Sec. 43.11 



DELINEATION OF SOURCE-SINK DIAGRAMS 



67 



flow patterns around source-and-sink combina- 

 tions in uniform flow is described here at some 

 length as an aid in the visuaUzation of this type 

 of flow and in understanding the nature and the 

 combination of stream functions. The more 

 famihar this action becomes to the marine archi- 

 tect, the more frequently is it recognized around 

 a ship form and the more interesting and useful 

 is this knowledge likely to become in practice. 



43.9 Variety of Stream Forms Produced by 

 Sources and Sinks. Thanks to Taylor's line 

 sources and sinks, and to mathematical methods 

 which have been developed in the three-quarters 

 of a century since Rankine's time, it is now possible 

 to produce stream functions and velocity poten- 

 tials for source-sink forms and combinations 

 hitherto undreamed of. This applies not only to 

 the 2-diml source-sink combinations of Sees. 43.2 

 to 43.7 but to the 3-diml source-sink combinations 

 of Sec. 43.8. Examples of these apphcations are: 



(i) Line sources and sinks along a longitudinal 

 axis parallel to the direction of uniform flow, to 

 form a large number of bodies of revolution, 

 having a great variety of shapes and proportions 

 [AVA, Gottingen, Rep. UM 3206, dated 30 Dec 

 1944; available in English as TMB Transl. 220, 

 Apr 1947] 



(ii) Sources and sinks offset from the longitudinal 

 axis to produce a rather blunt stern on a de- 

 stroyer form, pictured in Fig. 3.Q on page 69 of 

 Volume I [Lunde, J. K., INA, 1949, Figs. 1 and 2, 

 pp. 186-187] 



(iii) Assembhes of doublets introduced in a 

 uniform stream to produce special forms, as has 

 been done by Sir Thomas Havelock 

 (iv) Ring sources in a plane normal to a uniform 

 stream of relatively high velocity, to form duct 

 or pipe entrances with streamlined outer and 

 inner walls. Longitudinal traces through some of 

 the 3-diml bodies worked out in this fashion by 

 the Ilhnois Institute of Technology on Project 

 4955, ONR Contract N7onr-32905, under V. L. 

 Streeter, are illustrated in the First Phase Report 

 of this project, dated 1 February 1949, entitled 

 "Axially Symmetric Flow Through Annular 

 Bodies." 



(v) Infinitesimal dA sources spread over the after 

 area of a propeller disc and dA sinks spread over 

 the forward area to reproduce the velocity and 

 pressure effects of a screw propeller, following 

 H. Dickmann. A group of five pairs arranged in 

 this fashion is shown in Fig. I5.F. 



The number of forms which can be developed 

 by source-sink combinations is in fact limited only 

 by the ingenuity, imagination, and talent put to 

 work on them. The reward offered by this work 

 is the ability to calculate the characteristics of the 

 flow around these forms, under a great variety of 

 initial conditions. The useful and practical results 

 of these enterprising endeavors are described in 

 somewhat greater detail in Chap. 50, in a dis- 

 cussion of calculated ship resistance. 



43.10 Source-Sink Flow Patterns by Colored 

 Liquid and Electric Analogy. In Sec. 2.13, on 

 pages 34 and 35 of Volume I, there are explained, 

 in somewhat general terms, the means by which 

 radial-flow patterns around sources and sinks, 

 singly or in combination, are determined by 

 plotting traces of equal electric potential in a 

 weak electrolyte. 



The use of colored hquids, emanating from and 

 flowing into actual holes representing sources 

 and sinks, is mentioned in Sec. 3.8. Excellent 

 source-sink flow patterns for practical use, capable 

 of manual diagramming or photographing, are 

 delineated by this relatively simple, expeditious, 

 and economical technique [Moore, A. D., "Fields 

 from Fluid Flow Mappers," Jour. Appl. Phys., 

 Aug 1949, Vol. 20, pp. 790-804]. Colored hquid 

 moves from the source orifice(s) to the sink 

 orifice (s) through a thin horizontal space between 

 a light-colored slab containing the orifice (s) and 

 a sheet of plate glass just above it. Streamlines of 

 sorts are indicated by colored streaks left on the 

 slab. Motion pictures may be made of the colored 

 liquid while it is flowing. 



This method lends itself to the quick solution, 

 not only of 2-diml flow problems but to the deline- 

 ation of axisymmetric flow in three dimensions. 

 Further, fine sources and sinks may be represented, 

 using slots instead of holes. The slot width is 

 varied to correspond to the strength distribution 

 along that axis. Flow from or into relatively large- 

 area sources and sinks is represented by running 

 the colored Hquid through small sand beds 

 within the boundaries of the sources and sinks. 



Similar representations, employing a liquid flow 

 of constant depth over a broad-crested weir, were 

 utiUzed by J. F. Harvey to approximate heat-flow 

 patterns in boilers [SNAME, 1950, Vol. 58, 

 pp. 252-257]. 



43. 11 Formulas for the Calculation of Stream- 

 Form Shapes and the Flow Patterns Around 

 Them. The shapes of all the stream forms con- 

 structed graphically in the preceding sections^of 



