Sec. 42.8 



POTENTIAL-FLOW PATTERNS 



TABLE 42.6— (Continued) 



45 



the region of sharper transverse curvature than 

 alongside the region of lesser transverse curvature. 

 As the transverse distance from the body increases, 

 the isotachyls assume a shape that is more and 

 more nearly circular, exhibiting less and less effect 

 of the transverse body asymmetry. Thus the 

 velocity field at a reasonable distance resembles 

 that of a body of revolution of approximately the 

 same total volume. These features are the same 

 as for the flow around the 3-diml bodies of rec- 

 tangular and square section, described in Sec. 

 4.10 of Volume I and illustrated in Figs. 4.M and 

 4.N. 



H. Chu, P. C. Chu, and V. L. Streeter at the 

 Illinois Institute of Technology also investigated 

 the surface flow over an asymmetric body of 

 somewhat irregular transverse section and definite 

 fore-and-aft asymmetry [Illinois Inst. Tech., 



Uniform Stream Velocity. I Midsection of Elliptic Ellipsoid 



Normal to the Page, is Uoq! Heii^ht is Twice the Breadth; 



Isotoch\jls for Velocities 

 OS Indicoted 



Lenqth. Nortnol to the 

 Page, is Six Times 

 the Breodth 



Ton(^erttial Velocity at Body Surfoce is 1.073 \i^ 



Fig. 42. E Isotachyls in the Transverse Mid- 

 section Plane of an Elliptic Ellipsoid Having 

 Axes in the Ratio of 6: 2: 1 



Report on Project 4955, sponsored by ONR Con- 

 tract N7onr-32905, dated 15 Jun 1950]. This body 

 was formed by placing a combination of three 

 sources and one sink in a uniform stream, with 

 the sources and the sink symmetrically disposed 

 about a longitudinal body axis parallel to the 

 uniform-stream direction. Fig. 42. F is a fish-eye 

 view of the source-sink arrangement, with 

 enough transverse sections to afford an idea of 

 its shape. Fore-and-aft lines are drawn for the 

 maximum-beam positions along the length, and 

 for the keel line. Since the body is symmetrical 

 about its vertical centerline plane, and about a 

 plane through its midheight, the maximum-beam 

 line and the keel line are also streamlines. Two 

 other streamlines, marked "upper bilge" and 

 "lower bilge," respectively, were drawn as a 

 part of the project. The three component veloc- 

 ities in space, together with their resultants, were 

 calculated for the intersections of the four 

 streamlines with nine of the transverse sections. 

 The table on the figure gives the resultant 

 velocities in terms of the uniform-stream velocity 

 — C/eo , for the thirty-six intersections. A few of 

 these ratios are indicated on the diagram proper. 



It is rather remarkable that, considering the 

 flow along the maximum-beam streamline, the 

 slight hollowness between Stations —4 and 

 causes a slowing down of the flow to a value at 

 Sta. —1 that is only 0.73 of the uniform-stream 

 velocity. Further that the bulge at Sta. 1 causes 

 a speeding up of the flow to a value of more than 

 1.25C/„ . Considering the girth wise variations 

 around the several sections, the local velocity is 

 greatest at the midheight, where the section lines 

 have the sharpest curvature. It is smallest in way 

 of the bilges, where the section lines have the 

 least curvature. 



Unfortunately, the 3-diml stream function of 

 classic hydrodynamics loses its significance in 



