A fluid-flow model which automatically determines the flow regime was used to analyze a timewise-periodic pipe flow. Numerical simulation was employed to implement the model. The range of the instantaneous Reynolds number gave rise to four distinct flow regimes: laminarizing, fully laminar, turbulentizing, and fully turbulent. The period of the imposed harmonic oscillations was varied over a very wide range, and the magnitude of the oscillations was of the same order as that of the steady flow on which the oscillations were superimposed. A large-period limit at which the flow is quasi-steady was identified. The predicted quasi-steady fully developed friction factor for each regime was found to be in excellent agreement with steady-state results applied instantaneously. A metric in the form of the ratio of the turbulence production to turbulence destruction was used to exhibit the turbulence characteristics of each of the four flow regimes. The value of this metric was somewhat different in the laminarization and turbulentization regimes at the same instantaneous Reynolds number. This outcome suggests that the flow has memory.