Sec. 42.2 



POTENTIAL-FLOW PATTERNS 



TABLE 42.a— (Continued) 



33 



Other Shapes; Published Streamline Diagrams. 



The standard works of reference and the technical 

 literature on hydrodynamics are replete with 

 diagrams of flow nets, flow patterns, streamlines 

 and equipotential lines, photographs, and other 

 graphic representation of liquid flow around a 

 varied assortment of body shapes and through 

 ducts and passages of various kinds. Unfor- 

 tunately, the diagrams are widely scattered. A 

 large collection of these and other data has been 

 assembled by Dr. E. H. Kennard of the David 

 Taylor Model Basin staff, but efforts to have the 

 data published have so far been unsuccessful. 



Space is not available here to reproduce either 

 the photographs or the line drawings that the 

 marine architect might find useful for reference 

 purposes. However, brief descriptions and source 

 information for many of the existing illustrations 

 are assembled in categories and listed in Tables 

 42.a and 42.b. Table 42. c in Sec. 42.3 hsts similar 

 data for ducts and channels, where the water is 

 confined by solid boundaries or air-water inter- 



Corresponding data on potential-flow patterns 

 around yawed bodies, without circulation, are 

 listed in Table 42.d in Sec. 42.5. For hydrofoils 

 and bodies acting to produce lift, with circulation, 

 lists of references are given in Tables 44. b and 44.c. 



The flow directions, magnitudes, and patterns 

 around ships and their models, in a real Uquid like 

 water, are depicted and discussed in Chap. 52. 



Among the earliest of the flow diagrams 



published for the benefit of the marine architect, 

 accompanied by descriptions and discussions of 

 flow around floating bodies, are those of David 

 Steel ["The Elements and Practice of Naval 

 Architecture: or, A Treatise on Ship Building," 

 written about 1805 but published in London, 

 1822, pp. 110-115]. 



From this early beginning, which appeared to 

 be partly a matter of reasoning and partly of 

 observation, knowledge as to flow patterns 

 expanded along two characteristic lines: 



I. The experimental approach, in which various 

 clever methods were employed to generate in the 

 liquid visible streamlines that could be recorded 

 photographically. This was later expanded to the 

 experimental delineation of flow lines by doubly 

 refracting solutions and by electric analogy, 

 described in Sees. 42.12 and 42.13, respectively. 



II. The analytic approach, exemplified by the 

 source-sink diagram and the flow net, in which the 

 streamline positions were calculated and drawn, 

 or in which the graphic construction methods 

 were based upon the laws of hydrodynamics. In 

 general, the analytic approach is workable only 

 in liquids without viscosity. 



The earliest experiments with liquid streamlines 

 to produce good photographic records appear to 

 have been those of H. S. Hele-Shaw in Great 

 Britain ["Experiments on the Nature of the 

 Surface Resistance in Pipes and on Ships," 

 INA, 1897, Vol. 39, pp. 145-156, also Plates XX 



