Consider the flow past a circular cylinder, of radius \(a\), used in Example 6.11. Show that \(V_{r}=0\) along the lines \((r, \theta)=(r, \pm \pi / 2)\). Plot \(V_{\theta} / U\) versus radius for \(r \geq a\), along the line \((r, \theta)=(r, \pi / 2)\). Find the distance beyond which the influence of the cylinder is less than 1 percent of \(U\).

Data From Example 6.11

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Example 6.11 FLOW OVER A CYLINDER: SUPERPOSITION OF DOUBLET AND UNIFORM FLOW For two-dimensional, incompressible, irrotational flow, the superposition of a doublet and a uniform flow represents flow around a circular cylinder. Obtain the stream function and velocity potential for this flow pattern. Find the velocity field, locate the stag- nation points and the cylinder surface, and obtain the surface pressure distribution. Integrate the pressure distribution to obtain the drag and lift forces on the circular cylinder.