The basic properties of two-dimensional stream functions can be summarized as follows:
# The x- and y-components of the flow velocity at a given point are given by the partial derivatives of the stream function at that point.
# The value of the stream function is constant along every streamline (streamlines represent the trajectories of particles in steady flow). That is, in two dimensions each streamline is a level curve of the stream function.
# The difference between the stream function values at any two points gives the volumetric flux through the vertical surface that connects the two points.