THE SEQUENCE OF EVENTS 7 



(iii) . The profile of the wave broadens gradually as the wave spreads 

 out. This spreading effect is most marked in the region of high pres- 

 sures near the charge. 



These properties of the shock wave are illustrated in Fig. l.l(b, c), 

 drawn for two later stages in the explosion of a 300 pound charge. For 

 comparison, the pressure waves which would exist if the earlier state 

 shown in Fig. 1.1(a) were propagated as an acoustic wave are indicated 

 by the dashed curve. These sketches of course represent the conditions 

 at three instants of time. The pressure-time curve at a given distance 

 from the explosion will have the same general form, and the pressures 

 observed at distances of 50 and 500 feet are sketched in Fig. 1.2 (a, b). 



The illustrations given refer to a particular size of charge, and it is 

 natural to ask what conclusion can be drawn about another size of 

 charge. In other words, what scaling laws may be applied? The an- 

 swer for the shock wave is very simple and is provided by the "prin- 

 ciple of similarity," which states that if the linear size of the charge be 

 changed by a factor k, the pressure conditions will be unchanged if new 

 distance and time scales k times as large as the original ones are used. 

 As an example, the pressures for the 300 pound charge of Figs. 1.1 and 

 1.2 will be obtained also for a charge of half the linear dimensions (one- 

 eighth the weight), provided that we make the observations at dis- 

 tances from the smaller charge one-half as great and divide the time 

 scale by a factor of two. 



The theoretical justification of the principle, given in Chapter 4, is 

 not difficult, and it has been amply verified by experimental observation. 

 The validity of the principle depends, among other things, on the as- 

 sumption that no external forces act upon the system. Gravity is such 

 an external force, and of course it is always present. It is unimportant 

 compared with the internal forces involved in generation and propaga- 

 tion of the shock wave, but its effect cannot be neglected in the later 

 behavior of the gaseous explosion products. The principle of similarity 

 as stated above, therefore, does not apply to the phenomena following 

 the shock wave. 



1.4. Motion of the Gas Sphere 



The initial high pressure in the gas sphere is considerably decreased 

 after the principal part of the shock wave has been emitted, but it is 

 still much higher than the equilibrium hydrostatic pressure. The water 

 in the immediate region of the sphere or "bubble," as it is usually called, 

 has a large outward velocity and the diameter of the bubble increases 

 rapidly. This outward velocity is in excess of that to be expected from 

 the magnitude of the pressure existing at the time, owing to the after- 

 flow characteristics of spherical waves mentioned in section 1.2, an 

 effect which has also to be considered in careful analysis of the shock 



