This contribution investigates the morphodynamic equilibrium of funnel-shaped well-mixed estuaries and/or tidal channels. The one-dimensional de Saint Venant and Exner equations are solved numerically for the ideal case of a frictionally dominated estuary consisting of noncohesive sediment and with insignificant intertidal storage of water in tidal flats and salt marshes. This class of estuaries turns out to be invariably flood dominated. The resulting asymmetries in surface elevations and tidal currents lead to a net sediment flux within a tidal cycle which is directed landward. As a consequence, sediments are trapped within the estuary and the bottom profile evolves asymptotically toward an equilibrium configuration, allowing a vanishing net sediment flux everywhere and, in accordance with field observations, a nearly constant value of the maximum flood/ebb speed. Such an equilibrium bed profile is characterized by a concavity increasing as the estuary convergence increases and by a uniquely determined value of the depth at the inlet section. The final length of the estuary is fixed by the longitudinal extension of the very shallow area which tends to form in the landward portion of the estuary. Note that sediment advection is neglected in the analysis, an assumption appropriate to the case of not too fine sediment.