A Transient Response Approximation for Noncircular Fluid Transmission Lines

Abstract

A method is given for determining the transient response approximation for noncircular fluid transmission lines. The results are presented in terms of a characteristic frequency which depends only on the laminar viscous steady flow resistance and inductance of the noncircular line. The components of an equivalent circuit based on standard transmission line theory are analyzed, and approximations of the series impedance, shunt admittance, propagation operator, and characteristic impedance are presented. These circuit parameters are transformed into the time domain to give a simple approximation for the step response of noncircular fluid-filled lines. The solution is expressed as a single complementary error function. Results are shown for air at 27°C. The results are restricted to laminar flow conditions.