Figure 206 - Dividing surface 5 for a 



uniform line of sources in a 



stream. See Section 124. 



Figure 207 - Streamlines for a uniform line 



of sources in a uniform stream. The 



heavy curve is the dividing surface 



S. See Section 124. (Copied 



from Reference 7.) 



The surface 5 is a dividing surface, and the formulas may represent the flow past a 

 solid of revolution whose surface is S. Its shape depends upon the dimensionless quantity 

 ct/aU, and its size upon the length a of the line of sources, since [124f] can be written 



\a I aV \ at 



so that, for fixed a /aV, all dimensions vary as a. If a -► while aa remains constant, the 

 shape becomes that of Section 121. 



Streamlines drawn for equally spaced values of i/z/ST, for the same shape of S as in 

 Figure 206, are shown in Figure 207. Here Xq = 0.17 a, R = 0.90 a. 



Changing the signs of both U and a merely reverses all velocities and the signs of 

 and i/f. To reverse the solid end for end, the j;-axis may be drawn in the opposite direction. 

 (See Reference 2, Section 15.24; Reference 7, p.fil.) 



125. AIRSHIP FORMS [ 



Any combination of sources and sinks immersed in a uniform stream, as in the last two 

 cases, gives rise to a dividing surface which separates the fluid in the stream from that be- 

 longing to the sources and sinics. This surface can be taken as the surface of a solid body, 

 and the formulas for the combined field then represent streaming flow past this body; or it may 

 be the surface of a shell containing within it the sources and sinks. In the latter case, the 

 introduction into the mathematical formulas of terms representing a uniform stream serves 

 merely to procure satisfaction of the boundary condition on the shell. 



The dividing surface will be of finite extent provided the total strengths of sources 

 and sinks are equal. Otherwise it will extend to infinity, in the direction of the stream if 



314 



