Ronald C. Hirschfeld Steve J. Poulos Embankment-dam engineering 1973 Riley, Chichester Sussex 454 (Also published in the U.S. and Canada.)

Abstract

It is shown that the thrust, T, exerted by a jet on the tube from which it flows, and the corresponding die-swell ratio, D, are closely related and dependent on the axial velocity and stress profiles at the exit plane. Velocity-profile data, calculated by Tanner using a finite element method, have been used to demonstrate that for a Newtonian liquid the reduction in measured thrust from the expected value arises from a re-arranged, non-parabolic axial velocity profile and the related re-arranged non-zero axial stress profile at the exit plane. The axial stress re-arrangement is the major effect.Using the correction-curve thus derived to determine the normal stresses, ν1 + 12ν2 aqueous and non-aqueous polymer solutions gives values that are higher than the “correct” results by a significant, substantial amount. The difference is not due to neglect of the second normal stress difference, ν2, nor to the neglect of the wall pressure at the exit plane, which is shown experimentally to be very small. It is suggested that the difference, which is a function only of the shear stress (or rate of shear) at the wall, may arise from a difference in the stress profile associated with the velocity re-arrangement at the exit between Newtonian liquids and elasticoviscous liquids for which the extensional viscosity may be high.