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.
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