# Streamline

A line in the fluid whose tangent is everywhere parallel to the local velocity vector $(u,v,w)$ instantaneously is a streamline. The family of streamlines at time $t$ are solutions of

$\frac{dx}{u(x,y,z,t)} = \frac{dy}{v(x,y,z,t)} = \frac{dz}{w(x,y,z,t)}$

Streamlines cannot intersect since the velocity at any point is unique.

In two dimensions and for axisymmetric flows, a stream function exists which is constant on each streamline.