We investigate the long-term morphological evolution of a tidal channel through a one-dimensional numerical model. We restrict our attention to the case of tide-dominated estuaries, which are usually characterized by a funnel shape, and neglect the effect of intertidal areas and river discharge, imposing a closed boundary at the landward end. If the estuary is relatively short and weakly convergent the equilibrium bottom profile extends over the entire length of the estuary, whereas a beach is formed inside the domain when the initial length of the channel exceeds a threshold value. Hence it is possible to define an intrinsic equilibrium length as the distance between the beach and the mouth. In our analysis we examine how such estuarine length, which is independent of the physical dimension imposed to the system, is affected by three main parameters, namely channel convergence, tidal amplitude at the mouth and friction. We show that the degree of convergence plays a crucial role, as the analysis of real estuaries seems to confirm: a strong degree of convergence implies shorter equilibrium lengths. We also show that increasing the tidal amplitude at the mouth or the channel friction produces shorter equilibrium profiles. Numerical results suggest that tidal asymmetries vanish as the system approaches the final equilibrium state.