Composition of Ideal Fluid Flows Around Cylinder Using Bilinear Transformation

Abstract

Advent of conformal mapping eases to model a flow in sought-after domain without trade- off between laws of fluid mechanics and the theory of complex valued-functions. The far-reaching properties manifested by conformal mapping discern and facilitate solution of large class of two-dimensional flow problems. Bilinear transformation is amidst the conformal mappings. The properties, mapping a circular boundary onto horizontal line and composition of bilinear transformations is again a bilinear transformation are steppingstone to study a composition of a flow of an ideal fluid around a cylinder of circular cross-section mounted in the plane. This circumstance simplifies the proposition of combining two flows, which constitutes the primary focus of this paper. As an initial step towards advancing the investigation of fluid flow, an attempt is made herein. However, the process of adding the two fundamental flows is more intricate than it may initially appear.