An experimental test of the theory of waves in fluid-filled deformable tubes

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Abstract
It seems that no treatment of pulsating flow in deformable tubes is complete without a reference to the work of Womersley (1955) which for an infinitely long tube deals with the waves of axismmetric transverse motion and of longitudinal motion of the walls. This theory has so far been subjected to experimental test only for tethered tubes in which longitudinal wall motion is absent.A series of measurements of the longitudinal motion has been made on horizontal water-filled latex tubes suspended by an array of strings so that there is minimal longitudinal constraint except at the ends, which are fixed. One end of the tube is driven by oscillating flow produced by a piston; the other end is closed. Theory and experiment agree when the tube is long provided an entrance length greater than a wavelength is included. Tubes which are short enough for reflection from the closed end to be significant present a more complicated problem. It is found that in the entrance length the theory of Womersley cannot be applied. A more refined theory is required which takes into account a distributed end constraint more completely than as a simple boundary condition.Experiments on tethered tubes in which longitudinal wall motion is absent are also presented. These serve to demonstrate that the theory for such tubes agrees with measurements without any appreciable end effect and also shows that the small viscoelasticity of the latex rubber is correctly included.