Some of the streamlines on one side are shown in Figure 209, past the lower side of a 

 body with h/a = 0.054. 



Changing the sign of U in the formulas changes sources into sinks and vice versa, and 

 reverses all velocities. 



To reverse the solid lengthwise, the a;-axis may be drawn in the opposite direction. 



Other shapes can be obtained by using various distributions of sources and sinks along 

 the axis. It is not possible to produce in this manner any given arbitrary shape, but many 

 practical airship forms can be imitated closely by dividing the axis into segments and assuming 

 the proper source strength on each segment. Graphical methods for this purpose were discussed 

 by Weinig.228 



Two shapes thus obtained by Fuhrman^^^ are shown in Figure 210. (See rieference 1. 

 Article 97; Reference 2, Section 15.25; Reference 7, page 633; Reference 229. 



126. SPACE DISTRIBUTIONS OF POINT SOURCES 



The flow due to any assigned distribution of point sources can be found by integration 

 of the formulas for a single point source. The potential is mathematically identical with the 

 electrostatic potential due to a corresponding distribution of electrical charges in empty space; 

 each unit charge in the electrical problem represents an em.ission of \tt units of volume per 

 second in the hydrodynamical problem. 



The potential due to an axially symmetric distribution of sources on a plane can be 

 expressed in terms of Bessel functions. See Reference 1, Article 102, where the particular 

 cases of a uniform distribution over a circular area and of a distribution proportional to 



{a?- - r^)~ ^^'' are treated. 



127. TRANSLATION OF A SPHERE IN INFINITE FLUID 



Consider a sphere of radius a moving at velocity V through fluid that is at rest at 

 infinity, as illustrated in Figure 211. The boundary condition to be satisfied at the surface 

 of the sphere is that the fluid and the sphere must have a common com.ponent of velocity 

 normal to the surface. The magnitude of this component is V cos 6 in terms of angular 

 position on the sphere measured from a radius drawn in the direction of motion. 



A known type of flow in which the radial velocity varies as cos 9 and in which the 

 velocity vanishes at infinity is that of a point dipole. The radial velocity due to a dipole 

 located at the center of the sphere can be written, in terms of its moment fi, a^ in [119h], 



cos 

 At r = a this equals II cos for all values of 6 provided (x = a^V/2. 



318 



