Example 3.14.  Show that the harmonic function [Graphics:Images/HarmonicFunctionMod._gr_198.gif]  is the scalar potential function for the fluid flow  [Graphics:Images/HarmonicFunctionMod._gr_199.gif].  

Explore Solution 3.14.

Enter the complex potential  [Graphics:../Images/HarmonicFunctionMod._gr_211.gif].  

[Graphics:../Images/HarmonicFunctionMod._gr_212.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_213.gif]

 

 


Use Mathematica to make a contour plot of the velocity potential and streamline curves

[Graphics:../Images/HarmonicFunctionMod._gr_214.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_215.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_216.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_217.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_218.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_219.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_220.gif]

 

 

[Graphics:../Images/HarmonicFunctionMod._gr_221.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_222.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_223.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_224.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_225.gif]

[Graphics:../Images/HarmonicFunctionMod._gr_226.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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