# Streamline

From AMS Glossary

## streamline

A line with its tangent at any point in a fluid parallel to the instantaneous velocity of the fluid at that point.

The differential equations of the streamline may be written

*d***r**×**v**= 0, where*d***r**is an element of the streamline and**v**the velocity vector; or in Cartesian coordinates,*dx*/u =*dy*/*v*=*dz*/*w*, where*u*,*v*, and*w*are the fluid velocities along the orthogonal*x*,*y*, and*z*axes, respectively. In steady-state flow the streamlines coincide with the trajectories of the fluid particles; otherwise, the streamline pattern changes with time. A two-dimensional wind-vector field may be completely specified by streamlines and isotachs.*See*free streamline;*compare*trajectory.