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Consider three-dimensional potential flow. The following figure shows a doublet of strength u located at x = 1 and a doublet of strength located at x = a² 1. Show that the surface r = a corresponds to y = 0 if μ = -a³μ/1³, and hence deduce that the stream function for a doublet of strength located a distance / from the center of a sphere of radius a is 3 μl μα w(r, 0) -sin² ß + sin² a. Απξ 4rd³n Also deduce that the corresponding velocity potential is μl μα (r, 0) = cos B - cos a 2 Απξα 4rd³n² Show that the force, which acts on a sphere of radius a owing to a doublet of strength u located a distance / from the center of the sphere along the x-axis is F = 3pμ²a³1 2π(1²-a²)¹ a ²)¹ ex. 0 H Superposition of doublet of strength and doublet of strength * which leads to doublet of strength μ outside a sphere of radius a.