One of the most broadly used models for membrane fouling is the Hermia model, which separates this phenomenon into four blocking mechanisms, each with an associated parameter n. These mechanisms are complete blocking (n=2), intermediate blocking (n=1), standard blocking (n=3/2) and cake formation (n=0). The original model, which was obtained through experimental data, is given by an Ordinary Differential Equation (ODE) dependent on n. At the time, this ODE was only solved for these four values of n, which limits the effectiveness of the model when adjusted to experimental data. The aim of this paper is to not only mathematically prove the original Hermia model, but also to broaden the scope of this model for any real number n by using the original ODE, the equations of fluid mechanics and the properties of single and multivariable calculus. The final generalized Hermia model is given by a power-law for any n≠2 and is given by an exponential function at n=2 and can be fitted to ultrafiltration, microfiltration, nanofiltration and reverse osmosis data with acceptable values of R2 (>0.93). Here it is also shown that the accumulated volume as a function of time follows the same type of ODE. The values of n between the four original discreate values could be physically interpreted as the existence of new blocking mechanisms.