Plane of Symmetty 



Figure 79 - Streamlines from a line source at P near a circular cylinder. 



The equations will represent also the flow Inside a cylindrical shell of radius a due 

 to a line sink along the axis and a parallel line source of equal strength distant A, frorn the 

 axis; then in the formulas the constant h. stands for a^ f^i. 



If A is made negative, sources become sinks and vice versa, and all velocities are 

 reversed. (See Reference 1, Article 64; Reference 2, Sections 8.61, 8.62.) 



52. LINE DIPOLE AND CYLINDRICAL BARRIER 



Near a circular cylinder let there exist both a parallel line source and a line sink of 

 equal strength. Then, upon superposing the flows as described in Section 51, it is noted 

 that the images at the origin cancel each other and there remain only the image source and 

 sink at the inverse points. By imagining the external source and sink to coalesce while 

 suitably increasing in strength, so as to form a dipole, the conclusion is reached that the 

 image of a line dipole in a circular cylinder with parallel axis is a dipole located on the in- 

 verse line with respect to the cylinder. 



Let the given dipole be at a distance h^ from the axis of the cylinder, whose radius is 

 a, and let its axis make an angle a. with the line drawn from the axis of the cylinder through 

 the position of the dipole, as in Figure 80. Then, using [37r] for the potential due to a line 

 dipole, 



.119 



