We investigate the flux of particles in a smooth single-file channel where particles cannot cross each other as well as in wider channels of varying cross section where particles execute normal diffusion. All the channels are connected to an infinite reservoir at one end and the flux of particles is measured at the other open end. We perform random walk Monte Carlo simulation using lattice model. The flux decreases monotonically as the channel cross section is increased from single-file channel to wider channel and finally reaches a constant value for a sufficiently wide channel. The observation of enhanced flux in single-file channel as compared to a wider channel can be tested for efficient separation of particles through smooth nanochannels.