Hole-Pressures in Plane Poiseuille Flow over Transverse Slots

摘要

The derivation of the stress-integral form of the Higashitani-Pritchard-Baird-Lodge relation cannot be applied to plane Poiseuille flow. It ignores the contribution of the streamwise pressure gradient, and doing so can lead to contradictions. Furthermore, the variable change which leads to the stress-integral form of the HPBL relation is not valid in a second-order fluid approximation for slow flows. Correcting these deficiencies leads to a modified relation which appears intractable. Nevertheless, the Tanner-Pipkin result that P sub e = N sub 1/4 in a second order fluid is valid when properly interpreted. Keywords: Creeping flow; Viscometric flow; Johnson-Segalman fluid.