Johns son and Srfntvedt 



p(r F ) 2 



P C = P o " - 2,h.2 {3) 



p = pressure at the radial section close to the boundary of the 



vortex 



d'F'g 



r = — r — K . dr free vortex strength 



J; or 



T R = bound circulation 



Two cases A and B must be considered : 



A. P < P 



— o - cav 



The maximum cavitation thickness will be equal to the tip 

 vortex diameter. The radial thickness distribution is found from ob- 

 served shapes of thickness along the radius terminating at the radial 

 inception point (calculated or observed). 



B. P > P > P 



— o r cav c 



The diameter of the cavitating tip vortex is found from the 

 pressure distribution across the tip vortex radius assuming symmetri ■ 

 cal hysteresis as outlined in point 1 above. 



APPENDIX C 



PRESSURE FLUCTUATIONS ON THE HULL, METHOD OF CALCULA- 

 TION 



The velocity potential caused by a pulsating cavity may be 

 found by solution of the Volterra equation if the cavity formation be ac- 

 curately represented at any time during growth and collapse. The 

 vapour/liquid mixture representing a pulsating volume cannot be said 

 to constitute a surface of known shape. Consequently, an ideal mathe- 

 matical model of moderate complexity should be employed together 

 with empirical functions found by experiments. 



The net velocity potential ^ at any field point (x , y f , z ) 

 caused by the small volume source At Ax Ar : 



614 



