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Poiseuille Flow in Jet Viscometer Orifices

R. Schnurmann, R. S. Johnson

1968
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Proceedings of the Royal Society A
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Plates 12 and 13] A photomicrographic technique is described for determining the geometrical shape of glass jet viscometer orifices. These orifices are composed of a radiused entrance, a short constant diameter section, and a 'diffuser ty p e' exit in which pressure recovery takes place. The length/diameter ratio of the constant diameter section of these orifices governs the highest Reynolds number for attaining 95 % parabolic velocity profile, as calculated on the basis of Sparrow, Lin &
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... parrow, Lin & Lundgren's (1964) theoretical analysis of the development of parabolic velocity profile in the entrance region of tubes. Thirteen orifices were examined, and for these the highest admissible diameter Reynolds numbers were between 12 and 81. Thus, rates of shear, which can be calculated from the Poiseuille equation with an error of less than 1*5 %, can amount to 6 x 105 s_1 without the liquid passing through the orifice suffering a temperature rise by viscous heating of more than 0-05 °C. No kinetic energy correction is required for Reynolds numbers less than 10. For larger Reynolds numbers a correction should be made. The kinetic energy correction coefficient increases steeply with the Reynolds number, but the rate of increase depends upon the shape of the orifice profile. The largest kinetic energy correction coefficients of the thirteen orifices have values between 0-55 and 0*84. Within the range of Reynolds numbers admissible for 95 % development of parabolic velocity profile, substantial temporary viscosity reductions were found. Neither surface tension nor elastic properties of the liquid affect the flow behaviour under the described experimental conditions. I n t r o d u c t i o n Temporary viscosity reduction of liquids at high rates of shear is best measured with a jet viscometer, because the high shear stress acts only on a small volume of liquid as it passes through the orifice of the instrument, so th at even a t rates of shear of 106s_1, which the liquid encounters in the orifice, viscous heating of the liquid is negligible. This is only the case when orifices of a small length/diameter ratio of not more than 2*5 (Morris 1948) are used, because then the high rates of shear can be produced with a pressure head not exceeding 1 atm. The mean rate of shear is clearly defined, provided th a t Poiseuille flow is established in such a short zone. The range of Reynolds numbers over which 95 % approach to parabolic velocity profile in accordance with Sparrow, Lin & Lundgren's (1964) hydrodynamic theory is assured, depends upon the size and shape of the orifice. I t is the shape, and in particular the exit region of these small orifices, which governs the pressure recovery in the liquid passing through them and the rate of variation of the kinetic energy correction coefficient with the Reynolds number. Rates of shear up to 6 x 105s-1 can be obtained without producing by viscous heating a temperature rise of more than 0-05 °C in the sheared liquid. Temporary viscosity reduction is expressed in terms of (AP/$)0where A Pi s the pressure head under which a given volume V of liquid passes through 28 [ 429 ] Vol. 303. A.

doi:10.1098/rspa.1968.0059
fatcat:mbbyvsibiverpeuet3x6d5sqhe