Sec. 43.7 



DELINEATION OF SOURCE-SINK DIAGRAMS 



61 



and 0, and all the dx-sinks between and X, , 

 the curves KHO and OJR are produced. Sub- 

 tracting the area under the first from the area 

 above the second, both measured to the XOXj 

 axis, gives the net value of the combined source- 

 sink stream function at the point G. It is repre- 

 sented by the hatched area in diagram 2 of the 

 figure. 



Repeating this procedure for all points in the 

 entire field other than G and carrying through 

 the remainder of the operation is a tedious and 

 laborious task, despite the systematic method of 

 calculation outUned and described by D. W. 

 Taylor in the references cited. Nevertheless, it 

 can be and has been done, as witness the works 

 of the AVA, Gottingen, on 3-diml line sources 

 and sinks in their report UM 3206, mentioned in 

 Sec. 42.6. The general problem is simplified 

 immensely by: 



(a) Making the source-and-sink lines XO and 

 OX, of equal length and the source-and-sink 

 distribution symmetrical about 0, as was done 

 by Taylor. The method is explained and used in 

 a practical example by him on pages 392-396 and 

 Plates LXX-LXXIII of his 1894 INA paper. 



(b) Shortening the lines of sources and sinks to 

 cover only hmited intervals or portions of the 

 length near the bow and stern 



(c) Replacing the general source-and-sink strength 

 curves by straight fines; in other words, making 

 the strengths constant along the source-and-sink 

 lines or uniformly varying in those regions. The 

 latter two steps were adopted by H. Fottinger 

 and F. Horn in producing the simple 2-diml ship 

 forms described in Sees. 2.17 and 4.3 and illus- 

 trated in Figs. 2.S and 4.C of Volume I. They 

 were also used by Brand and others in producing 



3-diml bodies of revolution, one of which is 

 illustrated in Fig. 42.C. 



(d) Using a calculating machine developed by 

 H. Fottinger [STG, 1924, pp. 295-344; TMB 

 Transl. 48, May 1952, pp. 14-15]. 



43.7 Flow Pattern for the Two-Dimensional 

 Doublet and the Circular Stream Form. A source 

 and sink, both 2-diml, when placed infinitely 

 close to each other along a given axis, form a 

 doublet, described in Sec. 3.10 and illustrated in 

 Fig. 3.M of Volume I and in Fig. 43.J of Volume 

 II. The source-sink streamlines retain their 

 circular shape, as in Fig. 43. C. However, the 

 inner streamline circles between the source and 

 the sink diminish in size as the source-sink 

 distance 2s along the axis is decreased toward 

 zero. When this distance is reduced to an extremely 

 small value, the only circular streamhnes left in 

 sight are the outer ones, beyond both the source 

 and the sink. Furthermore, the visible streamlines 

 of the circular pattern now lie tangent to the 

 source-sink axis, regardless of their radius. This 

 is because the fine forming the locus of their 

 centers, normal to the axis, now crosses the axis 

 at the doublet position which is, in effect, a 

 common position for both. 



When the source and sink are brought together 

 to form a doublet their strengths m are increased 

 to hold the product m(2s) constant. The strength 

 of the doublet is then indicated by /i(mu), where 

 n = 2m(s). 



When the double-circular flow pattern around 

 a doublet is combined with a uniform flow in the 

 direction of the doublet axis the resulting 2-diml 

 stream form, depicted in half-section in Fig. 

 43. J, is circular. The derivation of this form is 

 set down in Sec. 41.8. It is convenient, for reasons 



Rodii of )^-5yslem Equol to ^.-^•^^■■-n 



Other Half Below Axis Identical Sink^ 



^ -6 V4 / 



where -;n la the Value of 'Ji^u at the Point M, 



n^b^ 



Fig. 43.J Construction Diagram for 2-Diml Doublet 



