  We derive a limit on energy savings in controlled channel flow. For flow in a
channel driven by pressure, shear, or any combination of the two, and
controlled via wall transpiration or spanwise wall motion, the uncontrolled
laminar state requires the least net energy (accounting for the energetic cost
of control). Thus, the optimal control solution is to laminarize the flow.
Additionally, we raise the possibility of beating this limit. By simultaneously
applying wall transpiration and spanwise wall motion, we show that it may be
possible to attain sustained sub-laminar energy expenditure in a controlled
flow. We provide a necessary design criterion for net energy savings.
