Example 11.31.  (Two sources of equal strength)  Let two sources of unit strength be located at the points  .  The resulting complex potential for a fluid flow is  

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                 Figure 11.95 (b)  Two sources of unit strength.

Explore Solution 11.31.

Enter the formula for the complex potential F[z].

Use Mathematica to make a density plot of the velocity potential.

Use Mathematica to make a contour plot of the stream function.

Use Mathematica to make a contour plot of the velocity potential.

Find the inverse of the function F[Z].

Use Mathematica to graph the stream functions using  f[x,y].

The stream function for a fluid with two sources of unit strength be located at the points  z = 1  and  z = -1.

The velocity potential for a fluid with two sources of unit strength be located at the points  z = 1  and  z = -1.

The streamlines and velocity potential for a fluid with two sources of unit strength be located at the points  z = 1  and  z = -1.

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