An empirical model is developed to capture the electrostatics of finite-length single-walled armchair carbon nanotubes for biological applications. Atomic partial charges are determined to match the electrostatic potential field computed at the B3LYP/6-31G* level of density functional theory, and a tight-binding Hamiltonian is selected which permits one to reproduce the dielectric properties in good agreement with density functional theory results. The new description is applied to study movement of a water molecule through a finite-length nanotube channel in order to demonstrate the method's feasibility. We find that atomic partial charges on the tube edges dominate the interaction between the nanotube and the entering water molecule, while the polarization of the nanotube lowers the electrostatic energy of the water molecule inside the tube.