In this study, an approximate analytic solution for phase-shift (and thus mass flow) prediction along the length of the measuring tube of a Coriolis flowmeter is investigated. A single, straight measuring tube is considered; added masses at the sensor locations, are included in the model, and thus in the equation of motion. The method of multiple timescales, an approximate analytical technique, has been applied directly to the equation of motion, and the equations of order one and epsilon have been obtained analytically for the system at resonance. The solution of the equation of motion is obtained by satisfying the solvability condition (making the solution of order epsilon free of secular terms). The measuring tube is excited by the driver, and the phase-shift is measured at two symmetrically located points on either side of the mid-length of the tube. The effects of system parameters on the measured phase-shift are discussed.

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