Mass flowmeters for fluids with density gradient

Abstract

Quadrature integration of flow velocity along prescribed parallel paths has been one of the preferred solutions for accurate computation of volumetric flowrate Q for over thirty years. The present work extends the quadrature volumetric flowmetering method to determining from sound speed c/sub 3/ along the same quadrature paths, the fluid temperature T, density /spl rho/ and mass flowrate M/sub F/ in the presence of a density gradient. Quadrature integration of /spl rho//sub i/ /spl times/ V/sub i/ products V/sub i/ obtained from c/sub 3i/ is useful to the extent the fluid is sufficiently pure and defined so that the uncertainty in sound speed c/sub i/ along each path generates only a small uncertainty in density pi along those same paths. Instead of "useful to the extent" one could just as well say "limited to the extent." Recognizing this limitation, it is interesting to compare the density and mass flowrate determined from (a) ultrasonic measurements of propagation across the fluid, as indicated above, with density and mass flowrate determinations based on two other known methods. These two methods are: (b) reflection coefficient measurement of fluid characteristic impedance Z, which would seem capable of leading to /spl rho/ after dividing by c; and determining /spl rho/ based on (c) torsional wavespeed in a waveguide of noncircular cross section.