m(x) = — .;. h 



'l — X nVl — X 



dyf, VI- 1 

 dt (x-t)V-t 



[13a] 



The cavity shape may now easily be found, since 



f' dv 1 r^ 



ycix) = 2/0(0) + J^ dx '^^ ^ ^"^^^^ 2ZrJo ™(^^'^^ 



f4 r Vx 



2/c(^) -2/0(0) = -2ff Jo n-x 



dX- 



irdy^ 



TT J-c dt 



/F^ 



dt 



Vx dx 



T^iX-t) 



2/c(^) -2/o(0) = - f^ [^ tan-^ |/g - V^ ]/i^] 



[141 



^2p<i^vr-, ___ 



77 J-^ rfi V=l 



where Equation [30] of Appendix 1, Part A, has been used. 

 In order that the cavity be closed, Equation [10]: 



,„ „ aU^ In , r° dvo VFl ,, 



But 



2Uc 2 



dt y-t 



[15] 



f/=c 



= 1+-^ 



So that (for a given body) the unique relationship between the cavitation number and 

 cavity length is finally obtained: 



1 + ^ ^U. 



4 r" c?2/o v^T^ 



d« v^^^ 



rf< 



[16] 



Equation [16] may be used to simplify Equation [14] 



y,ix) = — ^ [ ' sin' ' l/f + V^fl^ 

 1+ 2 L 



'a; 2 J 7rJ_^ dt ' x{t-l) 



[14a] 



