Water-filled pores of nanometer dimensions play important roles in chemistry and biology, e.g., as channels through biological membranes. Biological nanopores are frequently gated, i.e., they switch between an open and a closed state. In several ion channel structures the gate is formed by a ring of hydrophobic side chains that do not physically occlude the pore. Here we investigate whether a hydrophobic pore can act as a gate via molecular dynamics simulations of the passage of water through atomistic models of nanopores embedded within a membrane mimetic. Both the geometry of a nanopore and the hydrophilicity vs hydrophobicity of its lining determine whether water enters the channel. For purely hydrophobic pores there is an abrupt transition from a closed state (no water in the pore cavity) to an open state (cavity water at approximately bulk density) once a critical pore radius is exceeded. This critical radius depends on the length of the pore and the radius of the mouth region. Furthermore, a closed hydrophobic nanopore can be opened by adding dipoles to its lining.