The numerical simulation of a ﬂow through a duct requires an externally speciﬁed forcing that makes the ﬂuid ﬂow against viscous friction. To this end, it is customary to enforce a constant value for either the ﬂow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct ﬂow before and after a geometrical modiﬁcation that induces a change of the viscous drag, both approaches lead to a change of the power input across the comparison. Similarly, when carrying out direct numerical simulation or large-eddy simulation of unsteady turbulent ﬂows, the power input is not constant over time. Carrying out a simulation at constant power input (CPI) is thus a further physically sound option, that becomes particularly appealing in the context of ﬂow control, where a comparison between control-on and control-off conditions has to be made. We describe how to carry out a CPI simulation, and start with deﬁning a new power-related Reynolds number, whose velocity scale is the bulk ﬂow that can be attained with a given pumping power in the laminar regime. Under the CPI condition, we derive a relation that is equivalent to the Fukagata–I ... mehrwamoto–Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of naturally including the required control power. The implementation of the CPI approach is then exempliﬁed in the standard case of a plane turbulent channel ﬂow, and then further applied to a ﬂow control case, where a spanwise-oscillating wall is used for skin-friction drag reduction. For this low-Reynolds-number ﬂow, using 90% of the available power for the pumping system and the remaining 10% for the control system is found to be the optimum share that yields the largest increase of the ﬂow rate above the reference case where 100% of the power goes to the pump.