Laboratory experiments are used to investigate the processes governing steady convectively driven circulation in a basin that communicates with a large external reservoir over a shallow sill. The motion is maintained by a steady loss of buoyancy distributed over the surface of the basin. Turbulent convection associated with the forcing produces a horizontal buoyancy gradient across the sill and the resulting mean flow consists of a layer directed into the basin near the surface with a dense counterflow below.To first order, the magnitude of the exchange flow over the sill is determined by the horizontal momentum balance within the basin. Measurements of the mean and turbulent flow fields are used to show that inertia, buoyancy and friction may each contribute significantly to the balance. The interior flow produces a horizontal pressure gradient near the surface which must also contribute to the momentum balance. The density of the lower layer at the sill reflects the cumulative effect of interior processes, such as mixing, and these in turn influence the hydraulically controlled exchange flow over the sill. The basin dynamics are therefore coupled in a nonlinear fashion with the submaximal sill exchange. This coupling is investigated first by showing how interior processes are affected by changes in the magnitude of the forcing, and then by observing the associated variation of the how state at the sill. The flow state is defined in terms of its relative proximity to the theoretical maximal exchange limit. Results show that the exchange hows are submaximal with flow rate approximately 85% of the maximal limit. This state appears to change very little in response to increasing forcing.For a stratified basin, which exhibits a deep stagnant layer under the convectively driven near-surface exchange flow, the possibility of basin ventilation or erosion of deep fluid exists in the long term. This process and its dependence on external parameters is also explored.