•10 



HVl)R()l)V.\A.MIC:s IN Mill' DKSIGN 



Sfc.-f:^ 



of Volume I of this book thiTc mny be listed the 

 following: 



(») Two-dimensional ship h.'iviiiR n li-titiciihir form of 

 walorlinc, for which the flow puttcrn was derived 

 and publiiihiHl l>y D. \V. Taylor in: 



(1) INA. isoi, Vol. 35, Fig. 14, PI. LXXI 



(2) S and P, 1933, Fig. 4, p. 4; practically the 

 sanio figure aa in (1) 



(3) S and P, 1943, Fig. 4, p. 0; practically the 

 same figure aa in (1). 



(b) How anJ forward shoulder waterlines of a 2-diml ship 



generated by a uniform line source in a uniform 

 stream. Derived and published by H. Futtinger in 

 STG, 1924, Vol. 25, Fig. 11, p. 306; TMB Transl. 

 4S, May 1952, p. 14. 



(c) Same as (b) preceding e.\cept that the line source 



increases linearly in strength from the stem. Pub- 

 lished in STG, 1924, Fig. 12, p. 307; TMB Transl. 

 48, May 1952, p. 15. 



(d) Complete 2-diml ship with waterlines generated by 



the combination of a bow line source and a stern 

 line sink, each of constant and equal strength. 

 Generally similar to (c) preceding. Published by 



F. Horn in "Theorie des SchifTcs," Vol. V. Repro- 

 duced in RPSS, 194S, Fig. 2, p. 15, including dia- 

 grams giving the variation of p and U along and 

 beyond the .ship a.\is. 



(e) Three-dimensional ship having a lenticular form of 



lateral plane, for which a schematic flow pattern 

 was pubUshed by D. W. Taylor in: 



(i) INA, 1895, Vol. 36, Fig. 0, PI. XVI. It is to 

 be noted in this figure that the streamlines are not 

 spaced from the body a-xis at distances corresponding 

 to cquidifTerent stream functions in tubes about the 

 axis. 



(ii) S and P, 1933, Fig. 5, p. 4; practically same 

 figure as in (i) 



(iii) S and P, 1943, Fig. 5, p. 6; same comments 

 as for (i) preceding. 



(f) Ship-shaped forebody, 2-diml in character, introduced 



in a uniform stream flon-ing parallel to the ship a-xis. 



G. S. Baker and J. L. Kent give a plot of 2-diml 

 streamlines ahead of and abreast this forebody, 

 when there is no limitation on the extent of the 

 surrounding water ["Effect of Form and Size on the 

 Resistance of Ships," IXA, 1913, Part II, pp. 37-60, 

 and Pis. Ill, IV, especially Fig. 5 on the latter 

 plate). The lower portion of Fig. 5 gives graphs of 

 pressure variation with distance along the longi- 

 tudinal axis for two stream surfaces fairly close to 

 the ship. 



42.5 Flow Patterns About Yawed Bodies in an 

 Ideal Liquid. 'Iho itJcaI-lif|ui(i potential-llow 

 pattern.s about yawed bodie.s in a stream, avail- 

 able in the publi.Hhcd literature, amount to only 

 a very small fraction of those worked out for 

 axial flow. A partial list of references embodying 

 these patterns is presented in Table 42. d. One 

 HUch patt«:rn is that around the incUncd flat plate 

 in diagram 1 of Fin. 3.IJ in Volume I. 



.\ii excellent source of analytic information in 

 this particular field is the work of A. F. Zahm, 

 embodied in NACA Report 253, 1927, entitled 

 "Flow and Drag Formulas for Simple Quadric.-*," 

 pages 517-537. Fig. 3.C of Volume I of this book 

 is adapted from Fig. 23 of the Zahm report. 



More recent data, applying to pressures rather 

 than streamlines around a yawed body, may be 

 found in Admiralty Research Laboratory (Great 

 Britain) Report ARL/Rl/G/HY/19/1 of April 

 1954 by I. J. Campbell and R. G. Lewis, entitled 

 "Pressure Distributions: Axially Symmetric Bodies 

 in Oblique Flow." A copy of this report is in the 

 TMB library. 



42.6 Velocity and Pressure Distribution 

 Aroimd a Body of Revolution. For bodies of 

 revolution having appreciable diameters, the 

 same as for ships with appreciable beams, it is 

 customary to plot velocity and pressure distribu- 

 tions on a basis of body or ship length along the 

 principal or x-a.\is. This scheme is followed in 

 Figs. 4.C and 4.D of Volume L However, when the 

 diameter is large in proportion to the length, or 

 when one end or the other is blunt, the velocity 

 and pressure distributions are plotted to much 

 better advantage on a base of length along the 

 section contour, as in diagram 2 of Fig. 2.B of 

 Volume I or in the diagram of Fig. 4LJ of this 

 part of the book. 



AVhen working with 3-diml rather than 2-diml 

 flow, as with that around a body of revolution, 

 it is important that the nature of the 3-diml flow 

 pattern be clearly understood. In a number of 

 pubhshed diagrams in standard works of reference 

 the streamUnes approaching and leaving the 

 3-diml bodies of revolution have, apparently as 

 a matter of convenience in drafting, equidistant 

 radial spacing from the principal body axis. This 

 is equivalent to equidistant transverse .-ipacing 

 when a longitudinal section through the body axis 

 is diagrammed [Prandtl, L., and Tietjens, 0. G., 

 AHA, 1934, Fig. 58 on p. 109, Fig. 59 on p. 110, 

 Figs. G3 and 64 on p. 120, and Fig. 65 on p. 122; 

 Taylor, D. W., S and P, 1910, Vol. II, Fig. 20; 

 S and P, 1943, Fig. 5 on p. 6). The streamlines 

 so depicted do not correspond to cquidifTerent 

 3-diml stream functions, as do the traces in 

 diagram 2 of Fig. 2.M of Volume I, and those of 

 Figs. 42.A, 42.B, 43.M, and 43.0. 



Consider the symmetrical 3-diml flow of an 

 ideal liquid along a solid rod of circular section of 

 radius Ro , with its axis parallel to the direction 

 of flow, in a stream whose undisturbed uniform 



