Oscillatory flow superimposed on steady laminar flow in a pipe (or channel) is considered and guiding calculations are performed to inspect for conditions under which removal of particles and fouling layers from surfaces is superior. Calculations are performed to derive conditions of flow reversal, which is cited in literature as one of the requirements for removal of fouling layers. As wall shear stress is a relevant measure to evaluate removal of particle/fouling layers, calculations are performed to derive the conditions under which wall shear stress with superimposed oscillatory flow is energy efficient. The results are presented in the parameter space of a pressure gradient ratio (oscillatory/steady) and Womersley number. This phase plot would be useful for experimentalist to locate operating regions whence energy efficient removal can be achieved using superimposed oscillatory flow.