• Corpus ID: 219261026

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

@article{Mandre2020WorkminimizingKO,
  title={Work-minimizing kinematics of a flat plate moving parallel to its surface in a fluid},
  author={Shreyas Mandre},
  journal={arXiv: Fluid Dynamics},
  year={2020}
}

• S. Mandre
• Published 3 June 2020
• Engineering, Physics
• arXiv: Fluid Dynamics

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.