A one-range and a two-range model for the laminar velocity distribution in the entrance region of tubes and ducts are presented. These allow the calculation of the residence time distribution under the impact of the flow development in the hydrodynamic entrance region. For the dispersion-free case, an analytical solution is given. A cell model with place-changing probability (ZEMP) is applied for the consideration of dispersion. This approach allows the fast quantification of the influence of different parameters on the residence time distribution for relatively short pipes and ducts. The numerical results are compared with earlier presented results of semi-empirical models.