A numerical analysis of flow using streamline coordinates - The case of two-dimensional steady incompressible flow

The basic equations for a two-dimensional steady incompressible flow are derived using streamline coordinates. A two-dimensional liquid jet flow from a channel with parallel walls is considered as a numerical example. The basic equations are solved by a finite-difference method. The calculations indicate that: (1) the technique is very useful for flows with free surfaces; (2) the basic equations are simplified when the configuration of streamlines can be approximated before calculation; (3) for jet flow from a channel with parallel walls the flow is not affected by downstream conditions for a Reynolds number greater than 1000; and (4) for a Reynolds number greater than 100, jet width becomes constant further downstream than at a distance equal to one quarter channel width.