Hydrodynamics of a Viscous Fluid Pressed-out (or Drawn-in) by Bounding Wall : The 1st Report, Basic treatment

Abstract

(1) To study the flow of viscous fluid trapped between the teeth of a gear pump, the differential equation determining the pressure of flow pressed-out (or drawn-in) by the boundary walls has been derived on the basis of Navier-Stokes' equations (Fig.1). The inside pressure rises or falls respectively at the opening, as the sectional area of the flow is decreasing or increasing. The pressure distribution along the flow is parabolic, with maximum (or minimum) value at the innermost section. (2) The differential equation determining the pressure in the layer of laminar flow pressed-out (or drawn-in) by two adjacent plane or curved walls has been derived. To obtain a general view of the nature of flow, the solution has been worked out for the circular planes. The rise or fall of the inside pressure is proportional to the coefficient of viscosity and time rate of discharge, and is inversely proportional to the 3rd power of the thickness of fluid layer.