SECONDARY PRESSURE WAVES 371 



most conditions if the values k* = 0.2, 7 = 5/4 used for TNT are in- 

 serted. With these substitutions, we obtain / = 0.73PoL*C*/r, and 

 substituting values of L* and C* (from section 8.9) gives 



P W2/3 



(9.24) 7 = 0.47(rQ)^-/3-^-^^ 



where the energy rQ is in cal./gm., W is charge weight in pounds, and 

 r and Zo are in feet. The impulse is then expressed in the same units as 

 Po times seconds. If Po is chosen to be in Ib./in.^, Po = 0.446 Zo for Zo 

 in feet and the impulse in lb. sec. /in. ^ is 



W2/3 



(9.25) I = 0.21(rQ)2%,-i/6.lL— 



r 



STATIONARY 



TIME 



Fig. 9.3 Effect of bubble motion on form of the bubble pulse. 



This equation shows that the impulse varies with charge weight and 

 distance in the manner predicted for acoustic waves, as is to be expected, 

 and also decreases slowly for increasing depth from the factor Zo~^'^. As 

 already noted, the total positive impulse obtained here depends only 

 very sHghtly on migration, because the radius for which the pressure is 

 hydrostatic is large and but Uttle affected by migration. This fact, 

 plus the fact that the peak pressure decreases considerably if the bubble 

 has appreciable vertical velocity in its minimum, shows that the shape 

 of the pressure-time curve in the region of the maximum must also de- 

 pend considerably on the vertical velocity, in such a way as to keep 

 constant the total area between the curve and the hydrostatic pressure 

 Po. Thus, if the bubble acquires appreciable vertical momentum the 

 curve must be broader and lower near the maximum than if the bubble 

 remains stationary, as sketched in Fig. 9.3. 



A simple method has been used in a Road Research I.aboratory 



