NSWC/WOL TR 76-155 



And, combining (A15) , (A27) and (A30) , we write the time scale 

 factor as 



1/2 

 Ci = (9^±JL ^ j (1 + Xi) A _ (A31) 



where p is the water density. 



15. For our purposes the dimensionless period T 1 , is 

 conveniently approximated by the linear function 



T ' - 1.476 + 0.4 k ( A32 > 



Values of T ' calculated by Equation A32 are listed in Table 1 

 alongside the tabulated function. The approximation, Equation A3 2, 

 is good to better than 0.5% for values of k } 0.1. 



16. Finally, combining (A26), (A27) , (A29), (A31) and (A32) 

 we write for the period of oscillation 



* " (t *) 



1/2 , /. 



(1 + X]_) ' (1.476 + 0.4k T ) A i (A33) 



The physical quantities in Equation A33 may be expressed in any 

 consistent set of units. For English Engineering Units we have 



T, = Bubble Period (SECONDS) 



3 

 p = Density of the Water (SLUGS/FT ) 



2 

 Initial Value of Ambient Water Pressure (LBS/FT ) 



^i ' [pressure in LBS/FT 2 = (pressure in PSI) x 144] 



A. = Initial Radius of Bubble (FT) 



l 



A-10 



