We study theoretically the viscous flow through the swirl chamber of a pressure-swirl atomizer. The aim is to predict quantitatively the flow rate of a given liquid driven by a given pressure difference across the atomizer in order to explain the counter-intuitive experimental finding that, for moderate liquid dynamic viscosities, at a given driving pressure difference and atomizer geometry, a higher liquid viscosity results in a higher flow rate. The concept for the flow analysis is to subdivide the flow field in the swirl chamber into zones allowing for neglect of velocity components or boundary-layer simplification. The result is a quantitative prediction of the liquid flow rate for a given driving pressure difference and atomizer geometry, and for given liquid properties relevant for the discharge from the atomizer. Flow rates are compared to experimental data from various sources and show good agreement. Another part of the results is the diameter of the air core formed around the symmetry axis of the swirl chamber, which is of sub-millimetric order here. This result is compared to different experimental correlations and also shows very good agreement. For small values of the swirl velocity and/or very high liquid viscosities, the air core breaks down. The phenomenon of air core break down has been analysed, and it is shown that for high viscosities the air core breaks down due to weak swirl velocity. (C) 2013 Elsevier Ltd. All rights reserved.