Approximate analytic solution of potential flow around a rectangle

It is critically important to find a right scale to solve problems in fluid mechanics. However, it is sometimes obscure to define a correct measure for a given system. For example, in study of wake behind a circular object or behind a rectangular object, the Reynolds number of two cases cannot be compared uniformly, because the definitions of 'the characteristic length scale' are different for two cases. The comparison between two cases may possible only if Reynolds numbers are defined in the same context in two cases. The starting point of this study is to assume that the length scales of flows can be set up by surrounding length scale of potential flow. For quantitative evaluation of such length scales, it is critically important to solve for the potential flow around a rectangle, whose exact solution is not available. Instead, we solve for approximate and analytic solution by the discretization and the optimization using multiple linear regression.