Figure 147 — Streamlines past a circular cylinder resting pgainst 

 a plane wall, also the pressure p during steady motion, along 

 the wall for a; > and then around half of the circular surface. 



Thus M-» at jj = 0, the sole stagnation point; for sinh Q increases much faster than Q as 



X-f oo. 



On the y-axis, 4> = 0, r=-y, q^ \u\, and 



w = - 1 - cos — 



■2 V y 



y\ ' / y 



.2 . /.. - v2 2 „. .2 + 



na 

 sin — 



2 \ y 



[90h] 



On the cylinders, ar^ + (y + of = or, or r2 = ± 2ay, hence ^6 = and 

 n'^ a\U\ I itx 



9 = 



cosh + 1 



y 



n'^\V\ osc^ — 

 2 



1 + cosh I n cot — 

 2 



[90i] 



in terms of an angle 8 defined as in Figure 147. The maximum velocity, occurring at a; = 



and |y| = 2a, is ^2 |6'!/4 or 2.47 |f/|. 



220 



