Comparison of the exact and asymptotic solutions to the problem of oscillatory flow of a viscous fluid in a cylindrical pipe

The oscillatory flow of an incompressible viscous fluid in a cylindrical pipe under a given harmonic oscillation of the average velocity across the cross section was studied. The transfer function and amplitude-phase frequency characteristics were determined. Using these functions, the effect of the oscillation frequency on the shear strength relative to the average velocity across the cross section was evaluated. By comparing the exact and asymptotic solutions, new asymptotic formulas were proposed, which are of great importance for studying the oscillatory flow of viscoelastic fluids in cylindrical pipes. The obtained results can be used in biomedical research for the estimation of pressure losses, in the analysis of pulsatile flows in oil and gas pipelines for the optimization of pump parameters, as well as in the medical field for modeling the pulsatile flow in the assessment of the elasticity of human blood vessels.