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  [Graphics:Images/FluidFlowMod_gr_158.gif].  

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_185.gif]




[Graphics:../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_187.gif]





[Graphics:../Images/FluidFlowMod_gr_188.gif]

[Graphics:../Images/FluidFlowMod_gr_189.gif]

 

 

 

The inverse of  [Graphics:../Images/FluidFlowMod_gr_190.gif].  Use conformal mapping  z = g(w)  to make an image of the flow.

[Graphics:../Images/FluidFlowMod_gr_191.gif]





[Graphics:../Images/FluidFlowMod_gr_192.gif]

[Graphics:../Images/FluidFlowMod_gr_193.gif]

[Graphics:../Images/FluidFlowMod_gr_194.gif]

[Graphics:../Images/FluidFlowMod_gr_195.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell