State the form of the Laplace equation in axisymmetric spherical coordinates

State the form of the Laplace equation in axisymmetric spherical coordinates. Verify that the following functions satisfy this equation: r cos θ; cos θ/r 2 A linear combination is also a solution by superposition. Thus the following solution for φ obtained by taking the combination represents the potential flow around a sphere of radius R: φ = v∞ [ r cos θ + R3 2 cos θ r2 ] Verify that the impermeability condition is satisfied at r = R, the radius of the sphere, by showing that vr = ∂φ/∂r is zero at these locations.