The horizontal flow of buoyant gases toward an opening

Well-established equations exist for calculating mass flow rates of thermally buoyant gas layers out of openings. The present work presents an alternative method of deriving such an expression in two-dimensional flows for non-uniform approach velocities induced by the layer's buoyancy. The method makes a number of assumptions, leading to the application of the total energy equation at a virtual vena contracta outside the opening.

The resulting mass flow formula is quantitatively equal to the established formula for a wide exit and C_d = 0.6, i.e., for a deep downstand, and so agrees with published data as well as does the existing formula. The two formulae diverge for different values of C_d and for gas flows much hotter than 300 °C.

Since the new formula gives more pessimistic (i.e., larger) mass flow rates for wide openings with no downstand (and hence larger extract fans or vent areas in the smoke reservoir “downstream” of those openings), it is suggested that it should be used by designers of smoke ventilation systems in such circumstances.

It is also deduced that, for “realistic” buoyant-layer flows, the mass weighted average is typically 0.73 θ_max for θ_max 300 °C.