The Stream Function is defined for two-dimensional flows.
It is the flux across a line (any line!) between a given
reference point and the point at which the value of the
function is desired. Note that since streamlines are tangent
to the flow, the value of the stream function must be the
same along a streamline. If there were a flux across a
line, it would necessarily not be tangent to the flow, hence
would not be a streamline.
The usefulness of the Stream Function lies in the fact that
the velocity components in the x and y directions at a given
point are given by the partial derivatives of the Stream Function
at that point.
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