The dynamics of evaporation of drops of simple, completely wetting liquids is investigated experimentally and theoretically in the situation where no pinning of the contact line is occurring. When the contact angle is low enough, it is shown that a convenient approximation for the equation governing the dynamics of the drop is to keep only the evaporation term. The simplified equation has been studied mathematically and numerically. The agreement with experimental data is extremely good, allowing us to address more complex cases involving gradient and hydrodynamic effects.