Calibration of hole-pressure measurements in non-Newtonian flow by numerical methods

The crossed-triangle macroelement has been identified as and ideal element for Newtonian fluid flow calculations involving fluids with integral constitutive equations. In spite of an instability of the pressure approximation, these elements have been shown to have convergent velocities in Stokes flow, and there is strong evidence that pressure-smoothing schemes recover accurate pressures. Earlier studies by the author of Newtonian flow over transverse slots at low Reynolds numbers showed that excellent results could be obtained using the element. Studies of non-Newtonian flows in the same geometry showed good qualitative agreement with laboratory experiment but led to some puzzling predictions of the pressure difference between the top and bottom of the slot (the hole-pressure). In this paper, those puzzling predictions are reexamined, and the deviations from expectation are reinterpreted. They appear to make physical sense and have important ramifications for the calibration of devices which measure the primary normal-stress difference by continuous measurement of the hole-pressure.