Sec. 42.13 



POTENTIAL-FLOW PATTERNS 



49 



light and doubly refracting colloidal solutions, 

 mentioned in Sec. 5.6, it is possible to observe 

 certain interesting and useful types of flow 

 phenomena. The solution most commonly used 

 in the past has been water with a finely ground 

 clay called bentonite; the procedure is described 

 briefly by C. H. Hancock [SNAME, 1948, p. 52]. 

 B. Rosenberg, in TMB Report 617, issued in 

 March 1952, goes into the fundamentals as well 

 as the procedure. In this report there are listed 

 45 references on the subject. 



One of these references, plus three others not 

 in the hst, are given here: 



(1) Dewey, Davis R., II, "Visual Studies of Fluid Flow 



Patterns Resulting from Streaming Double Refrac- 

 tion," Dr. of Sci. Thesis, Dept. of Chem. Eng'g., 

 MIT, 1941 



(2) Takahashi, W. N., and Rawlins, T. E., "The Streaming 



Double Refraction of Tobacco Mosaic Virus," 

 Science, 1937, Vol. 85, pp. 103-104 



(3) Ullyott, Phillip, "Investigation of Flow in Liquids by 



Use of Birefringent, Colloidal Solutions of Vanadium 

 Pento.xide," Trans. ASME, Apr 1947, pp. 245-251. 

 A list of 23 references is given on pp. 248-249. 



(4) Peebles, F. N., Garber, H. J., and Jury, S. H., "Pre- 



liminary Studies of Flow Phenomena Utilizing a 

 Doubly Refractive Liquid," [Third Midwestern 

 Conf. on Fluid Mech., Univ. of Minn., Jun 1953, 

 pp. 441-454]. These authors describe similar tests 

 made successfully with an organic dye. On pp. 

 451-452 they list 26 references on this subject, 

 including the Dewey, Ullyott, and Rosenberg 

 references mentioned previously. 



42.13 Delineation of Flow Patterns by Electric 

 Analogy. The story on velocity potential in 

 Sec. 2.13 discusses rather briefly the parallel 

 between velocity potential and electric potential. 

 Diagram 1 of Fig. 2.P illustrates in schematic 

 fashion the use of an electrolytic tank for deUneat- 

 ing the equipotential Unes around any body or 

 surface in 2-diml streamline flow. Diagram 1 of 

 Fig. 42. H indicates the essentials of the setup for 

 delineating the flow around a 2-diml body of 

 lenticular shape, utilizing a weak liquid electrolyte 

 and direct current passing between the rows of 

 electrodes at the ends of the tank. If the latter is 

 of area sufficiently large compared to that of the 

 body around which the flow is being studied, it is 

 possible to replace the separate electrodes, con- 

 nected to resistances so as to pass equal amounts 

 of current, by single-plate electrodes. When the 

 equipotential lines are delineated by the probe 

 method it is necessary to sketch in the streamUnes 

 by hand, utilizing the principles of the flow net. 

 This means that the streamlines must cross the 



equipotential hues everywhere at right angles. 



Diagram 2 of Fig. 42. H shows how this method 

 is used to trace the streamlines directly. This is 

 accomplished by passing the current across the 

 flow, as it were, and shaping the body out of a 

 conducting rather than a non-conducting material. 



Three-dimensional axisymmetric flow is repre- 

 sented by using a tank having a cross section 

 corresponding to one sector of the axisymmetric 

 flow field, like a narrow sector cut out of a log. 

 Diagram 3 of Fig. 42. H illustrates such an arrange- 

 ment, with the current passed in the direction of 

 flow and the body a nonconductor. 



[Electrodes 



Broken Lines ore \ 

 True Equipotential 

 Lines for Flow from 

 Right to Left 



Equipotential Lines 

 (broken) Represent 

 Streamlines for Flow 

 From Right to Left 



Plan Vie 



End Section 



Auxiliori^ Current 

 to Represent Effect 

 of Circulation 



Fig. 42.H Schematic Diagrams of Electrolttic 



Tank Arrangements to Determine Streamlines 



AND Equipotential Lines Around Bodies 



Before 1928, as described in reference (2a) of 

 Sec. 42.14, G. I. Taylor and C. F. Sharman 

 showed that irrotational flow with circulation 

 could be represented and delineated in a simple 

 electrolytic setup by feeding some current into 

 the body representing the foil around which 

 circulation is taking place. The current entering 

 one boundary plate is that passing out of the 



