Flow control techniques for turbulent drag reduction in internal flows are typically evaluated under two alternative flow conditions, i.e. at constant mass flow rate or constant pressure gradient. Successful control leads to reduction of drag and pumping power at constant mass flow rate, whereas constant pressure gradient leads to an increase of the mass flow rate and pumping power. In practical applications, however, a compromise between the energy consumption and the corresponding convenience (flow rate) achieved with that amount of energy has to be reached so as to accomplish a goal which in general depends on the specific application.
Based on this idea, we describe the derivation of two dimensionless parameters which quantify the total energy consumption and the required time (convenience) for transporting a given volume of fluid through a given duct. Performances of existing drag reduction strategies are re-evaluated within the present framework.