t;u 



HVDROnVNAMICS IN SHIP DESIGN 



Sec. -13.6 



use uf n niultituile of nuinite sources and sinks, 

 not nt>ccs!«irily all of tlio siuno strength, willi 

 infinitciiimal spacing, crowilixl togetlier along a 

 line representing the longitudinal axis of a Innly 

 or ship. The sources are groupetl along the en- 

 trance; the sinks along the run. Despite the 

 minute strength of each source or sink, the 

 combineil strength of ench group of them along 

 the line is finite. 



[- — Line of Sinks-*-! 

 lOutline of 2-diml Streom 

 r^ Form-^^^sr 



-Line of Source9-»j 

 0^__l,-t-^T:urve of Strength Distribution ' 



Fio. 43.11 DEnsTTiON Sketch kor Li.ne Source 

 AND Line Sink 



Fig. 43.H depicts schematically such a line, 

 marked X,OX, with a row of sources from X to 

 O and a row of sinks from to X, . The strength 

 of each is represented by the height of a velocity 

 vector perpendicular to the source-sink line. 

 Source strengths are laid off above the line and 

 sink strengths below it. A line joining all the 

 ordinates is the source-sink, strength-distribution 

 curve. If each source or sink occupies a space of 

 dx along the line, then the total strength of all 

 the sources is the length OX times the average 

 strength or ordinate. Similady, the total strength 

 of all the .sinks is the length (JXi times the average 

 negative ordinate. 



The strength of any source or sink along the 

 line XOX, may be a.ssigncd at will, depending 

 upon the shape of the Ixxly or ship which it is 

 desired to form. The only limitation is that the 

 area below the curve of source ordinates, AXO 

 in V\g. 43.11, representing the total source output, 

 be ixaclbj (t/ual to the area above the curve; of 

 sink ordinates (JDX, , representing the total sink 

 input. Otherwi.s*' there will be some liiiuid lacking 

 or left over, and the resulting stream furni will 

 not \)C bounded by a closed curve. 



In practice, when working with line .sources 

 and sinks, it is convenient to plot a grajili of 

 ituurcc and sink strengths as in diagram 1 of 

 Fig. -13.1. The problem then is to find the stream 

 function of the combined llnw from the sources 



distributed along the XO-part of the line to the 

 sinks tlistributwl along the t)Xi-part, corre- 

 sponding to the "circular" stream flow for the 

 simple l2-diml sourcc>-«ink pair of Sec. 43.3 pre- 

 ceding. When the flow pattern of the resultant 

 source-sink stream function is found, it is com- 

 bined with the uniform-flow function ^t/ along 

 the reference a.\is to give the outline of the ship 

 form, defined by the streamline where ^.,- = 0. 

 Other values of the stream function ^., give the 

 2-diml flow pattern around the ship form, at a 

 distance from the boundary. 



At any selected point G in diagram 1 of Fig. 

 43.1 it is necessary to determine first, the flow 

 from all the dx sources; second, the flow into all 

 the dx sinks; and then to combine them. Taking 

 the line X,OX as the trace of the reference plane, 

 as before, the stream function at G due_to any 

 infinitesimal (/x-source, such as at E, is dx^BVljOg , 

 where 0^ is measured counter-clockwise from the 

 reference plane. The stream function at G due 

 to any rfx-sink, such as at F, is — rf.r(CF)fl;, . 

 Plotting these values as a separate graph, diagram 

 2 of Fig. 43.1, the source stream function is laid 

 off as the ordinate EH above E, and the sink 

 stream function as FJ below F. Proceeding in 

 similar fashion for all the rf.r-sources between X 



5ource-intensily curve 



Fio. 43.1 DEKiNrnoN Sketch nm the Stream 



Ki'NrrioN AT A Point in a Linb Souhck-Link 



Sink I''iei.1) 



