Work-minimizing kinematics of a flat plate moving parallel to its surface in a fluid

The minimum work needed to translate a thin flat plate immersed in a fluid a given distance $D$ parallel to its surface in a fixed duration $T$ is calculated. The Reynolds number for the flow is assumed to be large so that the drag on the plate arises from skin friction. The plate starts from rest with speed $\propto t^{1/4}$ and comes to rest with speed $\propto (T-t)^{1/4}$. For distances much longer than the plate, the work-minimizing kinematics consists of an optimum startup, cruising at a constant speed, and an optimum stopping.