37 



noted that a given distance between plates corresponds to one, and only one, 

 cavitation number, and vice versa. The second model, attributed to Prandtl 

 and Wagner, utilizes the single plate perpendicular to the flow but is char- 

 acterized by the reversal of the free streamlines at the end of the cavity 

 with the resultant reentrant jet, Figure 26, The essential features of the 



Figure 25 - The Two -Dimensional 

 Riabouchinsky Cavitation Model 



Figure 26 - The Reentrant Jet 

 Cavitation Model 



latter model were given in 19^5 by Kreisel, 14 and in 1 9 1 +6 by Efros. 64 The 

 Riabouchinsky model was also studied by Weinig 65 and Zoller. 66 The results of 

 the two theories have been examined by Gilbarg and Rock 67 and Gurevich. 68 A 

 comparison of various approximations of the drag and cavity shapes derived 

 from these theories has been made by Wehausen in an addendum to his transla- 

 tion of Gurevich's paper. An analysis of the two-dimensional finite cavity 

 has been carried out by Shiffman 69 from a somewhat different point of view 

 from that of the above writers. 



To avoid the zero drag (d 'Alembert 's paradox) which would result if 

 the pressures were integrated over both plates in the Riabouchinsky model, 

 only the drag of the forward plate is computed. To avoid this difficulty in 

 the Prandtl -Wagner model, the reentrant jet is assumed to go to infinity on 

 the second sheet of a Riemann surface, and the pressure over the downstream 

 face is taken to be the cavity pressure. Although this is a reasonable method 

 of computing the drag for this model on the assumption that in a real fluid 

 the jet is dissipated by the turbulent mixing and oscillations at the end of 

 the cavity, the jet has been observed to reach and penetrate the forward sur- 

 face of the cavity, as in Figure l8, and in the closure of the attached cavity 

 the jet has been observed to deflect the missile from its course. 56 Although 

 the origin of the jet in a real liquid is evidently in the transverse momentum, 

 the jet behaves as the theoretical one which originates through the require- 

 ment of constant pressure. 



For both models, i't turns out that the drag coefficient obtained by 

 integrating the pressures in the manner described above may be approximated 

 by the relation 



C D (a) = C D (0)(1 + a) 



