An exact solution of time varying pipe flow with a fluctuating velocity superimposed on the mean flow is analyzed. The velocity profiles, together with the profile parameters at separation, are computed from a computer program. The results are compared with the model for relaxed (steady) and unrelaxed (unsteady) separation criteria proposed by V. A. Sandborn and S. J. Kline. For very low frequencies, the correlation curves appear to have a reasonable agreement with the proposed relaxed separation criterion. For high frequencies, the correlation curves have been found to fall approximately on the unrelaxed separation criterion. This result demonstrates further that adjustment time is an important factor for separation to be relaxed or unrelaxed, a new concept proposed by Sandborn. In addition, J. T. Stuart's solution for the flow along an infinite flat plate with normal suction and periodic external velocity is further analyzed. The results again prove to agree with the proposed new concept.