The gas dispersion from an orifice located on the rear face of a flat paddle impeller blade situated in a cross-flow was investigated. An algorithm which balances the pressure loss as gas flows through the system with the pressure difference between the headspace and the fluid surrounding the orifice was developed to enable the modelling of the gas flow rate for variations in the bulk upstream velocity. The theory is developed to account for the application of an elevated headspace pressure, in a form suitable for application to gas/liquid or gas/liquid/solid systems. The gas flow rate predicted by the model is compared with the experimental measurements for different gas dispersion regimes and gas pathway restrictions.