cuAPiER i:; 

 Delineation of Source-Sink Flow DiaoTams 



43 . 1 General 



43.2 Delineation of Two-Uimensional Stream- 



Form Contours and Streamlines Around 

 a Single Source in a Stream 



43.3 Graphic Construction of a Two-Diniensional 



Flow Pattern .\round a Source and a Sink 



43.4 Graphic Determination of Velocity .\round 



Two-Dimensional Stream Forms .... 



43.5 Laying Out the Two- Dimensional Flow 



Pattern .\round Two Pairs of Sources and 

 Sinks in a Uniform Stream 



43 . 6 The Const ruct ion of Two-Dimensional Stream 



Forms and Stream Patterns from Line 

 Sources and Sinks 



43.7 Flow Pattern for IheTwo-Dimensioniil Doub- 



let and the Circular Stream Form . . . 



52 43. S Graphic Construction of Three-Dimensional 



Stream Forms and Flow Patterns .... C2 



43.9 \'ariety of Stream Forms I'roduced by 



52 Sources and Sinks fi7 



43.10 Source-Sink Flow Patterns by Colored 



51 Liquid and Electric .\nalog_v G7 



43.11 Formulas for the Calculation of Stream-Form 



57 Shapes and the Flow Patterns .\round Them 67 



43. 12 The Forces E.xcrtcd by or on Bodies Around 



Sources and Sinks in a Stream; Lagally's 



58 Theorem 08 



43.13 Partial Bibliography on Sources and Sinks 



and Their .\pplication 70 



59 43.14 Selected References on Lagally's Theorem . 71 



01 



43.1 General. Sees. 3.8 through 3. L3 contain 

 a description and discussion of radial flow and 

 the source and sink, the radial stream function 

 and velocity potential, and other features of 

 source-sink flow. Figs. 3.M through 3.P illustrate 

 a variety of simple stream forms resulting from a 

 graphic combination of the stream functions of 

 uniform and of radial flow. The present chapter 

 contains instructions for drawing manj' kinds of 

 stream forms and for delineating graphically the 

 flow patterns around them. In Sees. 41.8 and 41.9 

 there are a few typical formulas for calculating 

 the coordinates of some simple stream forms 

 rather than plotting them graphically. Both sets 

 of sections tell how these constructions and 

 formulas lead to a determination of the velocities 

 and pressures around the forms. 



It has been true in the past, and perhaps may 

 be for some time to come, that the stream forms 

 and streamline patterns created in this way have 

 found and will And infrctjuent u.se in practical 

 naval architecture, as contrasted to their frctiuent 

 occurrence in analytic investigations and their 

 use in the development of underwater non-ship 

 forms. Nevertheless, a knowledge of the mechanics 

 of drawing source-sink flow patterns and some 

 experience in drawing them gives one an insight 

 into and a working knowledge of certain phases 

 of hydro<Jyiiainics that can not be obtained in any 

 other way. A parallel ca.se is experience in the 

 coiutruclion of flow neta. Literally, the marine 



architect who expects a knowledge of hydro- 

 dj'namics to serve him should know how to draw 

 source-sink stream forms and flow patterns. 

 Frequent application of this "know how" will 

 greatly expand the usefulness of source-sink or 

 radial-flow knowledge in his work. 



43.2 Delineation of Two-Dimensional Stream- 

 Form Contours and Streamlines Around a Single 

 Source in a Stream. Notwithstanding that for 

 every source there must theoretically be a cor- 

 responding sink of ecjual strength, the plotting of 

 the flow around a single 2-diml source in a uniform 

 stream is first described as a preliminary to sub- 

 sequent operations. For the time being it may 

 be assumed that the companion sink lies at an 

 infinite distance downstream. The plotting method 

 is a single-step combination of the "radial" 

 stream functions for the soiu'ce and the "parallel" 

 functions for the uniform stream. 



Lay down first a set of radial equidiflerent 

 stream-f miction lines for the source. It is con- 

 venient, for reasons which appear presently, to 

 have two of these radial lines lie on the customary 

 X- and //-axes, and to jilace the imiform stream 

 parallel to the z-axis, as in Fig. 43. .V. The four 

 (juadrants around the source are then each 

 divided into a suitable number of equal arcs by 

 the remaining radial streani-function lines. The 

 stream functions from tht; source, identified aa 

 ^ao(p«i)) 'ii"*-' then marked with any convenient 

 set of positive numlicr.s, in tliis cxse 1 through 28, 



