Example 11.25. Find
the complex potential for an ideal fluid flowing from left to right
across the complex plane and around the segment
from
.
![]()
Figure 11.49 A uniform parallel flow.
Explore Solution 11.25.
Enter the complex potential and determine the velocity potential and stream function.
![[Graphics:../Images/FluidFlowMod_gr_186.gif]](../Images/FluidFlowMod_gr_186.gif)
Use Mathematica to make a plot of the stream function.
For illustration purposes, we choose A = 1.
![[Graphics:../Images/FluidFlowMod_gr_188.gif]](../Images/FluidFlowMod_gr_188.gif)
![[Graphics:../Images/FluidFlowMod_gr_189.gif]](../Images/FluidFlowMod_gr_189.gif)
The inverse of
. Use
conformal mapping z = g(w) to make an image of
the flow.
![[Graphics:../Images/FluidFlowMod_gr_192.gif]](../Images/FluidFlowMod_gr_192.gif)
![]()
![[Graphics:../Images/FluidFlowMod_gr_194.gif]](../Images/FluidFlowMod_gr_194.gif)
![[Graphics:../Images/FluidFlowMod_gr_195.gif]](../Images/FluidFlowMod_gr_195.gif)