Example 11.30.  (Source and sink of equal strength)  Let a source and sink of unit strength be located at the points and , respectively.  The complex potential for a fluid flowing from the source at    to the sink at    is  

            .  

            Figure 11.95 (a)  Source and sink of unit strength.

Explore Solution 11.30.

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 flowing from the source at  z = +1  to the sink at  z = -1.  

The velocity potential for a fluid flowing from the source at  z = +1  to the sink at  z = -1.  

The streamlines and velocity potential for a fluid flowing from the source at  z = +1  to the sink at  z = -1.  

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