Distorted Pressure Histories due to the Step Responses in a Linear Tapered Pipe : 6th Report, For Arbitrary Cross-sections

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Although much progress has already been made in solving problems in step responses of pressure in a linear tapered pipe, new developments are still needed before the two-dimensional wave equation can be solved routinely. This paper describes one such development. A new method of solving a one-dimensional wave equation in linear tapered compound pipes with arbitrary cross-sections has been devised. Results obtained by this theory are compared with experiments in pipes with square cross-sections. And we obtained the following conclusions: (1) Damping coefficients in an arbitrary cross-section are defined and are expressed analytically for some representative cross-sections. (2) The viscous solution of a wave equation obtained by Laplace transform explains well distorted pressure histories in a linear tapered pipe with an arbitrary cross-section. (3) Pressure waves in a square cross-section include higher modes of frequency and damp more rapidly than those in a circular cross-section. but fundamental characteristics as waves are independent of the cross-section of the pipe except for the small aspect ratio.
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