The object of our paper is the formation of optical fringes in a time average hologram produced by vibrating fluid in axi-symmetric tube. Fluid vibrations in axi-symmetric geometry according to the first harmonics are analyzed. This problem has a practical application in the analysis of transverse vibrations of fluid in an axi-symmetric pipe. The numerical model is developed using finite element techniques in axi-symmetric geometry. Irrotational motions of ideal compressible fluid are analyzed. Finite element model of the system is based on the approximation of nodal displacements via the shape functions. Thus the field of the amplitudes of the harmonic variation of the volumetric strain is calculated exploiting conjugate approximation techniques. Obtained volumetric strains are used for the numerical construction of interference pattern of the vibrating fluid. For this purpose the Abel transform which is usually exploited in axi-symmetric problems is generalized for the problems with the periodic variation of displacements. The obtained interference patterns are used in hybrid experimental – numerical procedures and help to interpret experimental results.

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