## THE STREAMLINES

The first animation is for the velocity field, represented here in term of the stream function.

For a case of zero circulation, the velocity field is symmetric with respect to the x axis and the two stagnation points lie at the intersections of the cylinder and the x-axis (left figure).

The animation on the right shows the stream function as the circulation increases to a maximum and then decreases to zero. The uniform flow is from right to left and the circulation is counterclockwise. You can see the stagnation points moving towards the lower face of the cylinder as circulation increases.

The streamlines become closely packed near the upper face and less packed near the lower face, indicating an acceleration on the upper face and a deceleration on the lower face. In fact the mass flux in in the stream tube defined by two adjacent streamlines is constant. When streamlines get closer to each other, the flow is accelerating and vice versa.