A 2-D Flow Field
A 2D fluid velocity field is represented using streamlines. A streamline is tangent to the velocity field everywhere. Streamlines for the velocity field are generated from the components of the velocity vector. You can vary the values of the coefficients, exponents, and constants of each component u and v of the velocity vector. You can restrict the range with the controls at the top.

Download the CDF file to view the simulation using the free Wolfram CDF player.

Details:

The velocity vector for a flow field defines fluid velocity in the  and  directions is:

,

where  and  are the  and  components of the velocity vector, and  and  indicate the direction of the vector component. For this Demonstration, flow is only in the  and  directions, so  simplifies to:

.

In this Demonstration, the components of the velocity vector are defined as:

,

.