The two major fluid flow systems of the human body, blood circulation and respiration, experience timewise pulsations. The variations of the fluid velocity during a pulsation/respiration cycle give rise to transitions in the flow regime during the course of a cycle. At the lowest fluid velocity encountered in the cycle, it is likely that the flow is laminar. As the velocity increases, the laminar regime may transist into a regime called transitional intermittent. Further increases in velocity may lead either to the fully developed intermittent regime or to the fully developed turbulent regime. Once the velocity attains a maximum and begins to decrease, the process of laminarization may be initiated wherein a succession of flow regimes may occur in opposite order to that described in the foregoing. The current capabilities of numerical simulation are limited to a single, user-specified flow regime, either laminar or turbulent. Consequently, the successive spontaneous flow regime transitions encountered in human-body fluid flows have been heretofore beyond the reach of biomedical investigators. Indeed, a thoroughgoing literature review failed to unearth any biomedical-oriented publications in which flow regime transitions have been taken into account. The present investigation is aimed at applying, for the first time, a flow transition model previously developed for steady flows to unsteady flows. The flows to be considered are timewise periodic, with amplitudes, periods, and mean values appropriate to blood flows in large arteries. Special consideration will be given to the magnitudes of the wall shear stresses that are created by such flows, since the accumulation of plaque depends decisively on the shear. The work will also take account of variations in the flow geometry.