The interactions of charged particles with carbon nanotubes are studied by means of the linearized hydrodynamic theory for electronic excitations on the nanotube surface. General expressions are derived for the induced potential, the self-energy, and the stopping power for a charged particle moving paraxially in a nanotube. Numerical results are obtained showing the influence of the damping factor, the nanotube radius, and the particle position on its self-energy and the stopping power. Results for stopping power in the linearized hydrodynamic model are compared with those obtained by means of the dielectric formalism in random-phase approximation, showing a close agreement between the two approaches for high speeds of charged particles.