Ideal fluid flows using complex analysis

ABOUT THE COURSE: The course is meant to impart competence in modelling engineering problems using principles of ideal or potential fluid flows, obtaining analytical solutions and deducing engineering design parameters. The course will focus on the use of complex analysis and highlight it as a classical and a much easier approach to obtain solutions using flow superposition.INTENDED AUDIENCE: Senior undergraduate and post-graduate studentsPREREQUISITES: Basic course on fluid mechanics

Syllabus

Week 1: Introduction to ideal flows, velocity potential and stream function, complex variables and analytic functions, Complex potential and velocity.Week 2:Use of complex potentials in developing elementary flows-uniform flow, source and sink, vortex flow, flow in a sector, flow around a sharp edge, Superposition of complex potentials for flow due to a doublet.Week 3:Use of superposition to obtain flow around a cylinder without and with circulation, source and uniform flow, calculation of force for flow around a circular cylinder with circulation.Week 4:Generalized derivation for forces on a 2D body, first theorem of Blasius, KuttaZhukhovsky law, Conformal transformations.