One-dimensional unsteady flow in a thin liquid layer is described by the equation

\[\frac{\partial u}{\partial t}+u \frac{\partial u}{\partial x}=-g \frac{\partial h}{\partial x}\]

Use a length scale, \(L\), and a velocity scale, \(V_{0}\), to nondimensionalize this equation. Obtain the dimensionless groups that characterize this flow.