Consider laminar flow down a wide rectangular channel making an angle \(\theta\) with the horizontal. The fluid has kinematic viscosity \(v\) and the volume flow rate per unit width is given by

\[ q=\frac{g y^{3} \sin \theta}{3 v} \]

where \(y\) is the fluid depth perpendicular to the channel bottom. Find Manning's \(n\) for the flow.