Hydrodynamics of a Viscous Fluid Pressed-out (or Drawn-in) by Bounding Wall : The 3rd Report, Pressure Distributions over the Fluid Layer and on the Boundary Wall

Abstract

This paper supplements to the 1st Report (1) the discussion of the pressure distribution over the fluid layer, and (2) the illustrative treatments for the layer of non-uniform thickness. (1) The pressure distribution over the section of layer is parabolic, in assumption that the fluid velocity in the direction normal to the wall is proportional to the distance from the fixed wall. (2) When the walls are drawn apart, the pressure on them is lower than that in mid-layer, and when pressed close, it is higher. (3) The assumption of uniform pressure within the layer does not satisfy the continuity for any point, but can do only for any section, that is no other than the basic equation obtained in the 1st report. (4) The pressure rise or fall on the bounding wall is noticable when the thickness of the layer is not uniform with narrow opening.