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 , 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.
A Simple but Complete Solution for the Step Response of a Semi-Infinite, Circular Fluid Transmission Line
J. T. Karam, Jr.
United States Air Force, Air Force Institute of Technology, Wright-Patterson AFB, Ohio; Automatic Control Center, Purdue University, Lafayette, Ind.
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Karam, J. T., Jr. (June 1, 1972). "A Simple but Complete Solution for the Step Response of a Semi-Infinite, Circular Fluid Transmission Line." ASME. J. Basic Eng. June 1972; 94(2): 455–456. https://doi.org/10.1115/1.3425443
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