Weight vector study of velocity profile effects in straight-tube Coriolis flowmeters employing different circumferential modes

The weight vector theory is applied to evaluate the effects of velocity profile on the sensitivity of Coriolis mass flowmeters employing different circumferential modes of a straight measuring tube. The study is limited to fully developed, axisymmetric steady flow. The measuring tube is modelled as a thin, elastic shell with clamped ends, and the vibrational fluid motion inside the vibrating tube is determined using potential flow theory. By applying a power series expansion with respect to the aspect ratio of the tube, the general form of the weight function is simplified, allowing (approximate) analytical evaluations of profile effects. The results show that large velocity profile effects are expected for the higher circumferential (shell-type) modes and rather lower (but generally also significant) velocity profile effects for the first circumferential (beam-type) mode.