A mathematical model based on the flow hydrodynamics is developed to calculate the treatment efficiency of ultrafiltration process. This model relates the treatment efficiency with the consideration of both fixed parameters and variable parameters. The fixed parameters are function of the intrinsic rejection coefficient, diffusion coefficient, and viscosity whereas the variable parameters can be related to the fluid velocity, volume flux, and cartridge dimensions. The model has been examined by solutions with solutes that have different molecular weights. The experimental data fits the proposed mathematical model very closely suggesting its suitability to evaluate the rejection efficiency in ultrafiltration. As such the mathematical model can be used to evaluate the intrinsic rejection coefficient that can be used to determine the solvent flux in Kedem Katchalisky model. The role of the particle size is investigated by using a log -log plot of the intrinsic rejection coefficient and the solute molecular weight. Results shows that modeling of the intrinsic rejection coefficient as log normal probability distribution function is possible. Fluid velocity on the membrane cartridge as an important parameter in the design of ultrafiltration systems
