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In cold atmospheric pressure plasmas (CAPPs), the residual charges that exist in the wake of the streamers play an important role in the acceleration of the working gas. This paper presents a model that links the drift of the net residual ionic charge density, under the effect of the local electric field, with the momentum increase of the gas. In the model, the ions and the neutrals are considered as separate phases and the conservation equations for the two phases are connected via the ionic pressure. The residual charge density is quantified through an approximate approach that considers the streamer events to be 'instantaneous', in order to avoid the excessive computational cost of resolving the propagation of each streamer. For the validation of the residual charge model with the 'instantaneous' streamer approach, comparisons are made with experimental data from three plasma jet reactors. The electrode configuration of the reactors and the varied parameters (applied voltage, gas flow rate) are chosen so as to cover a broad range of different cases, in order to assess the generality of the model. The comparisons concern the gas flow and visible plasma patterns. It is found that the numerically simulated flow structures are in agreement with the corresponding schlieren images and that the residual charge density is a fair indicator of the visible plasma channel. [ABSTRACT FROM AUTHOR]