We can see how a typical nondimensionalization for the Navier-Stokes Equations would turn out.   (Right side are positive terms.)

We substitute the Reynolds number into the equation.

Note that the Reynolds number, R U ρ/μ is multiplying the inertia (nonlinear) term and the time derivative term in this nondimensional equation.  What will happen if the Reynolds number is very small?  

You can go back and do the pressure term on your own.