Abstract

There are many problems in fluid mechanics that are difficult to solve in their original geometric form in a given domain; Conformal mapping easily translates an equation and a domain from its original form into another; after some mathematical manipulations one can get the solution and the solution can be sent back into the original form. In this study we exploited the conformal mapping technique in particular Schwarz-Christoffel transformations in analyzing ideal fluid flow problems in the complex plane. The complex potentials to a number of selected fluid flow problems were determined. More specifically; the stream function which is the imaginary part of the complex potential and is the solution of the flow problems; then streamlines of each flow generated to visualized the flow field and the flow pattern. The fluid velocity was found to be the conjugate of the derivative of the complex potential and fluid speed being the modulus of the fluid velocity.

Keywords

Conformal Map; Schwarz-Christoffel Transformation; Analytic Function; Upper Half Plane; Fluid Velocity; Fluid Flow; Stream Function; Complex Potential; Dirichlet Problem; Boundary Value Problem

Introduction