Plot of velocity potential for flow past a sphere

Now we can plot the answer in a contour plot.  

If you want to see where the sphere is in the picture we can make one.  

The result is shown here with the sphere blacked out (and unfortunately some frame).  Note that the contours smoothly change as we approach the sphere.  The darker, the shading, the lower the velocity.  

Velocity potential field for flow past a sphere

We see that potential lines get closer together as the velocity increases.  Further, the potential lines are curved when the velocity gradient is non zero.