Dip coating consists in the immersion of a substrate into a reservoir containing a film-forming fluid and then the withdrawing from the bath to produce the film. The objective of this work was to develop a mathematical model of the fluid-dynamic variables in a dip-coating process, considering that the film-forming fluid behaves as a generalized Newtonian fluid. An analytical and simple mathematical model that relates the main fluid parameters using a generalized Herschel-Bulkley model was proposed. This model was obtained on the basis of rigorous mass and momentum balances applied to a monophasic and non-evaporative system, where the main forces are viscous and gravitational. The parameters that can be estimated are velocity profile, average velocity, flow rate, local thickness, and average thickness of the coating film. Finally, the sufficient conditions for the model were obtained. The experimental validation and sensitivity analysis are presented in a complementary paper as part 2.