Consider the 2D symmetric separable solutions Φn(r,φ) in cylindrical coordinates  Identify the separable solution that satisfies the solid-wall boundary conditions on the cylindrical surface of radius rc and the asymptotic condition Φ≃r^2 as r→∞. Show that at large distances (as r/rc→∞), this solutions approaches the extensional flow Use the complex potential W(z)=Φ(r,φ)+iΨ(r,φ) of this flow and hence its streamfunction W(r,φ). Sketch few streamlines of this flow to illustrate its properties.

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A: See the detailed solution below.

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A: Conservative Vector Field and Line integral: