20 



Cavity Drag Coefficients for Various Bodies 



Model 



Co(0) 



a 



Reynolds Number 



Disc 



0.805 



1.0 



_. 



Hemisphere 



0.241 



2.024 



... 



2:1 Semiellipsoid I 

 and 2 Caliber Ogive J 



0.114 



3.65 



... 



1 





0.81 



2.72 X 10^ 



Circular Cylinder > 



X 0.55 



0.68 



1.75 X 10^ 



J 





0.73 



2 to 6 X 105 



The accompanying table summarizes the results examined by the writer. The value 

 of Cr,(0) for the disc is the result obtained by Plesset and Shaffer'*^ by assuming that the 

 pressure distribution in the meridian plane is the same as that of the two-dimensional compu- 

 tation. The values of Cr,(0) for the hemisphere, ellipsoid, and ogive are extrapolated from the 

 experimental data of Reference 28, from which the results for a for these bodies and the disc 

 were also obtained. The value of Crj(O) for the circular cylinder is from the computation of 

 Brodetsky.^^ The value a = 0.73 for the circular cylinder is given by Birkhoff-^^ based on 

 the experiments of Martyrer. The other values of a for the circular cylinder are based on 

 Konstantinov's experiments,'*^ which show differences depending on Reynolds number (based 

 on cylinder diameter). For comparison, the range of Reynolds numbers in Martyrer's tests is 

 also shown. It should be noted that Konstantinov's results are for constant Reynolds number, 

 whereas in Martyrer's tests the Reynolds number varied as the cavitation number was varied. 

 There may be some question, however, as to the accuracy of Konstantinov's results since 

 the forces were found by integrating pressure distributions rather than by direct measurement. 



SOME RECENT WORK ON NONSTATIONARY CAVITIES 



In addition to the steady-state theory for lifting surfaces, it will eventually be of con- 

 siderable interest to have results for nonstationary cavities for such cases (the interest for 

 nonlifting bodies is already well established). For example, the cavity on a blade of a sur- 

 face ship propeller of large diameter will grow and contract depending on the position of the 

 blade during rotation. Results for two-dimensional unsteady motions without circulation have 

 been obtained by Gilbarg'*'^ for polygonal obstacles. This problem differs from the steady- 

 state case in that the free boundary is a material line and not, in general, a streamline. Gil- 

 barg replaced the latter requirement by the approximating condition that the free boundary is 

 a streamline, and then used standard conformal mapping techniques to obtain solutions for 

 cavities behind a flat plate normal to the flow direction (symmetric cavities). He showed 

 that these solutions are exact for unsteady flows whose free boundaries are of constant shape. 

 In particular, two classes were distinguished: one in which the cavities have a cusped end 



