The Small Signal Response of Annular Pneumatic Transmission Lines

Abstract

The small signal frequency response of rigid pneumatic transmission lines of annular cross section has been obtained. Dimensionless expressions for the velocity and temperature profiles are obtained by solving the unsteady continuity, momentum, and energy equations for the boundary conditions of isothermal walls and no-slip flow at the walls. As a consequence, shear flow effects are included. By electric-pneumatic analogy the series impedance and shunt admittance per unit length of line are obtained and used to find the characteristic impedance and propagation operator. These quantities are shown to be dependent on both the signal frequency and the radius ratio of the annular cross-section. The annular line results are compared with previously obtained results for circular and rectangular lines.