11.11 • SOURCES ANO S rNKS 50 3(a) Source and sink of equal strength.(b) Two sources of equal Strength.F igure 11.95 Fields depicting electrical strength.
- EXAMPLE 11 .3 1 (Two sources of equal strength) Let two sources of unit
strength be located at the points ± 1. The resulting complex potential for a fluid
flow is
F(z) = log(z- 1) + log(z + 1) = log(z^2 - 1).
The velocity potential and stream function are
<fo(x,y) = Ln lz^2 - 11 and 1/J(x,y) = arg (z^2 - 1),
respectively. Solving for the streamline 1/J (x, y) = c, we start with
c = a.rg (z^2 - 1) = arg (x^2 - y^2 - 1 + i2xy) = arctan 2
2
x~
x - y -1