A Simple but Complete Solution for the Step Response of a Semi-Infinite, Circular Fluid Transmission Line

[+] Author and Article Information
J. T. Karam

United States Air Force, Air Force Institute of Technology, Wright-Patterson AFB, Ohio; Automatic Control Center, Purdue University, Lafayette, Ind.

J. Basic Eng 94(2), 455-456 (Jun 01, 1972) (2 pages) doi:10.1115/1.3425443 History: Received July 23, 1971; Online October 27, 2010


Presently, the only accurate solutions for the step response of a semi-infinite, circular fluid transmission line result from involved, time consuming, numerical finite series or integration techniques [1, 2, 3]. None of these solutions is practically suitable for either a rapid manual prediction for an arbitrary fluid line (liquid or gas), or for extension of the semi-infinite line results to the more meaningful problem of a finite line with arbitrary inputs. In the frequency domain (sinusoidal signals), a complete, verified solution exists [1, 4, 5] and theoretically could be transformed into the time domain. This was the scheme used by Brown and Nelson for liquid lines [2], but it required the numerical techniques referred to above and, in their own words, was a “very complex and tricky business.” However, simpler solutions for most operating regimes also exist in the frequency domain [6, 7]. These simple frequency domain solutions were transformed into the time domain and provided the basis for a simple solution for the step response.

Copyright © 1972 by ASME
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