Dependences of the total potential U_t calculated with the image potential U_im from the extended two-fluid model for straight (solid curve) and bent nanotube (dashed curve) on proton position y from the center of nanotubes in the cases of (a) (6,4) SWNT, (b) (8,6) SWNT, (c) (11,9) SWNT, and (d) (15,10) SWNT. Also shown are the results for the total potential U_t1f calculated with U_im from the one-fluid model with zero damping for the bent nanotubes (dash-dotted curve). The proton velocity is v = 3 a.u. The nanotube curvature angle is α = 4 mrad in the case of bent nanotubes. Vertical solid bars show the positions of nanotube walls. Vertical dotted bars represent the value R − a_sc for each nanotube, where R is the nanotube radius and a_sc is the nanotube atom screening radius.