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2. Let v(x, y) = (2). (a) Show that v(x, y) is an ideal flow. (b) Find the complex potential Þ(z) for v. (c) Find the stagnation point (s) of v. (d) Find the streamlines (trajectories) of v, and hence show that v(x,y) is a tangent vector to the streamline at z = x+iy (excluding the stagnation point(s)).

2. Let v(x, y) = (2). (a) Show that v(x, y) is an ideal flow. (b) Find the complex potential Þ(z) for v. (c) Find the stagnation point (s) of v. (d) Find the streamlines (trajectories) of v, and hence show that v(x,y) is a tangent vector to the streamline at z = x+iy (excluding the stagnation point(s)).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Vector Field Analysis and Complex Potentials** Let \(\mathbf{v}(x, y) = \left( \frac{y}{x} \right)\). **(a)** Show that \(\mathbf{v}(x, y)\) is an ideal flow. **(b)** Find the complex potential \(\Phi(z)\) for \(\mathbf{v}\). **(c)** Find the stagnation point(s) of \(\mathbf{v}\). **(d)** Find the streamlines (trajectories) of \(\mathbf{v}\), and hence show that \(\mathbf{v}(x, y)\) is a tangent vector to the streamline at \(z = x + iy\) (excluding the stagnation point(s)).
Transcribed Image Text:**Vector Field Analysis and Complex Potentials** Let \(\mathbf{v}(x, y) = \left( \frac{y}{x} \right)\). **(a)** Show that \(\mathbf{v}(x, y)\) is an ideal flow. **(b)** Find the complex potential \(\Phi(z)\) for \(\mathbf{v}\). **(c)** Find the stagnation point(s) of \(\mathbf{v}\). **(d)** Find the streamlines (trajectories) of \(\mathbf{v}\), and hence show that \(\mathbf{v}(x, y)\) is a tangent vector to the streamline at \(z = x + iy\) (excluding the stagnation point(s)).
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