11 



\[m f u^^^imt = aU^U^y^iO) - .t/.^.£f ^ dt 



[18] 



2Uc f" dvo .,rdy, t(r-l) dr 

 dt J^cdrV r(t-l) (t-r) 



So, finally, using the result of Appendix 1, Part B: . 



LpU J-cdr yt-l ^' li-cdt Vt(t-l) 



2 



For small a, it may be shown, using Equation [23b], <that 



D a= 



[19] 



1 rr2 1 j'. 



(l + o) [19a] 



This result is in close agreement with exact calculations for two-dimensional flows 

 based on the re-entrant jet (Wagner) model, ■^•'^ and, incidentally, with body of revolution drag 

 measurement*.^'^ 



THE INFINITE CAVITY CASE (a= 0) 



The case when the cavity is infinite and the cavitation number zero (necessarily) is 

 of particular interest since it has been the subject of many theoretical investigations. It is of 

 interest to see whether certain results of exact theory are also obtained in the present investi- 

 gation. 



The source distribution for the infinite cavity is given by: 



dyf) 



TT J-c y-t (X — t) 



This result was obtained by a solution of the appropriate boundary value problem for tr = 

 and is identical with the result obtained by taking the limit as cr -» in Equation [13a]. 



The shape of the infinite cavity is easily found from the source distribution. Equation 

 [20], in the same way as the finite cavity shape was found from Equation [13a]: 



/^ /n^ 2]x r" dy. dt 2 f° dyo , -lif^,, rom 



