Abstract Bioreactor‐based processes are the method of choice for efficient expansion of cells in a controlled setting. However, induced pluripotent stem cells (iPSCs) have proven to be extremely sensitive to the bioreactor hydrodynamic environment, making the use of suspension bioreactors to produce quality‐assured cells at clinical and commercial scales very challenging. The PBS vertical‐wheel (VW) bioreactor combines radial and axial flow components to produce uniform hydrodynamic force distributions, making it a promising platform to overcome the scale‐up challenges associated with iPSCs. In this study, hydrodynamic characterization through computational fluid dynamics modelling of VW bioreactors was performed. Analysis of these models proved that important volume average hydrodynamic variables could be maintained throughout scale‐up from the 0.1 L to the 15 L VW bioreactor scale. Each bioreactor scale (0.1, 0.5, 3, and 15 L) was modelled at a variety of agitation rates, leading to the generation of scale‐up correlation equations. These equations allow operators to define a working range of hydrodynamic variables at one scale and calculate the corresponding agitation rates at other modelled scales. A suggested operating range of agitation rates was determined for the successful culture of iPSCs in the VW bioreactor at each scale, corresponding to constant volume average energy dissipation rate. Agitation rates from the 0.1 and 0.5 L VW bioreactor scale were experimentally tested to biologically validate the suggested range. High cell‐fold expansion, healthy aggregate morphology, growth, and uniformity were demonstrated for all conditions tested within the suggested working range.