The Monolithic Stirrer Reactor (MSR) is a novel concept for heterogeneously catalyzed reactors and is presented as an alternative device to slurry reactors. It uses a modified stirrer on which structured catalyst supports (monoliths) are fixed to form permeable blades. The monoliths consist of small square parallel channels on which a layer of catalytic material can be applied. The stirrer now has both a catalytic and a mixing function. The main advantage of this reactor type is the ease of the catalyst handling, since the catalyst is easily separated from the reaction mixture and can be re-used. The goal of this work which is to study the hydrodynamic operation of the MSR and develop engineering models for its design. In particular, to evaluate the two main functions of the stirrer (i) mixing of the bulk fluid, and (ii) pumping fluid through the monolith to allow the catalytic reaction to take place. The amount of flow through the monolith, i.e., the fluid velocity in the monolith channels, determines the mass transfer rate inside the monolith - this is an important design parameter for the reactor. In addition to detailed three-dimensional computational fluid dynamics simulations with the CFD code Fluent, we performed experimental measurements of velocities in the bulk and in the monolith channels, of mixing and of power consumption in the MSR. Building on detailed CFD and experimental data, we developed a simple engineering model to predict the flow through the monolith channels.