Abstract A detailed study of a swirling flow in a tube is presented in the first part of the paper. A simplified analytical solution of the governing equations indicates specific modes of the tangential velocity and that the decay of the swirl effect is exponential. The problem is then solved in three dimensions using computational fluid dynamics (CFD) and a comparison with analytical expressions shows that the CFD code is reliable in terms of accuracy. The CFD results confirm that a fundamental swirling mode is reached within a short distance from the inlet. The torque swirl number is introduced to physically estimate the intensity of the swirl. A companion value is given: it is the average deviation.