202 



14 



is, for air, V/V^= (Po/p)'^^ = (Po/p)^'''*= 1/8.5. Hence, the work can be 

 calculated from the initial volume only and is nearly equal to 



where R^ is the initial radius. 



It may now be asserted that the radiated enexgy cannot exceed W, 

 It may well be almost equal to W, however. For the part of W' that is spent 

 in compressing the gas is approximately, or exactly if y = U/3, equal to 



4.P, ^- - 4.p„V = 4.p,i?/(|^ - l) = 4.p«/ [(A)^ - ^] 



by Equation [27a]. This is less than Wy5 if P Is greater than 20pj. Loss of 

 energy due to friction should also be small, unless departures from symmetry 

 cause appreciable turbulence. 



After the bubble has settled into its new position of equilibrium, 

 it may contract somewhat further as it loses heat of compression, and as the 

 gas dissolves in the water. If the pressure slowly decreases, the bubble 

 will re-expand without executing marked oscillations. 



Radius of Bubble 



IMPULSIVE PRESSURE 



At the opposite extreme from the case of steady pressiire stands the 

 impulsive case. Let the pressure be applied suddenly and let it disappear 

 again before the bubble has had time to change appreciably in size. Then the 



bubble will begin contracting at a 

 certain inward radial velocity Vj. 

 If compressibility of the water can 

 be neglected, the analysis gives 



where p is the density of water and 

 7 =jpdt, the applied Impulse; see 

 Equation [51]. If 7 is in pound- 

 seconds per square inch and Rq in 

 inches. 



20 



Figure 5 - Curve illustrating Behavior 

 of a Bubble under a Pressure Wave 

 of Very Short Duration 



= - 10,700 



Inches per second 



;20a] 



It is clear from this formula that enormous velocities are easily 

 produced, while the inertia effect on the bubble motion is relatively small. 

 From a Number 8 detonator at l8 inches, for example, the shock-wave impulse 



