Abstract
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.
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