82

WORLDWIDE EFFECTS OF ATOMIC WEAPONS

yield and type of shot (high air burst, tower, etc.), the form in which fission
products are likely to be found, fractionation, and other such problems.
For a more careful study, thermodynamic data of the oxides will be necessary
as well as time, temperature, and volume data on fireballs.
REFERENCES

APPENDIX Hil

SETTLING OF PARTICLES IN A STANDARD ATMOSPHERE”

1. A convenient review of the subject of nucleation, both experimental and theoretical, is
presented in V. K. LaMer, “Nucleation in Phase Transitions,” Ind. Eng. Chem., Vol.

44, 1952, pp. 1270-1339. Earlier work of interest may be found in: Becker and
Doring, Ann. Physik, Vol. 24, 1935, p. 719; J. Frenkel, “Statistical Theory of Condensation Phenomena,” J. Chem Phys., Vol. 7, 1939, p. 200; J. Frenkel, “A General
Theory of Heterophdse Fluctuations and Pretransition Phenomena,” ]. Chem. Phys.,
Vol. 7, 1939, p. 538; and J. Frenkel, Kinetic Theory of Liquids, Chap. 8, Oxford
University Press, 1946.

2. Retss, H., “Theory of the Liquid Drop Metal,” Ind. Eng. Chem., Vol. 44, 1952, p. 1284.

In this appendix known formulas for viscous drag are applied to the problem
of the settling of particles in the standard atmosphere. The atmosphere wil! be

taken as stationary, and so convection effects are not considered.

The results of fluid mechanics can be applied without modification ta the motion
of a solid particle through the air provided the particle dimensions are muchgreater
than the mean free path of the air molecules. In this case, the type of flow is

determined by the Reynolds number, R, which is defin:d tobe

*

R= upd
Gg

(1)

where x is the velocity of the particle, d is a characteristic dimension of the particle,
and p and are the air density and viscosity, respectively. For a spherical particle
of diameter d, we have Stokes’ flow with a drag force given by
Fy, = 3roud,

(2)

provided the Reynolds number does not exceed approximately 0.5. For larger
Reynolds numbers, Eq. (2) underestimates the drag force, but the error is less

than 20 per cent at R = 1; Stokes’ law will be used in the present calculations
up to R = 1.

The terminal velocity of fall, «, of a spherical particle of density p’ is obtained
by equating its weight to the drag force of Eq. (2); the result is
_ g(r’ — p)d?

OB.
~ see

4 180”

(3)

where g is the acceleration of gravity, and the approximation follows from the fact

techno

Observations have been made on the Stokes’ fall of particles with nonspherical
shape.) An ellipsoidal shape gives a reasonable approximation for the drag force
*Written by F. R. Gilmore and M.S. Plesset, California Institute of Technology.

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