Surface tension and energy conservation in a moving fluid

How do surface tension forces contribute to the energy budget in a flowing liquid with a free surface? One might expect that these forces always produce power when the fluid is flowing. Here we show, however, that there is no power term if the surface itself does not move, i.e., for a fixed control volume. The energy conservation law for a free surface in a control volume moving with a specified velocity, independent of the liquid velocity, is derived and extended to the full system energy including the bulk flow. The Laplace pressure and tangential capillary forces then appear naturally, and the power provided by the latter forces is given through the velocity of the control volume and not that of the flow.