On the Incompleteness of the Number of Physical Parameters of a Free Streamline Potential Flow Problem

摘要

The two dimensional free streamline problem of a rectangular plate perpendicular to the jet flow from a nozzle is solved numerically. Earlier theoretical discussions of this problem mention only three physical parameters. It is shown that this number must be equal to that of the independent geometrical parameters of the problem, which is four, otherwise the problem is not well posed. A fourth parameter is introduced. Numerical integration is preferred, although analytical integration is, in principle, possible. The determination of parameters and streamlines depends on the solution of nonlinear equations with inequality constraints.