Apply the nondimensionalization technique to the Navier-Stokes equation for the \(x\)-component; the incompressible Navier-Stokes momentum equation is given by

\[
ho\left[\frac{\partial u}{\partial t}+(u \cdot abla) uight]=-abla P+\mu abla^{2} u+ho g
\]

where \(ho\) is the density, \(P\) is the pressure, \(\mu\) is the dynamic viscosity, \(u\) is the flow velocity, \(t\) is time, and \(g\) is the gravitational acceleration.