## Streamlines

Particle traces calculated in a steady-state flow field are called streamlines. The streamline path can be generated in the positive, negative, or both the positive and negative time directions. By definition, a streamline cannot have flow across it. That is, there is no flow normal to a streamline.

### Description

3 Streamlines (blue) in a Velocity field V (red)

Streamlines are simply the lines created by infinitesimally small particles moving through the flow. As the time is steady state, it is not time-varying, and the particles are computed by simply moving them parallel to the flow vectors. Often various interpolation and integration techniques, such as Runge Kutta, are used to improve the accuracy between actual grid points. The streamlines are computed until one of several criteria is met:

• Maximum compute time
• Maximum streamline length
• Boundary of the Grid
• Velocity approaches 0 - In this case, the flow has stopped moving
• Streamline intersects itself - In this case, the flow has become circular, and the streamline is infinite in that direction

### Uses

Knowledge of the streamlines can be useful in fluid dynamics. For example, Bernoulli's principle, which expresses conservation of mechanical energy, is only valid along a streamline. Also, the curvature of a streamline is an indication of the pressure change perpendicular to the streamline. The instantaneous center of curvature of a streamline is in the direction of increasing pressure, and the magnitude of the pressure gradient can be calculated from the curvature of the streamline.