486 



[Pam] 



^000 



3000 



2000 



1000 - 



0^ 



a 3 

 3 

 U 

 U 



d* bubble 



slow pressure increase 

 fast pressure increase 

 very fast pressure increase 



slow pressure increase 



fast pressure increase 



A very fast pressure increase 



O^ bubble 



bubbles 



0,0 



05 



1,0 Reduced freq 15 



FIGURE 27. Pressure p at collapse. Different 

 conditions. 



Reduced freq. 15 



:/ht 



5 10 15 fosclHz)20 



FIGURE 28. Pressure p at collapse. Different 

 conditions. 



3/2 



R / p cAP 

 max 



p = density of water 



c = velocity of sound 



Other symbols as above 



Here it is necessary to know a time At propor- 

 tional to the duration of the pressure pulse. 



With the use of At some information about the 

 real collapse dynamics is introduced and therefore 

 coefficient (3) may be somewhat more universal than 

 (2). Note, however, that for the original use of 

 (3) similarity in cavitation was assumed. 



Of interest for future work is to what extent 

 the final pressure behavior can be described by 

 measured cavity data. In this case it is more 

 natural to think of methods to estimate d^V/dt^ in 

 (1) . It is then necessary to know V(t) or to assume 

 a relation between d V/dt^ and measured parameters, 

 such as collapse time and cavity size. In this 

 paper only the cavity area A(t) is presented. As 

 a first approximation it will be assumed that V(t) 

 is proportional to h}/^ or X^max' From the measure- 

 ments of A(t) attempts were made to estimate d^V/dt^ 

 by difference ratios in the conventional manners. 

 This failed, due to uncertainty in A(t) during the 

 final collapse. Then as a very rough assumption 



p+r T^ /H^ p 

 c max p max 



(5) 



From the films it was observed that the cavity 

 thickness seemed proportional to the length rather 

 than to the square root of the cavity area and the 

 following coefficient was obtained in cases where 

 the area was measured. 



3,0 



2,0 



dfy _ 

 dt2 



const 



(4) 



/ 

 /^ 

 /« 



slow pressure increase 

 fast pressure increase 

 very fast pressure increase 



t 



bubbles 



was tested. 



This is true only at very special circumstances. 

 The assumption was, however, used and from (1) and 

 (4) the following dimensionless pressure coefficient 

 is obtained 



10 Reduced freq 15 



10 



15 f„„ (Hz) 20 



FIGURE 29. Pressure p at collapse. Different 

 conditions. 



