The buoyancy-driven flushing of fluid from a rectangular box via connections in the base and top into quiescent surroundings of uniform density is examined. Our focus is on the transient flows that develop when the interior is either initially stably stratified in two homogeneous layers – a dense layer below a layer at ambient density, or is filled entirely with dense fluid. Experiments with saline stratifications show that four distinct patterns of flow are possible. We classify these patterns in terms of the direction of flow through the base opening and the propensity of replacement fluid through the top opening to induce interfacial mixing. Unidirectional or bidirectional flow through the base opening may occur and within these two flow types either weak or vigorous interfacial mixing. We identify the three controlling geometrical parameters that determine which flow pattern is established, namely the fractional initial layer depths, the relative areas of the top and base openings and the horizontal length scale of the top opening relative to the initial dense layer depth. We show that these parameters may be reduced to two Froude numbers – one based on the fluxes through the base opening and whose value sets the direction of flow, and a second based on conditions at the top opening whose value determines the vigour of interfacial mixing. Theoretical models are developed for predicting the conditions for transition between each flow pattern and expressed as critical values of the Froude numbers identified.