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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2010 • Question 7

Question

Math 6420 • PDE Fall 2010 • Question 7

The fourth quadrant \(x\ge 0\), \(y\le 0\) is occupied by an impermeable solid, around which air flows. Treating the flow as incompressible and irrotational use conformal mapping to map to a simpler problem and give one non-trivial solution for the complex potential \(f(z)\) in the original coordinates. Find the equation in polar coordinates for the streamline passing through \(z=-1\). What happens to the fluid velocity as one approaches the corner?

Raw LaTeX

The fourth quadrant \(x\ge0\), \(y\le0\) is occupied by an impermeable solid, around which air
flows. Treating the flow as incompressible and irrotational use conformal mapping to map
to a simpler problem and give one non-trivial solution for the complex potential \(f(z)\) in
the original coordinates. Find the equation in polar coordinates for the streamline passing
through \(z=-1\). What happens to the fluid velocity as one approaches the corner?

Topic Tags

Complex Potential Flow and Blasius Formula Conformal Mapping and Bilinear Transformations Distributions and Weak Solutions Linear Programming and Optimization