  The transport of energy in a moving fluid with a simply connected free
surface is analyzed, taking into account the contribution of surface tension.
This is done by following a "control volume" with arbitrary, specified
velocity, independent of the flow velocity, and determining the rates of energy
passing through the boundaries, as well as the energy dissipation in the bulk.
In particular, a simple conservation equation for the surface area is written
down, which clearly shows the contribution of the Laplace pressure at the free
surface and the tangential surface tension forces at its boundary. It emerges
as the mechanical conservation law for the surface energy in its general form.
For a static control volume, all contributions from surface tension disappear,
except that the pressure has to be modified by the Laplace contribution.
