18 





relation between cavitation number and cavity length (any profile), 



dt V^ 



2 ^ 



the origin of coordinates being chosen at the trailing edge (base) of the profile: Here, o is 

 the cavitation number, I is the cavity length, c is the body length, and y^ is the body ordinate. 

 His result for the drag coefficient as a function of wedge half-angle y is 



8y 

 ^^~ n 



General results for cavity shape and drag are given in Reference 34. Figure 5 shows the 

 comparison between the drag coefficients from Tulin's theory and the exact theory for various 

 wedge angles at zero cavitation number. Figure 6 shows the comparison of cavity lengths 

 from Tulin's theory and the exact Riabouchinsky model for various cavitation numbers for a 

 30-degree wedge. The success of this theory promises to be of much importance in engineer- 

 ing applications since Tulin has been able to extend the method to the computation of cavi- 

 tating flows about lifting surfaces in both the steady and unsteady cases. The computations 

 for the latter problems are now being carried out. He has also developed a linearized theory 

 for axisymmetric, three-dimensional flows, but the results are not yet in a form suitable for 

 numerical computation. 



Other results of immediate interest in technical application include work on wall ef- 

 fects in steady cavitational flows. In Reference 35, the authors consider the two-dimensional 

 cavity flow about tandem laminae situated normal to the flow direction in a straight-sided chan- 

 mel of finite width and in a free jet of finite width. Results are given for finite as well as 

 zero cavitation numbers. These results are of much interest in the design of water tunnels 

 for studies of finite cavities of very small cavitation number, it being shown that the "wall" 

 effects are much less severe with free jets than with rigid boundaries. Moreover, for a given 

 cavitation number, there is a limiting value of the ratio of lamina width to channel width for 

 rigid channels which cannot be exceeded (a "choking" phenomenon). 



Another problem which arises in flows with circulation is that of the stability of a 

 cavitating vortex. This question is of some interest in connection with the effects of cavi- 

 tation in the tip vortices of hydrofoils and propellers. Although no changes in the flow con- 

 ditions at the hydrofoil or propeller blade will occur as long as the cavitated region remains 

 detached, the behavior of such cavitating vortices will be of interest in gaining an under- 

 standing of the changes and effects that result when the cavitated region becomes attached 

 to the blade edge. An analysis of standing waves of infinitesimal amplitude on a vortex core 

 has been carried out by Ackeret^^ and his results verified, at least qualitatively, in experi- 

 ments by Lerbs.^^ More recently, Binnie^^ has considered the problem in a more general way 

 and has derived the properties of traveling waves, as well, giving numerical results for sever- 

 al cases. It will be recalled, as Binnie points out, that this is a classical problem of 



