CHAPTER 42 



Potential-Flow Patterns, Velocity and 

 Pressure Diagrams Around Various Bodies 



42.1 Various Methods of Drawing Streamlines 



Around Bodies 31 



42.2 Flow Patterns Around Geometric and Other 



Shapes; Published Streamhne Diagrams . 31 



42 . 3 Flow Patterns in Ducts and Channels ... 39 



42.4 Flow Patterns for an Ideal Liquid Around 



Simple Ship Forms 39 



42.5 Flow Patterns About Yawed Bodies in an 



Ideal Liquid 40 



42.6 Velocity and Pressure Distribution Around 



a Body of Revolution 40 



42.7 Velocity and Pressure Diagrams for Various 



Two- and Three-Dimensional Bodies . . 43 



42.8 The Distribution of Velocity and Pressure 



About an Asymmetric Body 43 



42 . 9 Flow, Velocity, and Pressure Around Special 



Forms 46 



42.10 Velocity and Pressure Distribution Around 



Schematic Ship Forms 47 



42 . 1 1 Pressure Distribution Along a Vee Entrance 48 



42. 12 Use of Doubly Refracting Solutions for Flow 



Studies 48 



42 . 13 Delineation of Flow Patterns by Electric 



Analogy 49 



42.14 BibUography on the Electric Analogy for 



Flow Patterns 50 



42.1 Various Methods of Drawing Streamlines 

 Around Bodies. For 2-diml potential flow around 

 a body of any shape, at any orientation with the 

 stream, there are several methods of determining 

 the streamline pattern. Listed briefly, these are: 



(a) Constructing a flow net made up of streana- 

 lines and equipotential lines 



(b) Determining the streamlines mathematically 

 or by graphic construction, if the body shape is 

 one that may be formed by placing one or more 

 sources or sinks, or source-sink pairs, in a uniform 

 stream 



(c) Plotting the equip otential-line pattern in an 

 electrolytic tank and constructing the streamline 

 pattern from it 



(d) Plotting the streamline pattern as an equi- 

 potential-hne pattern in an electrolytic tank 



(e) Placing the body in a circulating-water 

 channel and observing the streamline pattern by 

 one of several methods 



(f) Utilizing conformal transformation. 



By following the relatively simple sketching 

 process described in Sec. 2.20, a flow net for 

 continuous, irrotational, potential flow in two 

 dimensions in an ideal liquid can be constructed 

 for a great variety of boundary shapes, channel 

 boundaries, or both. Flow nets are reproduced in 

 Figs. 2.0, 2.P, 2.W; in diagrams 1, 2, 3, and 4 of 

 Fig. 2.X; and in Fig. 41.J. They are to be found 

 frequently in the literature, as hsted in Table 42.a. 



Despite its limitation to an ideal liquid, the 

 2-diml flow-net technique has a rather extensive 

 practical usefulness in applied hydrodynamics. 

 There are many instances in the course of ship 

 design or in the analysis of ship behavior where 

 an approximation to the flow pattern by this 

 method is most illuminating. For example, before 

 surface wavemaking has become pronounced, the 

 flow around the uppermost waterlines of a ship 

 is predominantly 2-diml in character, expecially 

 abreast the forward part of the vessel. Several 

 examples are to be found in Figs. 2.S and 4. A. 

 Other examples are the 2-diml flow patterns 

 around a sharp 2-diml bend in a duct, illustrated 

 in diagram 2 of Fig. 2.X, and around the stem 

 bar of a ship, shown without the equipotential 

 lines in diagram 1 of Fig. 2.V. 



Three-dimensional flow nets can be constructed 

 [Rouse, H., EH, 1950, Fig. 26 (lower), p. 33] but 

 the technique becomes complicated, as described 

 in Sec. 2.21. Practical methods for constructing 

 them are not considered here. 



It is important to note, as mentioned on page 

 44 of Sec. 2.20, that since the flow in a separation 

 zone is not potential in character, it can not be 

 represented in a flow net. Furthermore, this 

 technique does not take account of centrifugal- 

 force effects as the liquid changes direction around 

 bends and corners in channels and ducts. These 

 forces may be appreciable at high velocities. 



42.2 Flow Patterns Around Geometric and 



31 



