The hydrodynamic equations for a cylindrically layered sample of smectic A liquid crystal are considered. Governing equations for the flow, pressure and smectic layer undulations are derived using a perturbation ansatz. Expressions for the radial flow velocity and the layer displacement are derived analytically and presented in the purely radial flow case. An expression for the relaxation rate is found and a bound for the spatial wave number is determined when zenithal flow is also considered. Plots of the solutions are given for illustration. Vindication of previous results is discussed.