Error Cancellation in HPBL Derivation of Elastic Hole-Pressure Error

Abstract

Analytical studies of the hole-pressure error for non-Newtonian creeping flows over a transverse slot are pursued with particular interest in the theory of Higashitani, Pritchard, Baird and Lodge (HPBL). To correctly apply the HPBL theory a modified hole-pressure relation (MHPR) is employed. Some important mathematical properties of the MHPR are presented. By studying the MHPR in streamline coordinate formulation we find a fortuitous error cancellation phenomenon in the derivation of HPBL formula. For second-order fluid and Tanner's viscometric model (under certain assumptions) the error cancellation is proved to be exact. It is this error cancellation phenomenon that provides a complete theoretical explanation for the paradox between an apparently flawed derivation and the fortunate success of the HPBL prediction. Keywords: Hole pressure error; Error cancellation; Nonnewtonian fluid; Second order fluid; Modified hole pressure relation.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1989
Accession Number
ADA219854

Entities

People

  • D. S. Malkus
  • M. Yao

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Air Force
  • Base Flow
  • Cancellation
  • Constitutive Equations
  • Coordinate Systems
  • Couette Flow
  • Equations
  • Equations Of Motion
  • Flow
  • Flow Fields
  • Flow Visualization
  • Mechanics
  • Path Integrals
  • Scientific Research
  • Shear Flow
  • Shear Stresses
  • Two Dimensional

Readers

  • Approximation Theory.
  • Fluid Dynamics.