Show that, for irrotational axisymmetric flows in cylindrical coordinates, the streamfunction satisfies the following equation:

\[\frac{\partial^{2} \psi}{\partial r^{2}}-\frac{1}{r} \frac{\partial^{2} \psi}{\partial \theta^{2}}+\frac{\partial^{2} \psi}{\partial z^{2}}=0\]