Measurements of hole pressure at various depths for Newtonian and non-Newtonian fluids

Measurements of hole pressure for shallow recesses were made for two Newtonian and two non-Newtonian fluids. The study was conducted by mounting two pressure transducers opposite each other in the walls of a wide rectangular channel and measuring the pressures with one transducer flush and the other recessed. Data were obtained for recesses up to 60% of the hole diameter and for Reynolds numbers up to 400. For the Newtonian fluids, the hole pressure was negative and its magnitude increased with Reynolds number, reaching up to 90% of the wall shear stress. The magnitude also increased with recess depth, attained a maximum when the depth was 0.16 of the hole diameter, and then decreased for deeper recesses. The two non-Newtonian fluids were polymer solutions, one was concentrated and shear thinning the other dilute and non-shear-thinning. For both fluids, the hole pressure was positive and the magnitudes were up to ten times those for the Newtonian fluids, which indicates that elastic effects were much larger than inertial effects. It was also found that the ratio of the hole pressure to the wall shear stress was roughly constant, i.e., roughly independent of the Reynolds numbers. For all fluids, the hole pressure was detectable for recesses as small as 2% of the diameter.