Equations [54g] and [54j] can be written 



h4 



1.2^, 



= tan 



\a 2g} ' 



which shows that the shape of the oval as fixed by h/a and l/a depends only on the ratio g/a. 

 As g/a increases, the oval comes to resemble an ellipse and finally approximates a circle; 

 but for small g/a it is much more flat-sided and reeembles the profile of a ship having a 

 rounded bow and stern. 



The formulas may represent the flow past a cylinder whose cross-section has the shape 

 of the oval. In Figure 83 the oval is drawn for g = a. An example of the streamlines for 

 g/a = 0.17 is shown in Figure 84. Here l/a = 1.15, h/a = 0.41, h/l = 0.35. Details of the con- 

 struction according to the Maxwell-Rankine method are shown as described in Section 13; the 

 parallel lines represent streamlines for the uniform flow, whereas the circular arcs diverging 

 from a represent those for the flow due to the source and sink, all drawn for equal increments 

 of lit. In the original figure, however, twice as many lines and curves were drawn, for greater 

 accuracy. The heavy curve is the cylinder S. Only one quarter of the diagram is shown, 

 since it is symmetric with respect to both the x- and y-axes. According to the Bernoulli 

 principle, the pressure excess, p - p^, sinks from pf/^/2 at (1,0), to zero at about the point 

 indicated as P, and then remains negative to the middle, where, from [54f] with x = 0, y = h, 

 ?=|«|=1.29 \U\, p-p^= p(f/2 - q^)/2 = - 0.33p{/2. 



Plane of Synmetiy 



Figure 84 - One quarter of the streamline plot for a more slender Rankine oval. 

 Construction of the plot by the Maxwell method is shown. See Section 54. 

 (Copied from Reference 254.) 



Another plot, also containing some of the construction lines and arcs, is shown in 

 Figure 85. Here g/a = 0.27, l/a = 1.24, h/a = 0.57, h/l = 0.46. 



126 



