The turbulent plunging jet of a nearly incompressible fluid into a stagnant fluid is of great importance in many practical applications, especially for the engineering of hydropower. As an example, the dynamic load exerted by the impact of turbulent high-velocity jets into a pool must be estimated to evaluate the potential destabilization of a rock bed or dam's structure. Modelling plunging jets in the laboratory presents a challenge due to the complex two-phase environment, which requires models to be built at near-prototype scales. This paper deals with the application of a three-dimensional weakly compressible smoothed particle hydrodynamics (SPH) model to study a circular jet impinging into a water flat pool, at a near-prototype scale. To identify the level of reliability of the computed parameters, validation of the pool bottom pressures is carried out by comparison with existing experimental data. The self-similarity of the jet's centreline velocity is correctly reproduced and the computed maximum dynamic pressures near the stagnation point are reasonably accurate. The differences observed are mainly attributed to the non-consideration of the air phase.