Balaenid whales feed on large aggregates of small and slow-moving prey (predominantly copepods) through a filtration process enabled by baleen. These whales exhibit continuous filtration, namely, with the mouth kept partially opened and the baleen exposed to oncoming prey-laden waters while fluking. The process is an example of crossflow filtration (CFF) in which most of the particulates (prey) are separated from the substrate (water) without ever coming into contact with the filtering surface (baleen). This paper discusses the simulation of baleen filtration hydrodynamics based on a type of hydraulic circuit modeling commonly used in microfluidics, but adapted to the much higher Reynolds number flows typical of whale hydrodynamics. This so-called Baleen Hydraulic Circuit (BHC) model uses as input the basic characteristics of the flows moving through a section of baleen observed in a previous flume study by the authors. The model has low-spatial resolution but incorporates the effects of fluid viscosity, which doubles or more a whale's total body drag in comparison to non-feeding travel. Modeling viscous friction is crucial here since exposing the baleen system to the open ocean ends up tripling a whale's total wetted surface area. Among other findings, the BHC shows how CFF is enhanced by a large filtration surface and hence large body size; how it is carried out via the establishment of rapid anteroposterior flows transporting most of the prey-water slurry towards the oropharyngeal wall; how slower intra-baleen flows manage to transfer most of the substrate out of the mouth, all the while contributing only a fraction to overall oral cavity drag; and how these anteroposterior and intra-baleen flows lose speed as they approach the oropharyngeal wall.