We present a lattice model of water confined in a hydrophobic nanotube. Using analytical methods and computer simulation, we find conditions where filled and empty tubes can be degenerate in equilibrium. We further find that flow of water molecules through a filled tube with appropriate but simple stochastic rules can be interpreted as water conduction in a pulse-like fashion. These two results are consistent with an atomistic molecular dynamics study of this system [Hummer et al. Nature 2001, 414, 188-190]. Finally, we analyze transitions between the filled and the empty tube, and find that density fluctuations at the entrances to the tube play the rate-determining role in this process.