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This work presents analytical and numerical results for the pressure field distribution along the axis of tubular geometries with arbitrary axisymmetric cross sections with an arbitrary time- and position-dependent gas source. Several areas of applied physics deal with problems in high-vacuum and ultra high-vacuum technology that present tubular form. In many cases one finds tubes with non uniform cross sections, like parts of particle accelerators, colliders, storage rings, gravitational antennas, and electron devices, like klystrons, electron microscopes, and also parts of vacuum systems in general, for instance, bellows, conical pipes and others. In this work one can get the detailed pressure distribution is not determined. This work presents and describes in detail the pressure field in tubes with arbitrary axisymetric cross sections. Details of the mathematical and physical formulations and modeling are given; specific conductance and specific throughput are defined; and a detailed discussion about the boundary conditions is given. These concepts and approach are applied to usual realistic cases, like conical tubes and bellows, with typical laboratory dimensions.
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