caa a22 4500 465814182 CHVBK 20180323112123.0 cr unu---uuuuu 170327e19900701xx s 000 0 eng 10.1007/BF01339886 doi (NATIONALLICENCE)springer-10.1007/BF01339886 Cancellation of errors in the Higashitani-Pritchard treatment of hole pressures generated by viscoelastic liquids in creeping flow past a transverse slot [Elektronische Daten] [M. Yao, D. Malkus] Analytical studies of the hole pressure for non-Newtonian creeping flow past a transverse slot are pursued with particular interest in the formulation of Higashitani and Pritchard (HP). To correct the flaws in the treatment of HP's original work, 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 fortuitouserror cancellation phenomenon in the derivation of the HP formula: namely, the error caused by one key flaw is fortuitously cancelled out by the error introduced through another key flaw. For second-order fluids and Tanner's "viscometric model” (under certain assumptions) the cancellation of errors is proved to be exact. It is this cancellation of errors that provides a theoretical explanation for the paradox between an apparently flawed derivation and the fortunate success of the HP prediction. Steinkopff, 1990 H ole pressure nationallicence e rror cancellation nationallicence n on-Newtonian fluid, HPBL equations nationallicence m odified hole pressure relation nationallicence Yao M. Center for the Mathematical Sciences and Department of Engineering Mechanics, University of Wisconsin-Madison, 610 Walnut Street, 53705, Madison, Wisconsin, USA aut Malkus D. Center for the Mathematical Sciences and Department of Engineering Mechanics, University of Wisconsin-Madison, 610 Walnut Street, 53705, Madison, Wisconsin, USA aut Rheologica Acta Steinkopff-Verlag 29/4(1990-07-01), 310-322 0035-4511 29:4<310 1990 29 397 https://doi.org/10.1007/BF01339886 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01339886 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yao M. Center for the Mathematical Sciences and Department of Engineering Mechanics, University of Wisconsin-Madison, 610 Walnut Street, 53705, Madison, Wisconsin, USA aut NATIONALLICENCE 700 1- Malkus D. Center for the Mathematical Sciences and Department of Engineering Mechanics, University of Wisconsin-Madison, 610 Walnut Street, 53705, Madison, Wisconsin, USA aut NATIONALLICENCE 773 0- Rheologica Acta Steinkopff-Verlag 29/4(1990-07-01), 310-322 0035-4511 29:4<310 1990 29 397 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer