The motion of stars, gas and dust in galaxies is scientifically important, but difficult to describe to a general audience. The general view is that the stars are just rotating around the center of the galaxy, but, in fact, there is also a significant radial motion. We have here taken avantage of the concept of streamlines commonly used in Fluid Dynamics to visualize this process. Streamlines are lines that are everywhere tangent to the local mean flow vector and therefore illustrate in a very direct way the direction of motion in the galaxy. It is here demonstrated that the flow of stars in the Milky Way follow a spiral pattern, in fact very nearly what is called a logarithmic spiral. These spirals are reminiscent, of the pattern formed by the arms in the galaxy, but only approximatly so.