Consider the flow of a liquid of viscosity \(\mu\) and density \(ho\) down an inclined plate making an angle \(\theta\) with the horizontal. The film thickness is \(t\) and is constant. The fluid velocity parallel to the plate is given by

\[ V_{x}=\frac{ho t^{2} g \cos \theta}{2 \mu}\left[1-\left(\frac{y}{t}\right)^{2}\right] \]

where \(y\) is the coordinate normal to the plate. Calculate \(\Phi\) and \(\Psi\) for this flow and show that neither satisfies Laplace's equation. Why not?