Laminar flow in the entrance region of parallel plates

Explicit solutions are obtained for the pressure and velocity field for flow between parallel plates at low Reynolds numbers by linearizing the inertia terms in the Navier-Stokes equations, parallel and perpendicular to the flow. A uniform inlet velocity is assumed. The procedure permits an arbitrary inlet velocity symmetric with respect to the axis of flow. The distance from the inlet to the point where center-line velocity reaches 99% of the asymptotic value is in good agreement with the results reported by Morihara et al. (1973) for all Reynolds numbers examined (1, 10, 20, 50, 100, 200, 500, 1000). The size of the pressure gradient increases with decreasing downstream distance.