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.
