(B) 



Figure 7. 



effective in axially symmetric and compressible flow problems. Basic to the approach 

 are certain comparison theorems, of which the following is an important example. 



Let D and D be flow regions of two (plane or axially symmetric) flows having 

 uniform velocities q , q at infinity, where q ^ q . Let D and D be bounded by the 

 streamlines y and y, extending to infinity in both directions. If D CD, and if y and 

 y have a point P in common (Fig. 6), then the respective flow speeds q and q satisfy 

 at P the inequality q(P) ^ q(P), and furthermore, when q(P) =^= the equality 

 holds if and only if D = D and the two flows are identical. 



As illustrative consequences that are useful in cavitation we mention the 

 following : 



1. In plane symmetric or axially symmetric infinite cavity flow, let T x and T, 

 be obstacles in the upper half plane having the same endpoint A, and suppose that T 1 

 lies above (or touches) T 2 ; then the relative positions of the corresponding free stream- 

 lines detaching from A are reversed. This implies that the shape factor C in (18) is 

 larger for T 2 than for T 1 and hence the cavity drag of T 2 exceeds that of 7\. Because 

 of the formula (16) we may infer a similar inequality for small positive a. The same 

 idea can be used to obtain simple bounds on the drag of an obstacle. Indeed, let the 

 latter be a curve denoted by C extending from (0, 0) to (a, b) . It is assumed that 

 the infinite cavity flow, which may detach from any point on C, is physically acceptable 

 in the sense of the previous discussion. Then the drag on C is bounded from below 

 by the drag on E lt and from above by that on E 2 , where E 1 and E 2 are the following 



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