Figure 3 



dividing streamline meets the body at the vertex, and free streamlines detach from the 

 ends forming an infinite cavity; in this case the ratio of the two lengths cannot be 

 arbitrary and hence the flow is exceptional, ii. The free streamlines again detach from 

 the ends, but the dividing streamline meets the wedge at a point other than the vertex; 

 in which case the velocity is infinite at the corner and flow is physically unacceptable. 

 Hi. One of the free streamlines detaches from the vertex, determining a solution that 

 is simply the flow past an inclined flat plate; this flow is not always acceptable since 

 the free streamline may intersect the second side of the wedge. A way out of this 

 difficulty is to allow the free streamline detaching from the vertex to reverse direction, 

 forming a re-entrant jet (Fig. 4), while the portion of the flow not included in the 

 jet bounds an infinite cavity whose free streamlines separate from the ends. Except 

 for the feature of the two-sheeted flow plan, the latter model satisfies the physical 

 requirements and, furthermore, is observed experimentally [8]. Its basic idea can most 

 likely be extended to arbitrary curved obstacles to provide physically acceptable solu- 

 tions which are otherwise lacking without the jet. In these cases the flow would 

 contain multiple cavities. Such a theory is still unexplored. 



Calculations of axially symmetric flows 



Developments in the theory of axially symmetric cavitational flow reverse the 

 customary order of things in that the general theory is already well advanced and 

 boasts numerous qualitative results on existence, uniqueness, geometric behavior of the 

 free streamlines, extremal properties, etc., while, on the other hand, useful explicit 

 solutions are still unknown. (There do exist explicit solutions but without practical 



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