The rates and magnitudes of vibrational energy transfer between single-wall carbon nanotubes (CNTs) and water are investigated by classical molecular dynamics. The interactions between the CNT and solvent confined inside of the tube, the CNT and solvent surrounding the tube, as well as the solvent inside and outside of the tube are considered for the (11,11), (15,15), and (19,19) armchair CNTs. The vibrational energy transfer exhibits two time scales, subpicosecond and picosecond, of roughly equal importance. Solvent molecules confined within CNTs are more strongly coupled to the tubes than the outside molecules. The energy exchange is facilitated by slow collective motions, including CNT radial breathing modes (RBM). The transfer rate between CNTs and the inside solvent shows strong dependence on the CNT diameter. In smaller tubes, the transfer is faster and the solvent coupling to RBMs is stronger. The magnitude of the CNT-outside solvent interaction scales with the CNT surface area, while that of the CNT-inside solvent exhibits scaling that is intermediate between the CNT volume and surface. The Coulomb interaction between the solvent molecules inside and outside of the CNTs is much weaker than the CNT-solvent interactions. The results indicate that the excitation energy supplied to CNTs in chemical and biological applications is rapidly deposited to the active molecular agents and should remain localized sufficiently long in order to perform the desired function.