Water brakes combine high power ratings with a low moment of inertia and in case of high power ratings they are a good alternative to other braking systems. Despite these advantages water brakes are not widely used in dynamic testing as their nonlinearities make them hard to control. Mathematical models of hydrodynamic dynamometers are presented in this paper. A first principles approach is compared with a data-based model and a gray box model. The first principles model is hard to parametrize. In contrast a purely databased linear model is easy to tune but is not able to extrapolate. To increase the extrapolation ability it gets necessary to use a gray box approach which combines the simple structure of a first principles model with a data-based part. The resulting gray box model is best suited to the plant, of simple structure and can be used for the design of a model-based controller.