A study of the spatial stability of Poiseuille flow in an arbitrarily thick elastic tube to infinitesimal axisymmetric disturbances is presented. The differential equations of motion for the tube are solved analytically in terms of Bessel functions of complex arguments while those for the fluid are solved numerically by means of a power series followed by a step‐by‐step integration technique. The flow is found to be unstable for Reynolds numbers greater than a critical value that depends on the disturbance frequency and tube parameters. This critical Reynolds number varies almost as the square root of Young’s modulus for the tube material.

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