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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.

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