372 SECONDARY PRESSURE WAVES 



report (93) for illustrating the change in the bubble pressure pulse shape. 

 This consists in computing a shape factor, defined as the ratio of the 

 positive impulse to the area under a triangle of height equal to the peak 

 pressure and base equal to the duration of positive pressure: 



Shape factor = 



{Pm - Po) -duration 0.22T(P^ - Po) 



where T is the period of pulsation. A number of calculated values of 

 these quantities for different weights and depths of TNT charges are 

 given in Table 9.1, some of these values being taken from the Road 

 Research Laboratory report already mentioned. These values have 

 been computed neglecting the effect of the free surface and assuming 

 infinite depth of water, in order to illustrate the effect of migration which 

 decreases with increasing depth approximately as Zo~^^^. They are not 

 therefore directly applicable to most situations actually encountered. 

 The increase in peak pressure and decrease in shape factor with greater 

 depth, corresponding to a sharper pulse, and the slowly changing im- 

 pulse are evident from the entries, which also show the orders of magni- 

 tude of these quantities for various conditions. 



It is of interest to compare the computed impulse from Eq. (9.25) 

 with values of impulse for shock waves. Assuming rQ = 440 cal./gm. 

 for TNT at a depth do of 40 feet gives 



W2/3 



/(lb. sec./in.2) = 6.0 -^^^— 

 r 



Shock wave similarity curves for TNT give for the impulse, integrated 

 to five times the time constant, 



wo. 63 



7(5^) (lb. sec/in.^) = 1.3-^ 



The total positive impulse from the secondary pulse at a depth of 40 

 feet is thus of the order of four times the value 1(56) for the shock wave. 

 This by no means implies that the secondary bubble pulse is four times 

 as effective as the shock wave, even if impulse is the proper criterion for 

 effectiveness in the circumstances of interest. In the first place, it is to 

 be remembered that the secondary impulse calculation includes all pres- ■ 

 sures greater than hydrostatic. Much of this impulse comes from long 

 intervals of low, slowly changing pressure, and hence ordinarily is both 

 unimportant and difficult to observe. 



On the other hand, the shock wave impulse quoted is an under- 

 estimate because the pressure-time curve is integrated to a relatively 



