Analytical solutions for uniform potential flow past multiple cylinders

The problem of uniform potential flow past a circular cylinder is a basic one in fluid dynamics and the solution is well-known. In this paper, an analytical construction is presented to generalize this fundamental result to find solutions for steady irrotational uniform flow past a multi-cylinder configuration in a planar flow in the case when the circulations around the obstacles is taken to vanish. More generally, if a conformal mapping from a canonical multiply connected circular region to the unbounded fluid region exterior to a finite collection of non-cylindrical obstacles of more general shape is known, the formulation also provides solutions for the uniform flow past those obstacles.