Governing equation for the flow field in the form of a velocity potential

The governing equation for inviscid flows in three dimensions is Laplace's equation for the potential function, φ[r,θ]  

Note that this first cell is inactive, but shows the equation, the next one really works

laplaceeq = Simplify[1/(r^2*Sin[θ])*
   (D[r^2*Sin[θ]*D[φ[r, θ], r], r] + 
     D[Sin[θ]*D[φ[r, θ], θ], θ])]