Interaction between torsional waves propagating in an elastic pipe and an adjacent fluid

Abstract

The effect of an interior or exterior viscous fluid on the propagation of torsional waves in an elastic pipe has been studied theoretically for the application of ultrasonic technologies to the measurement of fluid properties. The theoretical analysis deals with the speed and attenuation of torsional waves affected by the adjacent viscous fluid. Expressions for the torsional wave speed and attenuation are obtained as functions of the viscosity and density of the adjacent fluid by exact and asymptotic analyses. Exact solutions lead to an implicit relationship between the quantities of interest with transcendental equations. Asymptotic solutions derived by the perturbation method lead to an explicit relationship. The approximate expression is in good agreement with the exact one for a wide range of parameter values. The results provide quantitative information of the wave speed reduction and attenuation affected by the fluid viscosity.