The problem of interest is a uniform, inviscid flow, with velocity U that has a sphere of radius R placed in the flow. There is a obvious axis of symmetry, the φ direction, (not to be confused with φ[r,θ], the velocity potential) which is oriented parallel to the flow. The problem will then be solved in the r and θ coordinate directions. The angle θ = 0, is at the three o'clock position on the sphere and θ=π at nine o'clock (which is the entire range of θ since the angle φ would go from 0 to 2 π if necessary -- but not in this problem).