194 



or, for y = 4/3, 



"-".eiK^) 4]fe) -71-- i ->•'' + ''. i7'i 



'"ifhm-^l-^ 



where R^ = R^-^ , the minimum radius, v is the particle velocity at the point 

 in question, and v, is the velocity of the surface of the sphere, which is 

 also equal to dR/dt; see Equations [38] and [39a]. At considerable distances 

 the Bernouilli term 1/2 pv^ may be dropped. 



The maximum pressure at any point occurs at the instant at which 

 the radius of the sphere is a minimum, without any time delay, in the approx- 

 imation in which compression of the water is neglected. At this instant both 

 Vg and V vanish; hence, from Equations [6] and [7a], the maximum pressure is 



Pmax = -^ (P, - Po^ + Po 



P.., = Po^ [(£;;) ^-l]+P„ [8a] 



where R^^„ is the minimum radius of the bubble. For y = V3, 



p..=po^[(#-r-i]+Po [8b] 



These formulas should be applicable to the pressure in the water 

 that is associated with the oscillations of explosive gas globes. As an ex- 

 ample, if i?n,gx/i?o =2.6, which appears to represent fairly well the first 

 outswing for a Number 8 detonator when Pq = 15 pounds per square inch, and 

 when i?n,„ is about 5 inches, then R^.^/R^ = 0.l6, and at a distance r = l8 

 inches from the center of the explosion 



Pmax - Po = 15 -^[(y^) " ij " ^^^ pounds per square Inch 



However, the pressure varies extremely rapidly near its maximum 

 value when the amplitude of oscillation is large. Thus a concentrated pulse 

 of pressure is emitted during the phase of extreme contraction of the globe, 

 whereas during most of the time the Increment of pressure due to the motion 

 Is small. In Equations [U3] and [37] the following formulas are obtained 

 connecting the pressure p at a distance r from the center with the radius R 

 of the sphere of gas and the time t, in the neighborhood of the time (j at 

 which i? = 7?i = i?„j„ , when y = V3: 



P = (P™.,-Po)(fr-ip-^ + P„ [9] 



