The rapid spread of micro/nanoelectromechanical systems necessitates detailed understanding of fluidics within nanoscale structures. In this paper, the dynamics of a water droplet in nanochannels are analyzed using molecular dynamics simulations. As the channel size decreases, the shear stress between the droplet and the solid wall becomes much larger than predictions based on conventional slip boundary conditions. Our analysis shows that the Navier friction coefficient is quite sensitive to liquid pressure, which tends to be significantly large in hydrophobic nanochannels because of the Laplace pressure. We propose a modified version of the Young-Laplace equation that can accurately estimate the liquid pressure in nanochannels. By accounting for these nanochannel characteristics, we have successfully derived an expression that describes the channel size dependence of the shear stress between the droplet and the solid wall.