Example 11.33.  Suppose that the lines    are considered as walls of a containing vessel for the fluid flow produced by a single source of unit strength located at the point    and a sink of unit strength located at the point  .  The conformal mapping    maps the infinite strip bounded by the lines    onto the w plane slit along the boundary rays    and  .  The image of the source at is a source at , and the image of the sink at is a sink at .  

          

                 Figure 11.97  A source and a sink on the edges of a strip.

Explore Solution 11.33.

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 density 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 flow in the infinite strip    with a two sources at  .  

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