The hydrodynamic drift ratchet provides a novel means to continuously separate particles at the microscale, based on particle size. Separation arises from a combination of diffusion and particle-wall hydrodynamic interactions. As there are currently no verified experiments, our aim is to determine numerically how these systems scale so that appropriate experiments can be designed. Using nondimensional variables, we derive the correct scaling parameters governing drift ratchets by simulating individual particle motion using a model that treats the particle dynamics at pore walls as elastic reflections. While our model does not quantitatively resolve the detailed hydrodynamic interactions, we show that it does recover the correct scaling behavior for these interactions. Our simulations demonstrate that the drift velocity relative to the characteristic pore size is independent of pore size if all the relevant nondimensional groups remain constant. Dynamic similarity can be used to facilitate the appropriate design and testing protocols for experiments.