Sec. 42.4 



POTENTIAL-FLOW PATTERNS 



39 



flow patterns around geometric and other simple 

 shapes 



Table 42. b Reference data for photographs of 

 flow patterns around geometric and other simple 



To save space in Tables 42. a and 42. b of this 

 section, in Table 42.c of Sec. 42.3, and in Table 

 42.d of Sec. 42.4, the authors' names in the refer- 

 ences are omitted. All photographs which have 

 been made with reflecting particles sprinkled on 

 the liquid surface or suspended within the Uquid 

 are marked "Al. Powder," regardless of whether 

 or not aluminum powder was used in every case. 

 "Normal" means that the long dimension of the 

 section or body was across the flow, normal to it. 

 "In line" means that the long dimension was 

 parallel to the flow. 



Of the streamline diagrams derived by analytic 

 methods, among the first to be published were 

 those of W. J. M. Rankine, appearing in the 

 literature of the Institution of Naval Architects 

 and of the Royal Society (of Great Britain), in 

 the period 1862-1872. Stemming from the work 

 of Rankine were the analytic streamlines about 

 ship-shaped and other bodies pubUshed by D. W. 

 Taylor in the references Usted in Sees. 3.8 and 

 43.6 of the present book, and in Volume II of 

 the 1910 edition of "The Speed and Power of 

 Ships." 



Many more streamline diagrams evolved from 

 source-sink combinations have been pubUshed 

 since then. Among the references, not well known 

 in America, may be hsted: 



(i) Legendre, R., "Hydrodynamique Graphique (Graphic 

 Hydrodynamics)," ATMA, 1933, Vol. 37, pp. 

 395-410. This paper contains a number of flow nets 

 and diagrams giving streamline and equipotential- 

 line patterns for a series of flow conditions. 



(ii) Brard, R., "Les M6thodes pour le Trace des Lignes de 

 Courant dans les Ecoulements Thfeoriques ou Reels. 

 Leur Role en Hydrodynamique (The Tracing of 

 Streamlines in Theory and Practice. Their Role in 

 Hydrodynamics)," ATMA, 1938, Vol. 42, pp. 

 65-83. So far as known this paper is not translated 

 into EngUsh. A full understanding of it involves a 

 working knowledge of complex variables and con- 

 formal transformation. 



In the early 1910's, representations of the wake 

 patterns and streamHnes alongside and abaft 

 surface-ship and airship models were pubUshed 

 in the technical Uterature. A brief Ust follows: 



a. Eden, C. G., "Apparatus for the Visual and Photo- 

 graphic Study of the Distribution of the Flow Round 



Plates and Models in a Current of Water," ARC, 

 R and M 31, Mar 1911, pp. 48-49 



b. Booth, H., and Eden, C. G., "The Wind Resistance of 



Some Aeroplane Struts and an Examination of Their 

 Relative Merits," ARC, R and M 49, 1912, pp. 95-96 



c. Bairstow, L., and Eden, C. G., "Experiments on 



Airship Models," ARC, R and M 55, 1912, pp. 48-51 



d. Eden, C. G., "Investigation by Visual and Photo- 



graphic Methods of the Flow Past Plates and 

 Models," ARC, R and M 58, Mar 1912, pp. 97-99 



e. Baker, G. S., "Methodical Experiments with Merchant 



Ship Forms," INA, 1913, Part I, pp. 162-180, esp. 

 pp. 167-168 and PI. XVIII. This plate shows four 

 photographs made at the stern of totally submerged 

 models, each composed of the underwater body of a 

 ship form with its mirror image superposed, in 

 inverted position. 



T. B. Abell published some unusual photo- 

 graphs of the wakes abaft simple ship-shaped 

 bodies, using filaments of colored Uquid and air 

 bubbles as indicators ["A Contribution to the 

 Photographic Study of the Mechanism of the 

 Wake," INA, 1933, pp. 145-152 and Pis. XVII, 

 XVIII]. 



N. W. Akimoff pubUshed the results of some 

 flow-pattern and wave studies about vertical 

 circular-section rods and elongated forms sus- 

 pended in a moving current of water ["tJber das 

 Wesen des Mitstroms (On 'the Behavior of the 

 Wake)," STG, 1934, pp. 149-163]. 



42.3 Flow Patterns In Ducts and Chaimels. 

 The naval architect and marine engineer are 

 interested in the details of liquid flow within 

 pipes, ducts, and channels, as well as of the flow 

 outside of bodies and objects of varied shape. 

 Flow-net diagrams for the motion of an ideal 

 Uquid within typical open and obstructed passages 

 are shown in Fig. 2.X of Sec. 2.20. 



Table 42. c Usts reference data for what might 

 be termed "inside" Uquid-flow patterns, subject 

 to the notes in Sec. 42.2 applying to Tables 42. a 

 and 42.b. 



A paper by H. S. Fowler and V. Walker, 

 entitled "Fluid Flow in Turbo-Machinery" 

 [lESS, 1953-1954, Vol. 97, pp. 113-152], contains 

 many informative diagrams of air flow through 

 ducts, bends, and axial-flow turbine and blower 

 blades. 



42.4 Flow Patterns for an Ideal Liquid Around 

 Simple Ship Forms. Available flow diagrams 

 around forms resembUng those of ships are rela- 

 tively scarce. Such as do exist are limited to the 

 more-or-less 2-diml flow about the designed water- 

 line, and that in an ideal Uquid only. 



Other than those embodied in Figs. 2.S and 4.A 



