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Streamline

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A line in the fluid whose tangent is everywhere parallel to the local velocity vector <math>(u,v,w)</math> instantaneously is a streamline. The family of streamlines at time <math>t</math> are solutions of
A line in the fluid whose tangent is everywhere parallel to the local velocity vector <math>(u,v,w)</math> instantaneously is a streamline. The family of streamlines at time <math>t</math> are solutions of
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<math>
+
:<math>
\frac{dx}{u(x,y,z,t)} = \frac{dy}{v(x,y,z,t)} = \frac{dz}{w(x,y,z,t)}
\frac{dx}{u(x,y,z,t)} = \frac{dy}{v(x,y,z,t)} = \frac{dz}{w(x,y,z,t)}
</math>
</math>

Revision as of 11:39, 12 September 2005

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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