In this Brief Communication, we determine an approximate relation that gives the mean time power required to control the wake flow downstream from a circular cylinder. The control law is the sinusoidal tangential velocity imposed on whole or part of the cylinder surface. The mean control power thus depends on four parameters: the amplitude and the Strouhal number of forcing, the control angle that defines the controlled upstream part of the cylinder, and the Reynolds number. This relation indicates that the control power grows like the square of the forcing amplitude, like the square root of the forcing Strouhal number, linearly with the control angle and varies like the inverse of the square root of the Reynolds number. We show that the values obtained with this approximate relation are in very good agreement with the corresponding values given numerically. Finally, the energetic efficiency of the control is discussed. We claimed that the most energetically efficient control law corresponds a priori to low forcing amplitudes applied to a restricted upstream part of the cylinder for relatively high values of the Reynolds number.