12 



The asymptotic cavity shape is given by 



lim yjx) 2 r° dvo dt 

 "^^"77" ^nL dt FT 



[22] 



It is to be noted that it has been shown (Reference 1, page 51) that the two-dimensional 

 cavity must have this asymptotic form, i.e., 



J. _^ ^ ^g 1^' = A constant which is a function of the body shape 



yx 



The cavitation drag may be found in the same way as it was found for the finite cavity 

 case. The result is identical with that obtained by taking the limit of Equation [19] as a-> 0. 



[) 



i.cj 



_ 2_ r p ^a i!_ 

 n lie dt y'-t 



[23] 



But, by using Equation [22], the drag may be written in terms of the asymptotic cavity 



shape 



|..' 



,'r«».wT 



Vx 



[23a] 



This is precisely the formula given by Levi-Civita (Reference 1, page 51) for the drag of a 

 symmetric body with infinite cavity. That this result has been obtained is an important justi- 

 fication for the linearized theory. 



THE SLENDER WEDGE. COMPARISON WITH EXACT THEORY 



In order to evaluate further the meaningness of the linearized theory for cavitating 

 flows it is of interest to use it to examine some characteristics of flow about a configuration 

 which has also been treated using more exact theory. Such a flow is that about the wedge 

 profile which has been discussed in detail for zero cavitation number, ^° and which, for nonzero 

 cavitation number, has been discussed through the use of the Riabouchinsky^^ and the 

 Wagner'^ models. 



Consider a wedge of chord length c, maximum thickness T, and a half angle y, as shown 

 in Figure 4. 



Figure 4 - Wedge Profile 



