Exact and limiting solutions of fluid flow for axially oscillating cylindrical pipe and annulus

摘要

The Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatoryflows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillatingcylindrical annulus. In both the cases, in addition to the exact expressions for the velocity profiles, particular emphasis hasbeen given for the determination of approximate velocity distributions for the high frequency and low frequency or quasistaticlimits. It is shown that, for sufficiently large value of an appropriate frequency parameter, the velocity distributioninside the axially or longitudinally oscillating cylindrical annulus can be approximated as a superposition of the velocitydistribution inside an axially oscillating cylindrical pipe of radius R_o and the velocity distribution outside an axially oscillatingcylindrical pipe of radius R_i , where R_i and R_o are the inner and outer radii of the axially oscillating annulus, respectively.