The hydrodynamic interactions between particles have significant effects in many engineering fields, such as fluidized beds and slurry sedimentation. This is because they can impact the macroscopic process parameters of these systems (e.g., particles' cluster sedimentation speed) [1-2]. To better understand the hydrodynamic interaction between particles and its effects on macroscopic process parameters, it is necessary to understand the hydrodynamic force interactions between individual particles as a function of their relative position and velocity. The first step in this direction is the interaction between a pair of particles, which remains an active area of research. It is established that drag and lift forces applied on a particle change in function of its relative position and velocity to another particle. However, the impact of these changes on their dynamics is limited. We first study the effects of the relative position between the particles and the Reynolds number on the drag and lift forces applied to them to constitute a pairwise fluid force model. This force model is the basis for a new reduced-order particle dynamics model that also includes lubrication, Basset, and added mass forces. We compare the results obtained for a series of sedimentation cases with the reduced-order model with those obtained from a resolved computational fluid dynamic solver coupled with a discrete element method (CFD-DEM) [3]. Comparing the fluid forces obtained between these to the model enables us to assess the impact of the particles' relative motion on the hydrodynamic forces applied to them (e.g., drag, lift, and forces). These sedimentation cases also allow us to evaluate the effects of the density ratio between the particle and the fluid on the virtual mass force and its impact on the dynamic of the particles. This study is a stepping stone toward a complete model for hydrodynamic forces in particle clusters.