To model particle and heat loss terms at the edge of a tokamak with a divertor or pumped limiter, a simple two-chamber formulation of the scrapeoff has been constructed by integrating the fluid equations, including sources, along open field lines. The model is then solved for a wide range of density and temperature conditions in the scrapeoff, using geometrical parameters typical of the PDX poloidal divertor. The solutions characterize four divertor operating conditions for beam-heated plasmas: plugged, unplugged, blowthrough, and blowback.