This paper presents a set of stereoscopic particle image velocimetry (SPIV) measurements of a turbulent round water jet (jet exit Reynolds number and turbulent Reynolds number ) discharged into an initially stationary ambient. The data were taken on the jet centerplane and at non-dimensional downstream distances ( axial coordinate and  orifice diameter), where the jet turbulence had evolved into a self-preserving state. Budgets of turbulent kinetic energy k and individual components of the Reynolds stress tensor are extracted from the velocity measurements and compared to recent experimental data of an air jet () and direct numerical simulation data (). The comparison reveals that the datasets are consistent with each other but that the turbulent transport of energy appears to differ between the present low-Re water jet and the high-Re air jet. Nonetheless, the non-dimensional profile of turbulent dissipation rate , obtained as the closing term (balance) of the k-budget, is very similar in all studies. The commonly used Lumley’s model for pressure–velocity correlation (pressure transport term in k-budget) is evaluated using the instantaneous pressure field computed from the time-resolved planar velocity data. We find that Lumley’s model is deficient in the jet core ( radial coordinate and  Guassian half-width), while performing adequately away from it. Finally, the present data are used to compute terms appearing in the exact transport equation of . Combining both the k and budgets, model coefficients in the commonly used two-equation turbulence closure model are evaluated from the present data. If a fixed set of model coefficients is to be employed in a jet simulation, the following values of the model coefficients are recommended to optimize predictions for the mean flow field, for k, and for : and .