= Solution
Near the closest point, in $X=x-Ut$, the gap is $h(X)\simeq h_0+X^2/(2a)$. The horizontal length scale is \b[$\ell=\sqrt{2ah_0}$], up to an inessential constant. Thus the aspect ratio $h_0/\ell\ll1$ follows from $h_0\ll a$. The <lubrication approximation> assumes an incompressible <Newtonian fluid>, no slip on the surfaces, slow variation of the gap, and negligible inertia relative to transverse viscous stress:
$$
\boxed{\frac{\rho U h_0^2}{\mu\ell}\ll1.}
$$
This is the reduced Reynolds-number condition; it is weaker than requiring a <Reynolds number> based on $\ell$ to be small. In the cylinder frame the geometry and flow are steady. <Pressure> is uniform across the narrow gap to leading order, and equal ambient <pressures> far to either side close the model. The calculation assumes a full liquid film; <cavitation> would change that <pressure> condition.
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