abstract: Was the Italian mechanics of fluids a case of revolution in science? Answering to this question is not straightforward because we have first to clarify what was the 16th- and 17th-century status of this science. It may be argued that the mechanics of fluids became an autonomous subject only in the 18th century. And that, even if we are able to trace spaces of discussion and development in the former centuries, they did not concern the science of fluids as such but only particular areas like hydrostatics and meteorology. This kind of objection neglects, however, a fundamental side of the story of the science of fluids. During the Renaissance age the social demand of technical and mathematical expertise in the business of water management gave birth to a new field of knowledge. Water management is of course as old as civilization. The novelty consisted in that peculiar mixture of art and science that, for the first time in history, the Renaissance practitioners and writers of waters were able to attain. In the 17th century it was the turn of a new Galilean, mathematical science of motion of water to be built. A new kind of mathematical measure of running waters was substituted for the simple engineering measure. And a clear distinction between compressible and incompressible fluids was drawn. It was Benedetto Castelli who accomplished this job in a 1628 tract written in Italian, whose 1661 English translation bears the title Of the mensuration of running waters. My talk will be divided in three parts. After some introductory remarks on the state of our knowledge on the Renaissance science of fluids, I will try to assess the novelty of Castelli's work in the panorama of the age. The last part will be devoted to explaining in which sense the mechanics of fluids may be considered an integral part of the Scientific Revolution. The story of the science of waters may even add, through the study of new primary sources and the development of new explanatory models, a new fundamental dimension to our understanding of early modern science.