Since many years precession is regarded as an alternative flow driving mechanism that may account, e.g., for remarkable features of the ancient lunar magnetic field [Dwyer 2011; Noir 2013; Weiss 2014] or as a complementary power source for the geodynamo [Malkus 1968; Vanyo 1991]. Precessional forcing is also of great interest from the experimental point of view because it represents a natural forcing mechanism that allows an efficient driving of conducting fluid flows on the laboratory scale without making use of propellers or pumps. Within the project DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) a dynamo experiment is under development at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) in which a precession driven flow of liquid sodium with a magnetic Reynolds number of up to Rm=700 will be used to drive dynamo action. Our present study addresses preparative numerical simulations and flow measurements at a small model experiment running with water. The resulting flow pattern and amplitude provide the essential ingredients for kinematic dynamo models that are used to estimate whether the particular flow is able to drive a dynamo. In the strongly non-linear regime the flow essentially consists of standing inertial waves. Most remarkable feature is the occurrence of a resonant-like axisymmetric mode which emerges around a precession ratio of Ωp/Ωc = 0.1 on top of the directly forced re-circulation flow. The combination of this axisymmetric mode and the forced m=1 Kelvin mode is indeed capable of driving a dynamo at a critical magnetic Reynolds number of Rmc=430 which is well within the range achievable in the experiment. However, the occurrence of the axisymmetric mode slightly depends on the absolute rotation rate of the cylinder and future experiments are required to indicate whether it persists at the extremely large Re that will be obtained in the large scale sodium experiment.