13 



The application of Equations [21], [22], [23c] and [16], respectively, to the wedge 

 flow yields the following linearized theory results: 



a = 0: 



= + —^ ( X + c ) tan I/— + Vxc — 



2 77 L r X 2 



[24] 



(J = 



lim j^(^ _ 4y '^^ 



[25] 



a = 0: 



(7 > 0: 



1 + — 

 ^ 2 



C = - = — ^ 



« 1, , 2 T 71- 



= VM^f KT^->o,[^f.^^iTf]} 



[26] 



[27] 



The application of exact theory results ^° for a = yields: 



(7=0: < 



y^ (exact) = ij ^ ( linearized) + (y^) 



lim iy^(.r) lim y^(x) 

 .r^oo (exact) = .r ^ oo ( linearized) + (y) [28] 



Vx i/ir 



C ^ (exact) = C^ ( I inearized ) + ( y^ ) 



The exact result for the drag coefficient is plotted in Figure 5 together with the linearized 

 result, Equation [26]. The linearized theory result for the finite cavity length, Equation [27], 

 is shown in Figure 6 together with the result, as calculated by Plesset and Shaffer ^^ using the 

 Riabouchinsky model. The finite cavity's maximum diameter as approximated by Equation 

 [14:d] is plotted in Figure 7 together with the results of the Plesset and Shaffer calculations. 



SUMMARY AND CONCLUSIONS 



1. The linearized theory is a meaningful first order theory for calculating flow character- 

 istics about slender two-dimensional forms for positive cavitation numbers. The justification 

 of this conclusion lies in the following results: (a) In the case of wedges at zero cavitation 

 number the linearized result for cavity shape and drag actually is the first order term in an 

 expansion in powers of the wedge angle, (b) for arbitrary bodies at zero cavitation number the 

 same asymptotic cavity shape is obtained according to both the linearized and exact theories, 



