Background <p>The nonlinear dynamic behaviour of the centrifugal pump rotor-bearing system is mainly influenced by the forces acting on the rotor shaft. Previous studies have primarily focused on the computation of flow parameters, such as pressure and velocity, in centrifugal pumps; however, their integration into rotor dynamic analysis considering the combined effects of gravity, nonlinear bearing excitation, hydrodynamic forces, and unbalance forces has not been investigated. </p> Objective <p>In this study, a new dimensional formulation is proposed to evaluate flow parameters around the impeller periphery under off-design operating conditions. Further, hydrodynamic forces are determined by integrating the asymmetric pressure distribution along the impeller periphery. Thus, the coupled effects of all forces on the system’s dynamic behaviour are investigated. </p> Methods <p>For this, a finite element model of the system is developed and solved using an implicit Newmark-<i>β</i> time integration scheme with Newton–Raphson approach. A novel MATLAB program is developed to compute and store the dynamic responses. </p> Results <p>The results show that the system exhibits sub-harmonic, harmonic, and super-harmonic responses over an operating speed range of 0–6000 rpm, as well as quasi-periodic behaviour, while no chaotic motion is observed.</p>