508 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS
- Let the lines x = 0 and x = ~ form the walls of a containing vessel for a fluid flow
in the infinite strip 0 < x < i that is produced by a single source located at the
point z 0 = 0. Find the complex potent ial for the flow in Figure 11.101.
Figure 11 .101- Let the rays x = 0, y > 0 a nd x ='Ir, y > 0 and the segment y = 0, 0 < x <Tr form
the walls of a containing vessel for a fluid flow in the semi-infinite strip 0 < x < Tr,
y > 0 that is produced by two sources of equal strength located at t he points z 1 = 0
and z2 =Tr. Find the complex potential for the flow shown in Figure 11.102. Hint:
Use the fact that sin ( ~ + z) = sin ( i -z).
Figure 11.10 2- Let the y-axis be considered a wall of a containing vessel for a fluid flow in t he
right half-plane Re (z) > 0 that is produced by a single source located at the point
.zo = 1. Find the complex potential for the flow shown in Figure 11.103.