Approximation dispersion equations for thin walled liquid filled tubes

The dispersion equation for an initially stressed thin walled viscoelastic tube filled with a linear elastic fluid is derived. The validity of the long wavelength approximation of an inviscid liquid in a viscoelastic tube is discussed. An approximate dispersion equation applicable in the higher frequency range is derived. Calculations confirm that long wavelength approximation is excellent for the analysis of blood flow through arteries. Even for large arteries, e.g., the human aorta, this means that the first 10 to 15 harmonics of a Fourier analysis of the pressure pulse can be analyzed. The inviscid approximation can be used to determine the phase velocity if the wavelength and viscosity are small.