An upstream potential flow analysis is performed for the entrance region of a narrow channel in the presence of fluid inertia forces. Existing thin film solutions for slider bearings have an anomalous singularity in the pressure gradient, due to the parabolic nature of the thin film equations. Although the geometry of the present paper is somewhat different than that of the slider bearing, the problem of the singularity is resolved and some information can be obtained regarding inlet flow in the more practical slider bearing case. The potential core flow solution consists of a uniform flow first-order solution, which accelerates due to the narrowing of the bearing, and a second-order displacement solution which decelerates due to the growth of boundary layers. The resulting pressure and velocity behavior are illustrated. To form a uniformly valid solution, the present upstream analysis must be matched to the downstream (thin film) result.

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