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Ideal Flow around a cylinder: Consider an ideal flow past a long cylinder of radius R. As shown, the cylinder is assumed to be aligned in the z direction, and far away there is a velocity U in the x direction.

(a) Calculate the potential function for this flow using appropriate boundary conditions.

(b) Calculate the stream function for this flow.

(c) Obtain the velocity profile around the cylinder using either (a) or (b).

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