Pulsating laminar flow in a cylindrical pipe with through flow

The fully developed unsteady laminar motion of a compressible viscous fluid in a pipe of circular cross-section is analyzed by dividing it into two components, the time-averaged mean flow and the oscillatory component. When a mean flow exists, the convective acceleration terms in the equation of motion have to be considered according to the compressibility of the fluid and the magnitude of the mean flow velocity. (The convective acceleration terms are negligible for oscillatory flow alone if acoustic approximations are valid.) The paper provides a mathematical treatment of the problem and shows the effect of the mean flow on the velocity distribution and propagation constant of the oscillatory component of motion, and also shows the effect on the transfer matrix.