm the (high velocity) explosions occur when water
water to its boiling point, then to boil it, and finally makes up about 20–25% of the volume of the
to heat up the steam produced, and is given by exploding mixture. If the magma has a very low
vesicularity the optimum water volume fraction is
H = V ρ [c (373 − T ) + L + c (T − 373)] about 30%.
st
w
w
w
w
w
w
e
(7.7)
7.3.2 Mechanisms of violent magma–water
where V , ρ , c , and T are the volume, density,
w w w w interactions
specific heat, and initial temperature, respectively,
of the water, L is the amount of heat needed to boil The physical interaction between magma and water
w
the water, and c is the latent heat of steam. Since which occurs in a very violent hydromagmatic
st

800 1500
1400
700
1300
600 Velocity 1200
1100
Velocity (m s –1 ) 400 Temperature 1000 Final temperature (K)
500
900
800
300
200 700
600
Fig. 7.4 The final velocity and
500
100 temperature of fragments ejected in
400 hydromagmatic explosions driven by
0 300 the intimate mixing of magma and
water. The most violent explosions
0 10 20 30 40 50 60
occur when the water forms 20–30%
Volume % of water in mixture of the volume of the mixture.