Vortices that develop over intakes are a hazardous hydraulic phenomenon. In this study, a 3D model was developed to study the flow field in air-core vortices. This model is based on the spiral patt of streamlines and the analytical solution of the momentum and continuity equations for deriving the three components of velocity. The model provides equations for free surface profiles and 3D patts of the streamlines. Moreover, a new relationship was suggested for calculating effective viscosity and its distribution across the vortex flow field. The performance of the proposed analytical model was compared with existing experimental data and the results of previous analytical models. The outcomes indicated that the proposed model could predict characteristics of the vortex flow with good accuracy.