Unsteady Flows in Lines with Distributed Leakage

Unsteady, nonuniform flows in pipelines which experience leakage are analyzed. Particular attention is given to the orifice manifold. Plows in a continuous manifold can be treated in several ways: (1) When the leakage is of such magnitude that capacitance can be neglected, the flow is governed by a parabolic equation; (2) more generally, if elastic properties are included the governing equations become hyperbolic; and (3) impedance methods provide analytic solutions for steady periodic flows. The response patterns to various input functions are shown; it is seen that the magnitude of the leakage strongly dictates the nature of the responses. A laboratory investigation of low-frequency oscillating flows in a discrete manifold is included. For such a class of flows the parabolic equation is valid; the problem encountered is one of mass transfer, and the responses are similar to those found in diffusion problems.