y = - 



1 -n 



- X tan nir. 



Thus the streamlines for i/( = i n' are straight lines inclined at angles + nn to the positive 

 ar-axis. These lines do not cross the axis but end at the points 



l\ - n cos nn ^ sin njr\ 

 \ n n n I 



at these points dx/dcf) = 0, (^ = 0, and a; as a function of (f> has its maximum value. 



The fluid is thus flowing into a diverging channel or spout with parallel walls inclined 

 at an angle 2 mi radians to each other. The opening is (2 sin mT)/n wide. The volume of fluid 

 that flows out per second, per unit of length perpendicular to the ajy-plane, is the total incre- 

 ment of across the opening or 2 tt. Part of the flow net for n = 1/4 is shown in Figure 96. 



If in the formulas 9S and i// are replaced by (f>/k and xp/k, respectively, i/f = i rrA; on the 

 walls and the volumetric rate of outflow is 2 n-^. \i k < O, the flow is reversed. If the expres- 

 sions given for z, x, and y are all multiplied by c, the opening is (2c sin nn)/n wide. Both 

 changes may be made. Velocities are multiplied by k or by 1/c, or, if both changes are made, 

 by k/c. 



For n = 1/2, the spout becomes a slotted plate and the transformation reduces to a mod- 

 ified form of that in Section 61. For 1/2 < n < 1, the transformation merely repeats itself with 

 changes of scale, orientation, and direction of flow. 



(For notation and method; see Section 34; Reference 1, Article 66.) 



64. TWO-DIMENSIONAL PITOT TUBE 



2 = w + Inw. 



[64a] 



Figure 96 - Flow net for fluid entering 



a diverging spout. See Section 63. 



(Copied from Reference 255.) 



143 



