Hole Pressure Error Measurements in Pressure-Generated Shear Flow

A slit die of length 24 in., width 6 in., and height h (=132, 116, or 18 in.) is used for shear flow at small values (10−4<Re<20) of Reynolds' number Re=ρh2σw/8η2 (where ρ, σw, η denote density, wall shear stress, and viscosity). Exit suction and entrance pressure are adjusted to give a pressure gradient while keeping the pressure nearly atmospheric at the center station, near which are located one hole-mounted and three flush-mounted diaphragm-capacitance pressure transducers; these give two determinations of the hole pressure error pH and three of σw. Scatter in replicate pH measurements is usually less than ±35 dyn/cm2. The reliability of the measurements of pH and σw is established through tests made by changing h and the hole diameter d and depth b, by reversing the flow direction and by comparing σw values with values of the shear stress σ measured with a Weissenberg rheogoniometer. The rheogoniometer was also used to measure N1, the primary normal stress difference, in steady shear flow. For glycerine (a Newtonian liquid), pH is zero, as expected. For each of three aqueous solutions of a polyacrylamide (Separan AP30) at 23°C, pH data lie within ±20% of values given by the equation: pH=−0.18 N1(σw) for 350⩽N1⩽3,600 dyn/cm2. For suitable values of h and d, doubling h and d has little, if any, significant effect on pH. If the second normal stress difference N2 is small compared to N1, the pH data are compatible with the predictions of the theory of Higashitani and Pritchard applied to holes of circular cross-section. Our pH data for Newtonian and non-Newtonian liquids disagree with those of Han and Kim. When wall pressures are measured and used to determine the state of stress in dilute polyacrylamide solutions flowing through slit dies, our results show that hole pressure errors can be safely ignored in shear stress (and viscosity) determinations, but not in determinations of normal stress differences.