Horizontal exchange flows driven by destabilising buoyancy fluxes through the surface waters of lakes and coastal regions of oceans are important in understanding the transport of nutrients, micro-organisms and pollutants from littoral to pelagic zones. Our interest here is in the discharge flow driven by cooling or destabilising forcing at the water surface in a water body with variable depth due to sloping bottom topography. Flow visualisation studies and measurements in a laboratory model enabled us to develop scaling arguments to predict the dependency of discharge upon surface forcing and the angle of bottom slope. The results were used to interpret both the laboratory measurements and field data from a small shallow lake with sloping sides and an essentially flat bottomed interior, as well as published results from the literature. The steady state horizontal exchange can be described by Q = 0.24 B-1/3 (l tan theta/(1 + tan theta))(4/3), where Q is the discharge rate per unit length of shoreline, a is the angle of the bottom slope, B is the surface buoyancy nux and I is the horizontal length of the forcing region over the slope. The flushing timescale of the wedge shaped littoral region was given by tau(i) similar to l(2/3) (1 + tan theta)(4/3)/(B tan theta)(1/3). While the buoyancy flux in the field is almost never constant in space or time and the slope from the shore is seldom uniform, we found that the exchange rate was relatively insensitive to buoyancy flux changes and only moderately sensitive to slope.