The energy theorem of electrodynamics is extended so as to apply to the plasmonic waves on
single-walled carbon nanotubes which propagate parallel to the axial direction of the system and
are periodic waves in the azimuthal direction. Electronic excitations on the nanotube surface are
modeled by an infinitesimally thin layer of free-electron gas which is described by means of the linearized
hydrodynamic theory. General expressions of energy and power flow associated with surface
waves are obtained by solving Maxwell and hydrodynamic equations with appropriate
boundary conditions. Numerical results for the transverse magnetic mode show that energy, power
flow, and energy transport velocity of the plasmonic waves strongly depend on the nanotube radius
in the long-wavelength region.