The wall thus appears to repel a cylinder that is moving toward or away from it (/3 = or n), 

 but to attract one that is moving parallel to it (^ = 7t/2 or 2>tt/2). 



A flow parallel to the wall and uniform at infinity may be added. Then the velocity of 

 the cylinder is to be taken relative to the fluid at infinity. If the cylinder is stationary, the 

 stream pushes it toward the wall. 



For the general case of two cylinders, see the references in Section 94 or Basset.^ 



96. TWO OR THREE LAMINAS 



The noncirculatory flow past two plane laminas, placed with their central axes par- 

 allel and with their faces perpendicular to the plane through their axes, has been treated by 

 Nomura. ^^^ The torques on the laminas tend to turn them perpendicular to the incident 

 stream. The resultant forces on the two laminas are equal and opposite; if the laminas are 

 of equal width, the forces tend to separate them and are proportional to cos (f) where is 

 the angle between the direction of the stream and the normal to their faces. See also 

 Ferrari. ^^^ 



The flo>v past a similar pair of laminas of equal width, with or without circulation, 

 has been studied with reference to biplane theory by Kutta,^^ Schmitz^^^ and Munk.^^^ 

 Lines of flow for two positions of the laminas, in a stream perpendicular to their faces, are 

 shown in Figure 163. 



Three parallel laminas were studied by Tani.^'^^ 



Figure 163 — Streamlines past two similar plane laminas 

 in two positions. (Copied from Reference 133.) 



241 



