If, as will be assumed, a < 77/4, g'^' has the same sign as has the product ad; the fluid 

 thus flows inward or toward the axis along the trailing wall of the angle and outward along 

 the leading wall. This is illustrated by Figure 168, in which relative streamlines are shown 

 for a = 9 deg. If ct>77/4, the flow pattern is more complicated, but such cases are of little 

 practical interest. If a = 77/4, cos 2a = and irrotational motion is impossible, in the ideal 

 case in which the walls extend to infinity. 



Figure 168 — Streamlines for the motion of fluid relative to the walls 

 in a rotating angle. (Copied from Reference 10.) 



The pressure in the fluid, from Equation [lid], is 



cos 2 6 



22 

 p = p (O T 



cos 2( 



~2 ) "" ^0- 



[lOlh] 



2 cos^ 2a 



The flow within the angle can be generaliz'ed by adding one or more terms of the 

 following form, derivable from a complex potential 



-,(2" + 1) 77/2a . 



(2n + 1) — 



<i> ^-A T 2a ^ 



(2/1+ 1) 



2a 



(2n + 1) 



xIj ^ A T 2a 



(2n+ 1) 



[101i,j] 



where n is any positive integer and A is an arbitrary real constant. The corresponding 

 contribution to qa vanishes at = ia , so that the boundary condition, qa = wr, remains 

 satisfied. 



249 



