Unified Approach to the Solution of Problems of Unsteady Laminar Flow in Long Pipes

Abstract

The paper presents a unified approach to the solution of laminar pipe-flow transients in which the forcing function may depend on the motion itself. The key to the solution procedure is a power series expansion of the local velocity in terms of radial position, involving a single time-dependent coefficient. The method of analysis is applied to the solution of two particular cases of transients, namely flow establishment, without and with inflow, respectively. It is found to yield results that are in excellent agreement with other known analytical solutions and experimental observations.