Convection plays a major role in a variety of natural hydrodynamic systems. Those in which convection drives exchange flows through a lateral contraction and/or over a sill form a special class with typical examples being the Red and Mediterranean Seas, the Persian Gulf, and the fjords that indent many coastlines. The present work focuses on the spatial distribution and scaling of the density difference between the inflowing and outflowing fluid layers. Using a long water-filled channel, fitted with buoyancy sources at its upper surface, experiments were conducted to investigate the influence of the geometry of the strait and the channel as well as the magnitude of the buoyancy flux. Two different scaling laws, one by Phillips (1966), and one by Maxworthy (1994, 1997) were compared with the experimental results. It has been shown that a scaling law for which g′ = kB02/3x/h4/3 best describes the distribution of the observed density difference along the channel, where B0 is the buoyancy flux, x the distance from the closed end of the channel, h its height at the open end (sill) and k a constant that depends on the details of the channel geometry and flow conditions. This result holds for the experimental results and appears to be valid for a number of natural systems as well.