Admissible Reynolds numbers for Poiseuille flow in jet viscometer orifices

Abstract

At low Reynolds numbers for which the flow through a jet viscometer orifice strictly obeys the Poiseuille equation, the effective hydrodynamic length L 0 which may be calculated from the volume flow rate, the applied pressure difference, the radius of the orifice, and the density and low rate of shear viscosity of the liquid is much larger than the length L of ‘constant diameter’ of the orifice. It was shown before that a close approach, say 95%, to fully developed flow in the ‘constant diameter’ section of these short orifices is possible at sufficiently low Reynolds numbers, but it is shown now that L 0 may be used to calculate the largest admissible Reynolds number for 95% approach to fully developed flow. The flow in jet visco-meter orifices may be described by the Poiseuille–Hagenbach equation. At very low Reynolds numbers there is strict Poiseuille flow. This is followed by a short range of Reynolds numbers in which the inertia force correction factor m ( see equation (1)) increases steeply with the Reynolds number to reach a plateau value at a diameter Reynolds number of about 20. Although L 0 is not constant over the whole range of admissible Reynolds numbers, it satisfies the Poiseuille-Hagenbach equation if it is used with the appropriate m -value for each orifice and flow condition. For quantitative measurements of the temporary viscosity reduction of a liquid by an applied shear stress, care must be taken to avoid the transition region in which m varies with Re , because the Reynolds number Re can only be calculated with the low rate of shear viscosity of the liquid. It is important to find the mean rate of shear for any particular temporary viscosity reduction. Within the admissible range of Reynolds numbers, this may be derived from the Poiseuille equation. It is shown that the temporary viscosity reduction curve of one liquid which was measured with three jet orifices of different m-Re characteristics was a unique curve.