64 



IIVDRODYN AMIC.S IN SIIII' 111 SICN 



Sec. -fJ.S 



TAULB 43.n — Data roK CoNSTKCcTisr. Tmhkk-Dimi. 1{mihi-I' 

 This tablo applies to (iingram I of Pii;. i:i.I,. 



I )i m;k\\is 



D. W., INA, 1895, PI. XVj. The respective radii 

 ijk may also be calculated by the formula 

 Ri = yl = R\k/n), or Rk = RV{k/n), where n 

 is the number of intervals into which a given 

 radius R is to be divided and k is the identifying 

 number of any cylindrical stream surface, counting 

 outward from the axis. Tables 43. a and 43. b give 

 data for JaJ'ing down these dimensions directly 

 for n = 20 or an integral portion thereof, without 

 the necessity for making a graphic construction 

 similar to Fig. 43. L. 



Separate radial diagrams for this 3-ciinil fluw 

 can now be drawn on tracing cloth or other 

 Huitable tran.sparent material, corresponding to 

 tho.so described previously in Sec. 43.3 for 2-diml 

 flow. The radial traces on the.se diagrams are 

 numbere<l with the .selected stream-function 

 values, starting from zero at what is to be the 

 upstream end of the source-sink axis and working 

 both ways, above and below the axis. The radial 

 lines belonging to the sink are numbered in the 

 same way and with the .same corresponding 

 numerals, but preceded by negative signs. In 

 other words, the lines for 4'o = 2 aiul ^^ = — 2 

 are on the upstream sides (if the snurcc and .sink, 

 respectively. 



If it Lh desired to combine an isolated 3-diml 



source with a uniform 3-diml flow, the radial 

 source diagram 1 of Fig. 43. L is laid down by 

 itself over the reference line, parallel to the 

 direction of uniform flow. As in the 2-diml case, 

 the companion 3-diml sink is considered to be 

 situated at an infinite distance downstream, to 

 the left in the figure. 0\'er the source diagram is 

 placed the uniform-flow diagram 2 of Fig. 43. L. 

 Over both of them is placed a sheet of tracing 

 paper upon which the 3-diml body and the stream- 

 lines around it are to be drawn. The cone-and- 

 I'unnol flow is now combined with the rod-and-tube 

 uniform stream exactly as was described pre- 

 viously in Sec. 43.2 for the single source and the 

 uniform flow, by adding the 3-diml stream func- 

 tions alRei)niically. The trace of the axi.symmetric 

 form represented 1)V ^.s- = in the 3-<iinil flow 

 of Fig. 43. M resemi)les that of the 2-diml flow 

 sliown previously in Fig. 43. B excejit that it is 

 somewhat more blunt. 



This construction again finds a practical a|)])li- 

 cation in the shaping of a bull) bow, where the 

 forward portion ni.uy i>e l)uill up around a biKly 

 of revolution having the form siiown by the heavy 

 line of Fig. 43. M and the after portion may 

 merge into the lower regions of the entrance, as if 

 directed toward a companion sink o( eipial 



